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Home , 34 equal temperament, 72 equal temperament, Diaschisma, Hexany, Jins, Joel Mandelbaum

Contents p. 3 Introduction p. 4 Ancient (pre-500 CE) and Early microtonal practices, systems, stylistics: Medieval (500-1400), Renaissance (1400-1600), Baroque (1600-1760), Ingram, Dumbril, Plato, Pythagoras, Heptagrams, Babylonia, Assyria, and Greco-Arab Texts p 7 Ancient practices and oral traditions p. 10 Al-Farabi, 17TET system, kitab al-Adwa, al-Andalas and barzok p. 14 Common microtonal practices, systems, stylistics (1600-1900): Baroque (1600-1760), Classical (1730-1820), Romantic (1815-1910) Bach, , Glarean p. 17 Jamaica and Africa, Koromanti and Angola, Ethiopian bowl (krar), Quadrille in Carriacou p. 18 Post-romantic and Pre-, experimental, Carrillo, Ives, Rimsky-Korsakov, Russolo, Experimentalism, , tone clusters, aleatorics, quarter-tones, polyrhythmic p. 19 Contemporary & modern microtonal practices, systems, stylistics: Modern (1890-1930), 20 th century (1901-2000), Contemporary (1975-present), Modernism, Dadaism, , microtonality, Verèse, Webern, Wyschnegradsky, Hába, Carillo, Villa-Lobos, Ives, Partch, Cowell p. 22 Yasser, infra-diatonicism, supra-diatonicism, evolving p. 31 Darmstadt, , dodecophony, Stockhausen, Boulez p. 30 22TET, Just 12-tone scale built on powers of 3 and 5, diminished 7th , 1960s Rio de Janiero , Bossa Nova, US jazz, flattened 5th and hexatonics in the , New Orleans resurgence, Copacabana p. 34 Pitch and cognitive acculturation, development of musical thought and thought in sound, schematic and veridical expectancy, mistuning perception p. 37 Just, Bohlen-Pierce scale, Wusta-Zalzal, Masonic ratios, 22 tone system of India, , Messiaen, Babbitt, Cage, Young, French Spectralists, 53TET, 19TET, Bagpipe tuning p. 48 Midi, scale perception, semiotics, notation, re-creation, Turkish, Eskimo, Indonesian in 5TET (Salendro), Thai 7TET p. 53 Xibeifeng, Xenakis stochastic emulator, fretboards and the 12th root of 2, world Fusion, evolving timbral domain, microtonality and after the fact of performance, societal technological status, cultural and logical outset, and aesthetical artistic nuance p. 56 Conclusion, truth in music, modality of believing, dynamic tonality, -stream music, sound painting, new directions p. 58 Glossary, p. 62 References

2 and its relationship to historical practice by Geoff Geer

Introduction

Intonation systems make up a large part of musical performance, often floating beneath the compositional surface, below the , stylistics, speed and dynamics. It is conscious organised order of performance and composition that determines what we deem as music. A clever melody or evocative line may be altered by taking it out of the underlying context of intonation systems. Today these systems can be extended through use of an understanding of previous centuries’ performance stylistics in tonality and microtonality, and cultural and contextual ideology and application. In the paper we will trace past tonal systems and practices and musical ways of thinking tonally and microtonally to determine whether any patterns emerge. Are 12TET,1 24TET or (small ratios) the best choices for today’s musicians? We will look at some of the leading historical musical thinkers and contrast their ideas with modern microtonal thought and practice, as well as the cutting edge research on tonality, technology and compositional practice for the 21st century. Are there logical patterns emerging in human musical thought and practices with regard to some examples of definite links to past and present practices? Musical practices and their tonal systems and theories build the sound track to transnational-migrations of peoples, politics, ideologies, capital and mass media images, acting as boundary-markers even as they cross boundaries, transforming and reinterpreting them—reconfiguring cultural imagination by expression of desires and memories. (Shannon, 2007) Microtonal music, as music that is not 12 tone equal temperament, has occurred worldwide, in the Americas, in Europe, in Asia, Africa, the Middle East, and Australia.2 Bach wrote pieces (as

1 12 Tone Equal Temperament, 12 equal divisions of the . 2 Examples include Byzantine liturgical music, Scottish bagpipe, Iranian chamber music, Indonesian , Za’atar Jewish music, Bakshish ensemble, and African xylophone. Tonal systems today include equal tunings 5TET (Indonesian slendro), 6TET (Tone Equal Temperament), 7TET (Thai traditional), 12-Equal or 12TET (Western .1800-present), 15TET, 16TET, 17TET(Arab), 18TET (Wyschnegradsky), 19TET (Guillaume Costeley), 22TET, 24-Equal or 24TET (quarter-tone), 26TET, 31TET (, Fokker), 34TET, 36TET (Wyschnegradsky),, 41TET, 3 harmonically as possible) using (according to Forkel, his biographer) thirds tuned slightly sharp, a prerequisite in transpositional functioning. Just intonation was generally used before this in various systems worked out through ratios, and is defined as small interval ratios. Bach was limited in composing by meantone temperaments, and today we can hear some of what he was unhappy with using special software that enables closer approximations, highly accurately, in Just intonation. Werckmeister, a Baroque era notable for his invertible , did away with the unnecessary applicability of keyboards of the time, which had more than 12 notes, of which many were euphonious. While Pythagoras may have developed whole number ratio tunings, the Harmonists had perhaps thousands of ratio tunings which were lost after the fall of the Roman empire, with some going to the Arab world for development. After this, during the early middle ages, consonance was based on a 1/1 , 2/1 octave, 3/2 perfect 5th, 4/3 perfect 4th, with 3rds and 6ths being dissonant. In 1300 the English monk Walter Odington came up with: 5/2 minor 6th, 5/3 major 6th, 5/4 major 3rd, 6/5 minor 3rd, though later it was realised that it had already been discovered. (Denton, 1996) These various ratios used throughout history differ markedly from various equal-tone and meantone temperaments that came later on, including 24-TET (quarter-tone equal temperament). In the 1500s thought that ratios 1 through 6 were consonant, leading to use of triads during the renaissance, which developed chordal and harmonic music based on ratios and Just intonation, yet there was also a growing body of work for fretted and keyboard instruments. Before this, music was predominantly vocal, and instrumental music then took off in the classical period. In the 20th century Partch envisioned instruments that could modulate and retain Just intonation. 24-TET instruments are very complex, and notational systems vary. During the Baroque period was used: 4ths and 5ths are about 2 cents off, 3rds and 6ths are slightly out, 8 scales are near perfect and 4 are very mis-tuned. With more complex music and modulations came the need for equal-temperament around 1750. In the middle-ages A 440 varied from 370 to 567 Hz and people had their own tuning forks. The church pitch was often a whole step higher than the choir pitch, and a compromise chamber pitch resulted from this at around 420 Hz. Alexander J. Ellis created charts of the pitch of instruments which can tell

43TET, 47-edo (equal division of octave), 50TET, 53TET (Turkish), 72TET. Linear tunings, that temper non-octave notes via a stack of perfect fifths, include Syntonic (generators P5 and 8ve), Meantone (quarter-comma, septimal), Schismatic (Helmholtz), Miracle (a regular temperament), Magic (generator 5/4 narrows or widens). Irregular temperaments include /Temperament ordinaire (Kirnberger III, Werckmeister, Young, Neidhardt, Vallotti, and Young). Other systems include Just intonation, Pythagorean, Partch’s 43-tone, Ptolemy's intense , tonality diamonds, numerary nexus, tonality flux, otonality, , scale of and non-equal temperament tunings. 4 us what we are hearing. (Denton, 1996) For the Russian ancient liturgical styles Joseph Yasser, whose major work was A Theory of Evolving Tonality, talks about the byways of tonal evolution and pleads for tonal restoration. Yasser asserts that pentatonic [infra-diatonic] theory precedes more advanced temperaments, and that quartal , rather than [3rds], is the proper harmony for the infra-diatonic. This was followed up by his attempt to demonstrate the pentatonic character of Gregorian chant. Yasser’s letter to Schoenberg criticised his chromatic 12-tone acoustic interpretation. Schoenberg tabulates the harmonic series to the 13th partial. For Schoenberg these six first partials are founded on the root, fourth and of the harmonic series, and constitute the diatonic scale, while adding the remaining seven partials forms a complete . Yasser asserted that the first few notes may sync well enough, but as the harmonic series evolves (phi ratio) there is greater error between the three ascending series’ pitches microtonally, and he maintained that Schoenberg did not take the trouble to check his flawed work. For example there is a 38 centitone difference between the Eb at the 7th and 13th partials, and the C# and Db at partials 11 and 13 are off by almost a , or 43 centitones. (Yasser, Schoenberg, 1953) A main problematic is how the instruments were built and their relation to written notation. With the old folk flutes for example, and their recreations, it would be hard to modulate due to their microtonal nature. Forkel says that Bach tuned his thirds slightly sharp for modulational functionality. Equal temperament is the aberration and a recent phenomenon, falling outside of the natural phi ratio phenomenon. While equal-temperament is practical for modulation and composition we must remember that voice and strings use it for reference and tonal centricity, along with others like . French music concrète, though criticised for being overly intellectual at times, delved deeply into microtones, as did the Spectralists, and this was at odds with the German tradition of notational elektronische music, although tonal elements existed there too. Interestingly, there was the 1932 Cairo convention on quarter tones where a canun was tuned to 24TET. Examples where played to Arab musicians who unanimously agreed that it was out of tune—it may be more accurate to use a Pythagorean system or divide the octave into 53 commas. (see A.J. Racy's Making Music in the Arab World)

5 Ancient (pre-500 CE) and Early microtonal practices, systems, stylistics: Medieval (500- 1400), Renaissance (1400-1600), Baroque (1600-1760), Ingram, Dumbril, Plato, Pythagoras, Heptagrams, Babylonia, Assyria, and Greco-Arab Texts

The 4th and early 5th centuries showed enharmonic and chromatic tuning to be more popular than heptatonic diatonicism, and records that in the 4th century it was common knowledge that diatonicism predated Hellenic and enharmonicity that either co- existed with pure diatony or overlaid it.3 Ingram’s popular view that earlier tunings were defective is cast into some doubt by the discovery of a near-Eastern cyclical diatonic system pre- existing Aristoxenus’ by two millennia.4 However, Philolaus attests in the 5th century that the earlier systems were defective, with some heptatonic systems derived from filled in notes. Arestoxenus names Eratocles as formulating the precept that modulation can only occur at consonant intersections, and Ion of Chios agrees that this was standard practice around 422 BC. Enharmonic and chromatic transposition/modulation was restricted to the bounding notes of each , not the inner notes that were often microtonal.5 Ptolemy's διατονικοΰ συνεχοΰς (diatonic continuous) led to the σύσιημα τέλειον (systima perfect), enabling modulation of the

συστήματα for complete enharmonic and chromatic modulations. (Franklin, 2002) Plato's term harmonia describes ethnic scales permissible or not in his Ideal State, theorised in The Republic where different political regimes are discussed—translated commonly as mode we do not know their exact nature although there is an account by Aristides Quintilianus. (De Musica I.9, p. 19.1-10, ed. Winnington-Ingram) Although Aristoxenus does not use harmonia in this sense he seemingly describes it as synonymous with tonos, though this is problematic due to the concept of eidos (species) of intervals like the octave, akin to the modern and medieval mode, without the concept of tonic, dominant and polychordia. A deciphered cuniform tablet, depicting notes on a lyre corresponding to a heptagram (c. 2000 BC) is thought to use thirds in harmony and a diatonic scale. (Kilmer, 1986, cited in Dumbrill, n..) The archeomusicologist Richard Dumbrill argued for over 30 years with colleagues as to

3 In past Greek tragic practices, the chromatic genus did not appear until Euripides, and used predominantly Dorian and Mixolydian, symbolic of dignity and pity. Lydian and Ionian were used and Sophocles was the first to use the Phrygian and Lydian tonoi, although very rare in the tragedy, were the Hypodorian and Hypophrygian. 4 Winnington-Ingram, an authority on ancient music, ought to be mentioned for his articles in The Classical World, which accompanied Choudbury and Bogges' medieval discussions on Greek tragedy (Choudbury, 1909; Bogges, 1968). Ingram mentions a work by Robert Browning (Browning, 1963) on Greek tragedy, connected possibly with Psellus, the Byzantium encyclopaedist and philosopher/writer (11th century) (Albert, 1900), of which there is no translation, and based on Aristotle and the music of tragedy most likely derived from Aristoxenus' works. (Feaver, 1969) 5 In Just or early the 4th and 5th fell very close to their 12TET counterparts. 6 whether or not instead of a heptatonic, with diatonic Assyrian roots, that an enneotonic (9 tone) scale may have been prevalent, and produces it as archeological evidence. Dumbrill points out that Occidental diatonicism may have roots not in ancient Babylonia, but stem from a Pythagorean myth that germinates in mediaeval traditions. In Plato’s Republic (545c-546d) the [9] muses mention two ,6 or superimposed heptachords, which make up an enneachord. Babylonian practice would be taught through metaphors and metonymy and by ear, allowing for wider or smaller non-complex ratios other than Just. Unlike Greek tunings governed rigidly by ratios,7 in Babylonia there may have been a multiplicity of tonal systems practicably tuned by ear, and the octave may have been unknown. (Dumbrill, n.d.) All Greek musical knowledge originates from 10th and 11th century Western adaptations and translations [of Arabic texts]. and ‘magadised’ are generally thought to have existed in Greek music, yet scholars are perplexed as to whether there was simultaneous use of perfect 4ths and 5ths, indicative of the infra-diatonic scale (5+2)8, yet similar to the sub-infra-diatonic scale (2+3). The Siamese (5+2) infra-diatonic system lacks the distinct characteristics of Western diatonicism, as the main part consists of only 5 notes, and 2 subsidiaries (embellishments), and is a closed system. In European diatonicism this is not the case, and there has never been any standard indication of temperament historically generally, owing to written melodies often being converted into other temperaments. The historical point of transition between sub-infra-diatonic (2+3) and infra-diatonic (5+2) is unclear. (Yasser, 1932, p.152) Ethics, philosophies and values have always been linked to performance and music, and may extend to cultural idioms like techniques, gesture and stylistics. For many traditions there appears to be scant evidence for past musical practices and traditions,9 and Early Music

6 Dumbrill claims there is no evidence that Pythagoras existed, or that he wrote about music if he existed, that he was a fictitious pun invented by the early Greeks, and in light of Near Eastern cuniform mathematical mastery, there was nothing left for him to discover – and that modern academia is misled on this point. 7 Greek tunings were dominated by ratio and string length, yet Aristoxenus preferred string tension and relaxation, yet many medieval transpositions of Eastern theory, such as al-Farabi, cite their foundation on Greek theory, and may have muddied Aristoxenus’ theories. 8 Yasser’s term infra-diatonic encompasses 5 primary notes with two subsidiary, such as 7TET. Diatonic is 7+5 or standard 12 chromatic notes, and supra-diatonic are systems with greater numbers that 7+5 such as 12+7 or 19TET. This is based on the supposition that tonality is evolving from basics like 1, 5, and 4, or that the cycled in 5ths will make up diatony, and includes progressive use of higher ratios in the harmonic series. 9 In breaking down the taxonomy of world instruments into similar attributes one can consider the physical attributes (construction) and culture in the production of musical creation/stylistics heritable and traditional, passed along in instrument making and in cultural gestures that overlay learned implicit tonal understanding. Theoretically one could ask ‘which came first?’ as they are part and parcel of ongoing cultural and human musical development. That instrument creation plays/played a part in the theory behind evolving construction is also a fascinating idea, and has a lot to do with timbres, moods, tonality, pitch, and musical creational thought aspects. 7 Performance scholars and performers have looked to living traditions to inspire and bolster ancient and past European traditions. Often, surface facets are avoided and the larger-scale structural features are favored in developing new work. Further, Early Music ethnography can be discerned via original texts and writings from the musicians. Interestingly, Western generally is not well represented in terms of , perhaps due to missing historical gaps and inconsistencies.10 (Shull, 2006) The (diatonic comma) is a small interval ( ratio 531441:524288 or 23.45 cents) in Pythagorean tuning,11 and equals 12 Just perfect 5ths. Later Greek ratios were codified by Ptolemy, expanding Pythagoras’ 3 limit Just 4th and 5th to include a Just major 3rd in limit 5. Stemming from 1/1, the ratios for limit 5 Pythagorean Just are: ratio 1/1 81/80 128/125 25/24 256/243 135.128 16/15 27/25 800/729 10/9 9/8 256/225 cents 0 21.51 41.06 70.67 90.22 92.18 111.73 133.24 160.90 182.40 203.91 223.46 ratio 125/108 75/64 32/27 6/5 243/200 100/81 5/4 81/64 32/25 125/96 675/512 cents 253.08 274.58 294.13 315.64 337.15 364.81 386.31 407.82 427.37 456.99 478.49 ratio 4/3 27/20 25/18 45/32 64/45 36/25 40/27 3/2 1024/675 192/125 cents 498.04 519.55 568.72 590.22 609.78 631.29 680.45 701.96 721.51 743.01 ratio 25/16 128/81 8/5 81/50 5/3 27/16 128/75 225/128 16/9 9/5 729/400 cents 772.63 792.18 813.69 835.19 884.36 905.87 925.42 976.54 996.09 1017.60 1039.10 ratio 50/27 15/8 256/135 243/128 48/25 125/64 160/81 2/1 cents 1066.76 1088.27 1107.82 1109.78 1129.33 1158.94 1178.49 1200.00

Ancient practices and oral traditions

Ancient practices and oral traditions that passed musical information historically are important to review - some pitch syllables are: interval 1 b2 2 b3 3 4 #4 5 b6 6 b7 7 Western Do re Re mi mi fa Fa sol la la ti Ti India Sa re Re ga ga ma Ma pa da da ni Ni China Shàng chě Chě gōng gōng fán12 Fán liù wǔ Wǔ yǐ Yǐ (gongche) 上 尺 尺 工 工 凡 凡 六 五 五 乙 乙 simplified ル 人 人 フ フ り り 久 ゐ ゐ 10 See later section on recording and archiving of European folk . 11 Another definition of the Pythagorean comma is the difference between a Pythagorean apotome and a Pythagorean limma; between chromatic and diatonic semitone: or between twelve just 5th's and seven octaves; or between three Pythagorean and one octave. The opposite in Pythagorean tuning is the diminished 2nd (difference between limma and apotome) equal to a ~ 23.46 cents. 12 Fan and Yi are between 4 and #4 and ♭7 and 7. This is a simplified version and there are more characters for other octaves and variances for Kunqu and Chinese Opera. 8 Balinese Ding dong13 deng dung dang Japan I ro ro Ha ha Ni ni ho hi Hi to To Arabic Dāl rā' rā' Mīm mīm fā' Fā' sād lām Lām tā' tā' ط ط ل ل ص ف ف م م ر ر د Byzantine Ni pa pa Vu vu Ga ga di ke Ke zo Zo Η, η Α, α Α, α Β, β Β, β Γ, γ Γ, γ Δ, δ Ε, ε Ε, ε Ζ, ζ Ζ, ζ

The old Chinese gongshi notation is still used for traditional instruments, and incorporates a movable do (shang). Like tablature for specific instruments it may have originated with a fixed do system, later using a movable do.14 Traditional musicians still use the score, yet perform from memory. While Western solfege is thought by many to have sprung from Latin roots, there is conjecture it may have Arabic solmization system origins from an influx of Islamic contributions in medieval Europe. The syllables are: dāl, rā', mīm, fā', ṣād, lām, tā'. Masonic sources site ancient solfeggia in hertz as 396, 417, 528, 639, 741, and 852 (in cents: 0, 89, 498, 828, 1084.8, and 1326.4 or 126). In 1935, due to poor music (and sight-singing) standards in Hungary, Kodály revised the curriculum that incorporated a movable-do solfege system of syllables, showing relative, and not absolute, pitch.15 Particular cultural facets and idioms do impact on aesthetic stylistics indicative of time and genre, yet there are musical elements that lie outside the bounds of standard notation – these devices carry microtonality and and in the attributes of African Vocality may be categorized: shouts (intoned or non-intoned), head-voice or falsetto, microtonal utterance like blue notes and glissandi, interpolated vocality, Afro- (form of recitative), multiphonic sounds (same generator), guttural sounds (from the throat), and vocal rhythmization (predominantly rhythmic). All these qualities are speech derivative and imbue emotional emphasis much the same as language. (Duran and Stewart, 1997) Microtonally passionate speech as a type of musical iconography triggers recognition and emotional response to the listener – specific expressions of the human voice. The spiritual Go down Moses begins with a melody going up and continues up with ‘way down to Egypt land.’

13 The graph approximates equivalents in 12TET. 14 The pitch notation was skeletal, making room for improvisation, and evolving offshoot variants make historical determinacy of pitch, system and practice hard to imagine how it may have sounded – and the variant systems of notation became harder to learn. 15 Kodály was first exposed to this in England – a moveable-do system was already in place by Sarah Glover and amended by John Curwen for choral training, which was felt to bolster a grasp of tonal function. Kodály even felt that moveable-do solfege should come before an understanding of the staff. 9 Monteverdi’s opening of the opera Arianna employs a similar irony of a falling vocal contour ‘Lasciatemi morire’ (Let me die!). In 1584 Zhu Zaiyu (Chu-Tsaiya) and then Simon Stevin in 1585 are accredited with the exact calculations of the equal temperament, both independently though Stevin's less accurately. Fritz Kuttner was critical that either achieved equal temperament.

Al-Farabi, 17TET system, kitab al-Adwa, al-Andalas and barzok

After c. 872 Al-Farabi had logically divided the octave into 25 units, which he demonstrated on the .

Fract 1/1 256/ 18/1 162/ 54/4 9/8 32/2 81/6 27/2 81/6 4/3 3/2 18/1 19/9 2/1 ion 243 7 149 9 7 8 2 4 1 C D A C Cent 0 90 98 145 168 204 294 303 355 408 498 702 853 996 1200 s

Consisting of limma and comma intervals this system is still valid in the Arab world.

C D E F G A B C 4/4 1/4 3/4 4/4 4/4 1/4 3/4

These ratios add to 24/4. The simplest way to describe quarter-tones is: 50 cents or, E = the note exactly in the middle of (half way between) E and E♭, and E‡ = the note exactly in the middle of (half way between)

E and E♯. The quarter-tone is half way between the natural and the sharp or flat (50 cents in equal temperament).16,17 Please note that a standard half-flat is a mirrored flat, and that the alternative strike-through flat is used in this paper. Safi al-Din al-Urmawi’s 17TET system (13th c.) was the main system until replaced by 24TET (quarter-tone scale), and kitab al-Adwa (KA) is one of the most influential Arab treatises on music. (Wright, 1995)

17TET Interval Fundamental Cents

16 The E in maqam rast is usually taken generally to be higher than the E␢ in maqam bayati. 17 note. A ¼ tone = half a semitone (50 cents), a ½ tone = a semitone (100 cents), and ¾ tone = a semitone + ¼ tone (150 cents). It must be stressed that the ¾ tone is not, as its name suggests, ¾ of a tone (three quarters of a tone), but a ‘three ’. Thus two three-quarter tones constitutes a . 10 1 0√2 1 0 2 17/1√2 1.0416160106505838 70.588235294117626800 3 17/2√2 1.084963913643637 141.176470588235087000 4 17/3√2 1.1301157834293298 211.764705882352898000 5 17/4√2 1.1771466939089177 282.352941176470608000 6 17/5√2 1.2261348432599308 352.941176470588337000 7 17/6√2 1.277161683956088 423.529411764705993000 8 17/7√2 1.330312058198122 494.117647058823490000 9 17/8√2 1.3856743389806951 564.705882352941116000 10 17/9√2 1.4433405770299566 635.294117647059014000 11 17/10√2 1.5034066538560549 705.882352941176477000 12 17/11√2 1.565972441175087 776.470588235294068000 13 17/12√2 1.63114196696555 847.058823529411552000 14 17/13√2 1.6990235884354028 917.647058823529447000 15 17/14√2 1.7697301721873238 988.235294117647240000 16 17/15√2 1.8433792818817307 1,058.823529411764610000 17 17/16√2 1.9200933737095864 1,129.411764705882310000

The 18th degree is 1200 cents. Al-Farabi extracted the intervals 8ve, 4th, 5th, 7th, whole tone, and quarter-tone on the Oud.18 Also defined was Wusta-Zalzal, greater than a tempered minor 3rd and less than a tempered major 3rd, with the ratio 27/22.19 In past and present) Arab musical practice there is a similar idea to the Western that is a template for development and is modulation in the Maqam. One or more notes are incorporated into the scale of the Maqam producing a second compatible maqam. This modulation can proceed, transitioning into a Maqam or Maqamat,20 and finally will return again at the end to the original Maqam. During the Taqasim or tahmelah (free rhythmic forms) it is common for soloists to modulate many Maqams. Further, this is commonly done by replacing the maqam’s upper with a compatible Jin ‘of the same size’. The Maqam is built upon the diwan. One diwan is usually eight notes, and sometimes extends scalar-wise upwards comprising two diwans. Maqam is more than a scale for the following reasons:

18 Also, the gambus, an oud offshoot, came to Southeast Asia from Yemen traders in the1500s, and is still in use in Malay folk and religious musics. (Al-Jawharah, 2010) 19 In many films depicting the music of the Middle or Near East, a wolf 4 and/or wolf 5, for example, may be heard - E, F♯, G, A , B – the wolf 5th resting 50 cents between the and 5th. The wolf 2 or 3 may be heard, E, F‡, G‡ and part of specific maqamat, and are just some of the colourful Mid-Eastern nuances in practice [from 24TET perspective], and in Gypsy music from India through to Turkey, Greece, and Spain. One contemporary example of microtonality in practice is in Gypsy music, such as in the band Taraf De Haidouks. 20 This style of evolving compatible scales is prevalent in Gypsy and many European folk musics, as well as jazz. 11 -A Maqam can incorporate microtonal variations that are very subtle: so that tones, or quarter-tones are slightly altered. -A Maqam has rules defining the starting note (Qarar) and ending note (Mustaqar), which can in some instances be different to the tonic or dominant (Ghummaz). The second jins starting note begins on the dominant. The Samaie genre is composed of four sections (Khana, plural Khanat) each being followed by the Taslim (refrain).21

1 Structure A T B C D 2 Sections/Khanat First Taslim Second Khana Third Khana Fourth Khana Khana 3 Start 3rd Dominant Dominant 2nd Tonic 4 End Dominant Tonic Tonic Tonic Tonic 5 Range 9 9=1/2 9+1/2 12 11 6 Modulations (outside Farhafza Farhafza Hijaz Hijaz Hijaz the maqam) Ajam and Nahawand Bayati and Nahawand Nahawand Nahawand and Hijaz Nahawand and Ajam 7 Time Signature 10/8 10/8 10/8 10/8 6/8 8 Length 8 4 8 8 24 9 Sections Farahafza F Farahafza Hijaz Hijaz Hijaz 10 Repeats 1 1 1 1 2

Examples of transposing melodic development: Bb C D Eb F G A Bb 1 tone 1 ½ 1 1 1 ½

Indeterminacies abound within geopolitical and cultural areas, for example the distinctly European sounding Levantine and North African ‘Andalusian’ musics that, though different, claim a common al-Andalus commonality. These indeterminacies are likened to the Sufi idea of barzok, the wonder of the imaginable and indeterminable, which are bounded by constriction, yet also have potentiality and horizon. Moroccan Andalusian and European musicians perform well together due to a shared musical commonality, whereas European musicians performing with Levantine musicians (East Mediterranean) may avoid microtonal modes.22 (Shannon, 2007) Far Eastern music also abounds with microtonality. In the 8th century the shakuhachi flute came into Japan from China, with later resurgence, and does not use tongue articulation for pitch

21 Although the tempo is 3+4+3 modern musicians may regard the 10/8 time as 5+5 and is largely regarded as one of the important instrumental Arabic forms. 22 Syria and Morocco sound strong musical ties to medieval Spain. Andalusian music and heritage help bolster pan- Arab ideologies that coincide with Syria’s Ba’thist ideologies. Heritable and proven historical practices with Andalusian links help authenticate Syria’s heterogeneous pasts tied to Christian, Muslim and Jewish histories which counter what some deem vulgar and unauthentic. (Shannon, 2007) 12 reiteration but grace-note articulations, with shaking of the head from side to side. There is no diaphragmatic vibrato, and whilst the holes produce pitches roughly in sync with equal- temperament, since there is no valve or fixed-key system microtonal inflection is of relative ease: glissandi may be produced. (Lependorf, 1989) This can be contrasted to today’s modern . Frank Denyer wrote The tender sadness of tyrants as they dance (1991) for the shaku-hachi and Western bass flute, a combination which creates a previously unheard sonority, one that can be both delicate and ruthless. They play together the whole way through, employing ancient techniques like vibrato, microtonal inflections and modern techniques like ghost tones whereby the player breathes into the flute while fingering notes as well as vocal sounds and tap dancing shoes used to knock heavily against the floor. (Gilmore, 2003)

Common microtonal practices, systems, stylistics (1600-1900): Baroque (1600-1760), Classical (1730-1820), Romantic (1815-1910) Bach, equal temperament, Glarean

Standard equal temperament is defined thus: each semitone ratio is exactly the same as it ascends to the octave,23 regardless of how many intervals there are. Generally it is in the 12- semitone octave (12-tone equal temperament, 12TET), although others exist such as 17TET, 19TET, 24TET 31TET, 53TET and others. Prior to this, temperaments had narrowest 5ths throughout diatonic notes producing purer thirds, with wider 5ths between the chromatic notes (sharps/flats) indicative of the writing period style and treatises, enabling transposable modes [well temperament]. One possibility of a very early circular temperament was described by the early 16th century organist , though well temperaments only phased in during the Baroque, persisting into the Classical period. Some were closer to meantone and others nearer equal temperament, with no wolf 5th. Keys with greater sharps and flats sounded further out of tune because of the 3rds, and modulations were used sparingly (i.e. interchange, ornaments, transitions). The period temperaments include Werckmeister, French Temperament Ordinaire, Neidhardt, Kimberger, Vallotti, and Young.

23 Non standard divisions in place of an octave include the tritave, stretched octave, and other non-octave scales. 13 Meantone (averaging between notes), Helmholtz, Pythagorean, schismatic and miracle temperament are examples of regular temperaments, where ratios are calculated via powers of a limited number of generators. Meantone intervals are calculated by the width of the 5th and an 8ve for the [unison].24 [Easley Blackwood attributed the label ‘R’ to the ratio of the whole tone to diatonic semitone.] In the past, small ratios were used to achieve musical scales, such as the Just system, however, serious harmonic problems were encountered after the Middle Ages as music became more complex, with greater polyphony and key changes, and these perfect intervals no longer sounded harmonic – due to wolf intervals. (Enevoldsen, 2010) Commas include the Pythagorean comma (23.46 cents), the syntonic comma (21.5063 cents) Mercator’s comma (21.8182 cents, or 55√2), and Holder’s25comma (22.6415 cents).

Table of commas Name alternative cents Ratio Skhisma 1.95372078 32805:32768 8 perfect 5ths + 5 octaves 7934159400 major 3rd Septimal 7.71152299 225:224 2 major 3rds + Octave 1319534110 septimal major 3rd Kleisma 8.10727886 15625:15552 6 minor thirds Tritave [8ve + 5th] 2071810140 Small 17.5761311 99:98 undecimal 5728168290 comma 0 Diaskhisma 19.5525688 2048:2025 3 octaves 4 perfect 5ths + 0878068610 2 major 3rds Syntonic Didymus' 21.5062895 81:80 4 perfect 5ths 2 octaves + comma comma 9671485360 major 3rd Pythagorea Ditonic 23.4600103 531441:5242 12 perfect 5ths 7 octaves n comma comma 8464900870 88 Septimal Archytas' 27.2640918 64:63 Minor 7th Septimal minor 7th comma comma 0010023040

24 21.5 cents, the difference between four Just 5ths - and two octaves and a Just 3rd - gives a chromatic diesis, or syntonic comma, of ratio 81:80, as a Just 5th [3/2] is 701.96 cents, and a Just 3rd [5/4] is 386.31 cents. It is also the diatonic comma. 25 Holdrian comma, or Holder koması in Turkish. Holder’s comma (22.6 cents) is equal to one step of 53-et, or the 53√2, an irrational number that does not describe the compromise of intervals within a tuning system and approximates a syntonic comma (21.5 cents).

14 Diesis Lesser diesis 41.0588584 128:125 Octave 3 major 3rds 0549554760 Undecimal Undecimal 53.2729432 33:32 Undecimal tritone Perfect 4th comma quarter-tone 3014412520 Greater 62.5651480 648:625 4 minor 3rds Octave diesis 0221040120 Tridecimal Tridecimal 65.337340 27:26 Tridecimal tritone Perfect 4th comma third-tone 826851658 20

19 tone equal temperament (19TET) naturally came about during the of the Renaissance. The ratio of four minor 3rds to an octave was almost 19th of an octave (648:625 or 62.565 cents), and goes back to the 16th century, used for example in Seigneur Dieu ta pitie (1558) by Guillaume Costeley, thought to have been written for/in 19TET. In 19TET, due to the powers of syntonic tuning, the perfect 5th rests at 694.737 cents: each division is a frequency ratio of 21/19th or 63.16 cents. Some of the ratios in 19TET are closer to Just intonation than 12TET (like 5/3 major 6th, and 5/4 major 3rd), and this is a good starting case in support of its use. 2627 19TET is also a sensible equal temperament as it gives a purer major 3rd and minor 3rd (6/5), and their inversions, major and minor 6ths, over 12TET - although it has a limited amount of accessible pitches per octave. Tim Perkins (Tune Up, Antelope Engineering) describes 19TET as harmonically usable.28 (Sethares, 1991) The 19TET step is 1200/19 or 63.16 cents, slightly more than half a standard quarter-tone. 19TET can be extended into standard notation without too much complication. Although the notes are written on the staff as C, C♯, D♭,D, D♯, E♭, E, E♯,

F, F♯, G♭,G, G♯, A♭, A, A♯, B♭, B, (B♯, C♭), the notated enharmonic equivalents are not the same and each note in succession is 1/19th higher than the previous note. During the 16th and 17th centuries a particularly dissonant form of a diminished 6th was used, popularly arising out of the quarter-comma meantone temperament and spanning seven semitones, called a wolf fifth (procrustean/imperfect 5th). The quarter-comma is a variant of Pythagorean tuning in which its P5 is diminished by a ¼ of a syntonic comma as opposed to the Pythagorean Just intonation of frequency ratio 3/2. The quarter-comma's purpose was to obtain 26 There is an interesting 19ET from Woolhouse (1835) dividing the octave into 730 parts. 27 All notes are within 8 cents of Just intonation on a major C triad in 19TET, as opposed to 14 cents for 12TET. 28 In 19TET there is a perfect minor 3rd. A septimal 3rd may also be produced. A major and , as well as whole tone, may be fairly well approximated, though slightly and noticeably out. The septimal minor 3rd is 2 2/3 semitones, Just interval 7:6. The septimal major 3rd is 4 ½ semitones, just interval 9:7. 15 Just intoned 3rds of ratio 5:4, and described by in Toscanello de la Musica (1523) as 'sonorous and Just as united as possible'.29 Modern equal temperament was invented in the 1500’s,30 in order to accommodate increasingly complex polyphonic music, and to increase the sense of harmony during modulation and key change. The 12TET system breaks the octave into 12 equivalent parts, resulting in a semitone of non-simple ratio – approximately the 12th root of 2 (12√2 or 21/12) or 1.059.31

Semitones Interval32 Just intonation Equal Temperament Difference 0 Unison Consonant 1/1=1.000 20/12=1.000 0.0% 1 Semitone Dissonant 16/15=1.067 21/12= 1.0594630943592953 0.7% 2 Whole tone Dissonant 9/8=1.125 22/12=1.122462048309373 0.2% 3 Minor 3rd Consonant 6/5=1.200 23/12=1.189207115002721 0.9% 4 Major 3rd Consonant 5/4=1.250 24/12=1.2599210498948732 0.8% 5 Perfect 4th Consonant 4/3=1.333 25/12=1.3348398541700344 0.1% 6 Tritone Dissonant 7/5=1.400 26/12=1.4142135623730951 1.0% 7 Perfect 5th Consonant 3/2=1.500 27/12=1.4998261905048882 0.1% 8 Dim 6th Consonant 8/5=1.600 28/12=1.5874010519681994 0.8% 9 Major 6th Consonant 5/3=1.667 29/12=1.683985480334983 0.9% 10 Dim 7th Dissonant 9/5=1.800 210/12=1.7817974362806785 1.0% 11 Major 7th Dissonant 15/8=1.875 211/12=1.8887492632848886 0.7% 12 Octave Consonant 2/1=2.000 212/12=2.000 0.0%

Holder’s comma of 22.6415 cents, or 53√2 (Arabian Comma), was used widely in the 17th century. Mercator’s comma of 55√2, or roughly 21.8182 cents, was close to the syntonic comma of 21.5063 cents. Further, Mercator thought the 53√2 would be of use due to the fact that a cycle of 53 Just 5ths approximated 31 octaves. 53√2 is closer to Just intonation.

Maqam rast,33 in Holdrian commas: C D E F G A B C 9 commas 8 commas 5 commas 9 commas 9 commas 8 commas 5 commas

29 Zarlino and de Salinas later described the theory more exactly. 30 In full use by the 19th century. 31 The table corresponds to Seeger’s early 20th century dissonant counterpoint, and the Just tuning systems of Pythagoras and Ptolemy, with dissonance increasing in larger ratios. The Just inverse ratios add to give an octave, for example 5/3 x 6/5 = 30/15 or 2. 32 The chart shows how the only perfect interval is the octave in equal temperament, and how the difference is spread out overall for transpositional functionality. 33 The illustration is not using half flats or sharps and is approximate. Nihavend uses medium 2nds (somewhere between 8-9 commas). The medium 2nd or neutral second (n2) is larger than a minor 2nd and smaller than a major 2nd, Just interval = 11:10 or 165 cents (greater undecimal neutral 2nd ). The intermediate neutral 2nd ratio is 12:11 or 150.64 cents. The lesser undecimal neutral second is derived as the interval between the 11th and 12th harmonics (from the harmonic series), and the greater undecimal neutral 2nd is derived as the interval between the 10th and 11th harmonics. 16 Maqam nihavand in Holdrian commas: C D F G C E♭ A♭ B♭ 9 commas 4 commas 9 commas 9 commas 4 commas 9 commas 9 commas

The 4th century saw the split of the Roman Western Empire and the Greek Eastern which later became the Byzantine [Roman] Empire. The collapse of the Western Roman Empire in the 5th century (Christian takeover) was steady thereafter, due to the extent of Roman culture and art, into the beginnings of Europe’s Renaissance.34 The first half of 16th century music theory witnessed Henry Glarean as the prominent musical theorist. Glarean, author of the Book of the Twelve Modes and the Dodecachordon (1547), proposed 12 modes, eight plus an additional four: Aeolian (modes 9 and 10) and Ionian (modes 11 and 12), and comments that Ionian was the main mode frequently used by composers during this time.35 According to Ronald Turner-Smish and Mark Lindley, schismatic tuning was used briefly in the late medieval period.36

Jamaica and Africa, Koromanti and Angola, Ethiopian bowl lyre (krar), Quadrille music in Carriacou

At the end of the 1600s, in and around Jamaica, many African traditional musics used microtones in much the same way as blues and rock guitarists accent notes - by bending the string. Sir Hans Sloane observed slaves playing music in Jamaica and notated it in 1687. In the ‘Koromanti’ first two sections seven notes are used, and the third section eight: the extra note was likely the result of the French musician Baptiste’s attempt to record microtones not representable in standard European notations, which would have been somewhere between the 34 Invasions following through from Late Antiquity through to the Middle Ages and the formation of new kingdoms in the Western Roman Empire began, whilst in the 7th century Northern Africa and the Middle East dissolved from the Byzantine Empire (Eastern Roman Empire) becoming part of an Islamic Empire, generally thought of as a pseudo-completion with antiquity. Migratory tonal systems are accountable. 35 In Isogage in musicen (1516) Glarean addresses the basic , perhaps used for teaching. Dodecachordon comprises a massive body of work with over 120 compositions, music theory and philosophical and biographical text. A chronology of modal use beginning with Boethius (16th Century) is discussed in plainsong and monophony ending with a study of modal use in polyphony. Later theorists like Zarlino accepted the twelve modes and although the difference between plagal and authentic is no longer of interest today, the six condensed modes remain. 36 The schisma is the ratio of Pythagorean comma and a syntonic comma: 531441:524288/81:80 = 32805:32768, bearing in mind that the pythagorean comma is the distance of roughly a quarter-tone (between 75:74 and 74:73) and that eventually the syntonic ratio of 81:80 later used by Ptolemy raised or lowered the original pythagorean tonal system to produce just major and minor 3rds. 17 standard semitones, falling between the keys of a . Modern musicologists think that the mode Baptiste transcribed was a heptatonic scale with the 3rd and 7th partially flattened.37 (Rath, 1993) (Burton, 2012) In 20th century (and perhaps earlier) practice it is possible that European harmony influenced blues and jazz with the idea of tonic, subdominant and dominant as triadic 1, 3, 5.38

African Jamaican music: Koromanti and Angola Pitch-class Koromanti Angola (Upper) Angola (Lower) Both 3rds 33 14 9 23 Intervals 316 26 45 71 3rds/Intervals 0.10 0.54 0.20 0.32

Farther east, the Ethiopian bowl lyre (krar) is used for music that is highly chromatic with microtonal embellishments and slides. Some krar tunings (Kignet) are fairly exotic like the Anchihoy with strings 3, 4, 5 comprising a minor 3rd and nearly tone-and-a-half, and its use is as an accompaniment to embellish vocal melodies [much like ancient Greek music]. (Kebede, 1977) Quadrille music in Carriacou is similar to European quadrille dance music, with two sections of eight bar phrases which are instrumental and in the major key. However, the last remaining quadrille violinist in Carriacou, Canute Calliste, borrows from African microtonalism in which some notes are slightly flatter or sharper than heard in European or North American fiddle playing. (Miller, 2005) (Cultural Equity, N.D) Contemporary microtonal practices across genres have been affected by the blues.

37 The Akan in Jamaica (from the Kwa speaking West African Gold Coast region to Cameroon, around Ghana) on the other hand had no common use of microtones and preferred notes from the natural harmonic series, yet microtones were in common use slightly south around the Angola region, perhaps not causing Baptiste to misrepresent in notation – use of heptatonics with slightly lowered 7th. 38Another rare early American account of African music was made in the late 1700’s by De Bercy of nearly free slaves in Santo Domingo, though sadly the transcription lacked the accuracy of Baptiste’s. Lyrics are often an indicator of a music’s origins. 18 Post-romantic and Pre-modernism, experimental, Carrillo, Ives, Rimsky-Korsakov, Experimentalism, polytonality, tone clusters, aleatorics, quarter-tones, polyrhythmic

The late 1800s encompassed experimentalism, which later led to the expanded tonality of early 20th century works.39 Rimsky-Korsakov’s Oriental sounding Scheherazade may be considered late Romantic, and a precursor to experimentalism.40 Ives,41 who experimented with quarter-tones, and Korsakov, are a midquel between Romantic and later Expressionist (and microtonal and tonal) practices. Partch created a family of microtonal string, keyboard and percussion instruments tuned to his Just 43-note scale. Instruments like this were built before in the Low Countries in the 17th century, a time when Huygens talked about use of a 31-note octave capable of diatonic scale transposition in Just intonation.42 Partch extended Just tuning ratios into 7, 11 and 13 limits. Partch's Daphne of the Dunes, for example, sounds like notes extend past the 12 notes we know, yet all is beautifully harmonic and based on phi. extended Just intonation further (high prime limit) that contained hundreds of pitches per octave. In 1895 Carrillo wrote quarter-tone string quartets, later using a 96 division system and created a harp-zyther. Helmholtz wrote in 1863 in On the Sensations of Tone: ‘ the system of scales, modes and harmonic tissues does not rest solely upon unalterable laws, but is at least partly also the result of aesthetic principles, which have already changed, and will still further change…’ (Wood, 1986)

Quarter-tones began to be used in western music around the beginning of the 20th century with : Alois Hába's first work for quarter-tones was Op.no. 9a: Fantasy in quarter- tones for solo (1921) and 's first was Quatre fragments, for 2

39 A short list of 20th century microtonal composers include: , Alois Hába, , Walter Smetak, Easley Blackwood, Ivan Wyschnegradsky, , , Michael Harrison, Per Nørgård, Warren Burt, , Harry Partch, Ben Johnston, Syzygys, Chico Mello, Tony Conrad, Arnold Dreyblatt, Bent Sørensen, The First Vienna Vegetable , Sei Miguel, Pascale Criton, Georg Friedrich, , , Julián Carrillo, Ron George, Bosty, Piotr Kurek, Burkhard Stangl & Kai Fagaschinski, Blues for Spacegirl, Bertrand Denzler, Antoine Beuger, and . 40 Korsakov jusxtaposed keys by a , as in C major and ,with distinct and easily comprehensible rhythms and had an Eastern feel that was absent in late 19th century work. 41 Ives’ 12TET Central Park in the Dark may be regarded as one of the first Experimentalist pieces, with the strings in 3rds, 4ths, and 5ths representing the park’s woods, and ragtime quotes from Hello My Baby and Washington Post March (Sousa) finally ending in tensions of cacophony, with similarities to Experimentalists of the time like Varèse, Ruggles, and Hovhaness The microtonalist Harrison, who studied under Schoenberg at a dance school in California where he worked, helped Ives to come to public attention, conducting the acclaimed Symphony No. 3. 42 A 31-tone organ still rests in Haarlem at the Teyler Museum 19 in quarter tones (2nd version), Op. 5 (1918). Prior to this it is doubtful if there was a developed 24-tone equal-tempered system with pairing of technology and notation.

Contemporary & modern microtonal practices, systems, stylistics: Modern (1890-1930), 20th century (1901-2000), Contemporary (1975-present), Modernism, Dadaism, serialism, microtonality, Verèse, Webern, Wyschnegradsky, Hába, Carillo, Villa-Lobos, Ives, Partch, Cowell

In 1912 Henrey Cowell used tone clusters in The Tides of Manaunaun. In 1913 Russolo wrote The Art of : Futurist Manifesto and in 1914 conducted intonarumori ( instruments). 1916 saw Dadaism (anti-art) rise in Zurich with and sound poetry at the Cabaret Voltaire. Prior to tape slicing and analog and digital sequencing, repetition and form lay more in the performance domain. This craft has been handed down to modern producers, In 1917 Verèse suggested instruments that could ‘open up a whole new world of unexpected sounds.’ Satie’s ballad Parade utilized typewriters, revolvers, sirens and ships’ whistles. Webern, like Verèse, was not exposed early on to Eastern musics, yet both drew interesting parallels – Webern’s tendency to clarify structures of motifs with variegated textures in high definition of timbre, register, duration, articulation etc. is comparable to Asian musics, whereby whole structures would seem static/erratic without motific definition, which derive meaning/coherence from differing devices like timbral changes, vibratos, pitch inflections, articulation. Coherence played a vital role in 20th century composition, as overarching structure of the whole greater than (and related to) its constituents. At this time Villa-lobos was torn between European classical and Brazilian folk.43 As neoclassicism and serialism began, a third movement soon sprang up: microtonalism. Stravinsky and Bartók had exposure in their youth to Eastern and folk musics, and some of which Stravinsky had assimilated was likely folk of Asian origin, whilst some may have come from the orientalist Rimsky-Korsakov, who would have been exposed to the Asian music that spilled over into Russian popular musics. In Les Noces’ opening, large intervals greater than a 2nd are used with sliding attack typical of some singing styles in Asia.44

43 Villa-lobos’ Amazonas and Uirapurú were derived from ancient indigenous Brazilian folk material and legends. 44 Bartók’s serious investigation of East-European folk included the Magyars of the Ural Mountains which contained, at the time, uncorrupted ancient musical elements. Bartók also studied Arab and Turkish music, influencing his compositional aesthetic as an ethnomusicologist – covering melody, harmony and rhythm and 20 Hába may well have marked the beginning of microtonalism in the 1920’s which was followed by a die-down, with a resurgence in the 1960’s till present, many composers taking it seriously, with multi-tempered compositions being a sign of 20th and 21st century style, ranging from Wyschnegradsky45 to Carrillo, due largely in part to awareness of non-Western music, mainly Arab, Indian and Chinese. Hába’s interest in quarter-tones was largely due to influence from Slovakian . also began experimenting and composing at this time, tuning a first piano a quarter-tone higher than a second resulting in176 pitches (from 88).46 Whilst Scriabin pondered new tonal systems, Ives and Couper wrote them down, and Hába and Carillo had a large amount of microtonal work, yet Wyschnegradsky had an impressive output and scope including theory, highlighted by 24 for two pianos tuned a quarter-tone apart. He described his tonal system as having two divisional heptachords, separated by a semitone, instead of the standard double tetrachordal division.47 With + and – taken as quarter-tone adjustments, a basic scale comprises C, C#, D, D#, E, F, F+; G-, G+, A-, A+, B-, B+, C. (Burge, 1978) Here Wyschnegradsly’s deemed diatonized chromaticism is similar to Yasser’s supra- diatonic system, although not in 19TET, and transpositions total 24.48 Easley Blackwood’s 16- notes Andantino is certainly as subtle as any of Wyschnegradsky’s work, with rich microtonal harmonic content and sweeping microtonal phrases that are not heard anywhere else, in nature or most other musics, and are extremely sensible and exhilarating, enchanting and sophisticated. In Finland, due to the Kalevala (distinct folklore set apart from Swedish and Russian hegemony), folklore collectors of the 19th and early 20th centuries sought to record music which they thought might be disappearing, due in part to publications such as Kansanmusiikki (Folk instrumental idioms. Bartók did not however delve into microtonal inflection and stylistics. 45 Wyschnegradsjy is extremely subtle in microtonalism, in, for example, Two Preludes. 46 Couper also studied with Nadia Boulanger, and after experimenting with quarter-tone tuning, resluting in the ballet piece Xanadu (1930). 47 Today the tetrachord may be taken to include either the 4 or #4 (traditionally, and for Wyschnegradsky, the 4 is implied). 48 One writer describes Wyschnegradsky thus: ‘It reveals a singularly rich variety of mood and texture, this brought about by a balance between the etude or pattern-type piece and the contrasting tone poem. There are languorous dances and a scherzo, Bartokian motor rhythms, hints of fireflies and fireworks, and a haunting peasant song. One finds harsh two-voice counterpoint in bold octaves, a dirge-like passacaglia, and in no. 11, quasi campana, clangorous sounds in large clusters, notated as "a vertically striped half-moon" spanning the interval. Almost throughout, the pianos engage in melodic and harmonic hocket. Whenever possible, the composer has scrupulously marked dynamics and use of the pedals for each instrument.’ (Burge, David, 1978) Wyschnegradsky used third- tones (18-tet, 66.666 cents), sixth-tones (36-tet, 33.333 cents), and twelth-tones (72-tet, 16.666 cents). In Quarter- tone Piano Prelude #1 & #2 by Diesel Bodine (Scott Crothers) it is interesting to note that the harmonics and melody are embellished with microtones. It seems the microtones are not that harmonically or melodically functional, but peripheral embellishments, similar to Wyschnegradsky’s usage, although Wyschnegradsky’s microtonal use is very systematic and even, harmonically interconnected, and employs tonal clustering that is consolidated within overall structures. 21 Music). Both lower and higher Finnish education systems take folk music seriously. Konsta Jylha and his band, Kaus-tinen Purppuiipelimann, draw on ancient folk traditions while incorporating new ingenuity to the practice, as in reinterpretations. Folk music in the higher sector education has helped revive mass consumption and appreciation and development in the Finnish arts, which stress teaching it in changing-world contexts.49 (Ramnarine, 1996) In the U.S. Charles Ives went on to write Choral for Strings in Quarter-tone (1914) and Three Quarter-tone Pieces for Two Pianos (1924) and Some Quarter-tone Impressions (1925). Ives uses two pianos normally pitched with one tuned a quarter-tone down (or up) in the upbeat 3 Quarter-Tone Pieces, which works well over-all as the two seem in parallel and phase interweaving at moments into a seeming fusion.50 (Ives, 1924) In Prague around this time Czech composer Alois Hába was also working on quarter-tone pieces, utilizing two keyboards with one tuned a quarter-tone higher. Hába produced many microtonal compositions with quarter-tones and sixth-tones. A septimal sixth-tone is 34.98 cents (50:49). It is the difference between 7:5 (lesser septimal tritone) and 10:7 (greater septimal tritone, inversion of the lesser tritone). The sixth-tone is tempered out of 12TET, 24TET, and 22TET, but fits in to 19TET, 31TET or odd octave divisions. Partch, on the other hand, devised ‘monophony’ with an octave split into 43 unequal parts. He writes in (1949) that all stem or expand from unity or 1/1, and that modulations to non-dominant and non-common scale degrees are possible; and that it is ‘not capable of parallel transpositions of intricate musical structures’; and that it is not tone specific – conversely capable however of ordinary and extra-ordinary unheard of modulations resulting in expanded tonality. In The Complete John Cage Edition – Vol. 27: The Works for Violin 5, there is precision microtonality, and the chorals are derivative of Satie’s Douze petits chorals and Socrate. For One, the first note F is drawn out at length, followed by a short pause and then another F, and this keeps with introduction of new notes. The effect is hypnotic as one loses a sense of pitch-relation. Performed by Irvine Arditti, it works through Zukofsky’s idea ‘to make a

49 Researcher Anneli Könt gave classes of Estonian folk songs where one song, Sinimani seele, had a melody range of a tone, whereby a lead singer calls and chorus answers. The lead line may change by microtone or intervals greater than a 5th, while the chorus reply of contemporary folk students adjusted each time to the change. (Ramnarine, 1996) 50 George Ives’ son Charles recalls his father’s construction of his ‘Quarter-tone Machine’ consisting of 24 violin strings: ‘One afternoon, in a pouring thunderstorm, we saw him standing without hat or coat in the back garden; the church bell next door was ringing. He would rush into the house to the piano, and then back again. ‘I’ve heard a chord I’ve never heard before – it comes over and over but I can’t seem to catch it.’ He stayed up most of the night trying to find it on the piano. It was soon after this that he started his quarter-tone machine.’ 22 continuous music of disparate elements, single tones, unisons, and beatings’.51 (Haskins, 1990) (Dervan, 2003)

Yasser, infra-diatonicism, supra-diatonicism, evolving tonality

Joseph Yasser deems a basic 5-note structure as a structural basis for a denoted 7-note diatonic set, and the remaining two notes have secondary functional auxiliary filling. This is deemed the 5 + 2 complex and Yasser terms it infra-diatonic. In the Chinese heptatonic system (7TET) the two parentheses notes are termed pien-tones (‘becoming’): F G A (B) C D (E) f. Mododic works from the Song dynasty most commonly contained modes on G(shang), D(yü), and somewhat F(kung). This may have influenced the early Japanese ryō system in which the prevalent modes were on G (Ichikotsu-chō = shang) and D (Ōshiki-chō = yü). In the later Togaku court pien-tones were modified thus: ryō =  G A B (C) D E (F) g (derivative of shang) and ritsu =  D E (F) G

A B (C) d (derivative of yü). Alternating the pien-tones from E-B and F-C produces a major- minor shift.52 (Gauldin, 1983) Within the first 10-note set of the harmonic series is 1, 2, 3, 5, ♭7 and a lydian ♭7 diatonic scale in the first 13 notes [1, 2, 3, #4, 5, 6, ♭7], after which microtonality becomes increasingly greater. Just intonation is the older way of viewing [and teaching] the harmonic series. Yasser views a 5+2 (infradiatonic) [pentatonic 5 + 2] as a precedent for a 7+5 [diatonic 7 + chromatic 5] tonality, that will one day be followed by a Just expanded tonality, or supradiatony (Yasser, 1932), perhaps like Partch’s 43-note Just scale, based on ratios, limits, and tonality diamonds. Perhaps a good instrument to begin this tuning on would be a harp or zither, although transposition would be non-movable as opposed to voice or fretless strings, or trombone.53 For the Paris Conservatoire it became dogma that all major or minor dominant chords were ‘natural’, whilst others were ‘artificial’. This is in line with

51It has been suggested that 432hz tuning would be a close and more natural and harmonious choice, as dividing by 3 (resulting in 5ths, that string instruments tune in) won’t give numbers that recur, creating dissonant beating., which is the case with A440hz, A442, and A443. Although this only occurs on the open strings. This theory works because it is arbitrarily in base 10. 52 Further, Hexatonics, and tetratonics, are two frameworks that are very much overlooked. Nonatonics (9), decatonics (10), undecatonics (11), dodecatonics (12), triskaidecatonics (13), tetradecatonics (14), pentadecatonics (15), hexadecatonics (16), heptadecatonics (17), octadecatonics (18), would be part of either extended or upper- structured scales or part of other temperaments such as 19TET. 53 Partch’s instruments for 43-just include the zymo-xyl (uses blocks of wood, much like a xylophone), diamond marimba, and others. Partch’s concepts include expanded Pythagorian Just limit tuning ratios and otonality and utonality. 23 dissonant counterpoint’s view that dominants drive forward composition in architectural space. The fundamental is the first harmonic of which other harmonics are said to be partials. The human brain perceives higher harmonics as being closer together than lower harmonics, closer to the fundamental, creating a perceived stretching effect that may account for octave perception discrepancy. Frequencies in the harmonic series are whole number ratios [of the fundamental] and directly related to Just intonation. If harmonics are present in a note which constitutes a harmonic series of any frequency, the human brain perceives the overall note as the fundamental, even if not present. These combinations of partials or harmonics of the fundamental are perceived as timbre or colour. Strong high in often mask their fundamental. David Cope (1997) forwards the idea of intervallic strength, where consonance results from lower harmonics in the [harmonic] series and dissonance from higher harmonics in the series.54 Shenker linear progression5 of melody over harmony cannot progress without a passing note from a sequence within the harmonic series, for example 3, 2, 1 over a

54 In practice this may be subjective to what we’re used to, and very high ratios may approximate small (consonant) ratios. 5 The Schenkerian graph may straitjacket work, effectively compounding problems further. This makes it less than welcome in ethnomusicology, and although some music anthropologists have never learned to read notation, understanding a Schenkerian graph requires a high degree of musical literacy and discipline in 24 25 Notable small (Just) ratios [truncated] along the harmonic series up to limit 15 and mirrored 2:1 (Yasser, 1932): Raito Interval cents Centitones Mirror Mirror in cents Tonic 1 0 0 2/1 1200 12 th √2 ♭2 100 50 7 1100

th 16/15 ♭2 111.73128526978 56 15/8 or 7 1,088.26871473022000000 0 10/9 w2 182.40371213405998000 91 9/5 or ♭7th 1,017.59628786594002000 0 0 12 2 √2 2 200 100 12√210 or ♭7th 1000 9/8 2 203.91000173077483500 102 16/9 ♭7th 996.089998269230000000 0 8/7 w2 231.17409353087507100 115 7 / 4 o r ♭7th 968.825906469124929000 th 0 [1/7, 6 harmonic] blue 7/6 w♭3 266.87090560373751100 134 12/7 7 933.129094396262489000 0 [1/6, 5th harmonic] 12 3 12 9 th √2 ♭3 300 150 √2 or 6 900 th 6/5 ♭3 315.64128700055260000 158 5/3 or 6 884.358712999447400000 0 [1/5, 4th harmonic] (11/9) 3 347.40794063398187200 174 18/11 6 852.592059366018128000 0 27/22 3 354.54706023140554600 177 44/27 6 845.452939768594454000 0 (Wusta-Zalzal) 5/4 3 386.31371386483481700 193 8/5 ♭6 813.686286135165183000 0 [1/4, 3rd harmonic] 12 4 √2 3 400 200 12√28 ♭6 800 9/7 3 435.08409526164990700 217 14/9 764.915904738350093000 4/3 4 498.04499913461258200 249 3/2 or 5th 701.955000865387418000 0 [1/3, 2nd harmonic] 12√25 4 500 250 12√27 or 5th 700 15/11 4 536.95077236546553200 268 22/15 w5 663.049227634534468000 0 11/8 4 551.31794236475670700 276 16/11 5 648.682057635243293000 0 7/5 w#4 582.51219260429011100 292 10/7 or #4th 617.487807395709889000 0 12 26 #4 600 300 #4 600 10/7 #4 617.48780739570988700 308 7/5 or w#4th 582.512192604290113000 0 26 th 13/9 w#4 636.61766003853575200 319 18/3 or ‡4 563.382339961464248000 0 12√27 5 700 350 12√25 or 4th 500 3/2 5 701.95500086538741800 351 4/3 or 4th 498.044999134612582000 0 [1/2, 1st harmonic] rd 11/7 w♭6 782.49203589563178000 391 14/11 or 3 417.507964104368220000 0 12 8 12 4 rd √2 ♭6 800 400 √2 or 3 400 rd 8/5 ♭6 813.68628613516518300 407 5/4 or 3 386.313713864834817000 0 13/8 6 840.52766176931059200 421 16/13 or 3rd 359.472338230689408000 0 5/3 6 884.35871299944739900 442 6/5 or ♭3rd 315.641287000552597000 0 12 9 √2 6 900 450 12√23 or ♭3rd 300 12/7 6 933.12909439626249300 466 7/6 or w♭3rd 266.870905603737507000 0 7/4 ♭7 968.82590646912492900 485 8/7 or w2 231.174093530875071000 blue 0 12 10 12 2 nd √2 ♭7 1000 500 √2 or 2 200 nd 9/5 ♭7 1,017.596287865940020 509 10/9 or w2 182.403712134059980000 000 13/7 7 1,071.701755300185660 536 14/13 or ♭2nd 128.298244699814340000 000 15/8 7 1,088.268714730222240 554 16/15 or ♭2nd 111.731285269777760000 000 12 11 √2 7 1100 550 12√2 or ♭2nd 100 2/1 8ve 1200 600 2/2 0

27 From full string board to within the octave fundamental

5th 1 3/2 2 0 1/2 1 6 4th 6th 4/3 5/3 1/3 2/3 3 b7 3rd bv7th 5/4 6/4 7/4

1/44 2/4 3/4 b3 B4 b6 b7 b3rd B4 b6 7 6/5 7/5 8/5 9/5 1/5 2/5 3/5 4/5 3 498 884 7 3 4th 6th 7 7/6 8/6 9/6 10/6 11/6 1/6 V 2/6 V 3/6 4/6 V 5/6 2267 3 498 4 b6 884 6 10497 2 3rd B4 bv6 6th 7v 8/7 9/7 10/7 11/7 12/7 13/7 1/7 2/7 3/7 4/7 5/7 6/7 231 435 617 782 933 1072

28 

29 cadence. The lydian ♭7 mode and the dominant 9 (#11) are very low in the harmonic series, and consonant. The #11 is the sixth harmonic (lydian chromaticism of George Russell), consonantly low in the harmonic series, corresponding with the ability to produce a pentatonic and heptatonic scale naturally, working upward sequentially in fifths, starting in a . The 14th harmonic produces the natural 7th, and the flat 3rd occurs at the 17th or 18th (due to the curve) harmonic above the fundamental – enabling the . The last figure on p. 27 shows how the harmonic series may represent where ratios fall in terms of the two primary in the octave, although skewed from their actual position.55 The fundamental (first harmonic) is designated 1f; the second harmonic (first ) is 2f (an octave), and includes the set root and 5th; the fourth harmonic is 3f (two octaves) and includes the set 1, 3, 5, ♭7; the eighth harmonic is 4f (three octaves) and includes the set 1, 2, 3, #4, 5, ♭6, ♭7, and 7. Thus, each time the repeats [in multiples 2, 3, 4, 5, etc.] an even set occurs which is doubled in number from the last. The #4 or ♭5 pivotal tetrachord point is precisely at 12√26. This mirror technique of Just ratios could be used in music in the future. 2:1

Symmetry and reflection of a dorian 1, 2, ♭3, 4, 5, 6, ♭7 or 2/2, 9/8, 6/5, 4/3, 3/2, 5/3, 9/5, 2/1 would be 2/1, 10/9, 6/5, 4/3, 3/2, 5/3,16/9, 2/2 or 1, w2, ♭3, 4, 5,6, ♭7 where the more dissonant larger ratios near the octave bounds begin to swap (invert) more microtonally. Note that in the table above, the wolf 2nd (w) (231.174 cents) is identical to 1/7 in the harmonic series (the 6th harmonic). This is true for 3/2 (P5th), which is 1.5, and ½, which is 0.5. To convert the harmonics to cents a one is added before using log2(1200). Kirnbergers’s well-tempered scale is the same as Just intonation with exception of the 2nd, a major whole tone, out by -10.061 cents, 5th out by –5.292 cents & Major 6th out by +5.291 cents. The pentatonic, or infra-diatonic mode (infra-diatonicism), is filled in to achieve a partial [such as a hexatonic dorian (no 6) mode] or fully diatonically expanded modern mode. However, tones, modes and intervals change with the system of tonality. There are essentially two ways of looking at expanded supra-diatonic modes: we can wait for a new system and notational

55 For example, touching a string halfway is ½, producing an octave (first harmonic), yet 2/2 + ½ = 3/2, showing the 5th at halfway between root 1/0 and octave 2/1. Further, touching the string at 1/3 or 2/3 will produce a 5th, yet also 3/3 + 1/3 = 4/3, a 4th, and 3/3 + 2/3 = 5/3, or 6th. The skew is not represented in the diagram, as 3/2 should not be at ½ for example, and thus this diagram is for comparison purposes only, as the upper 5-8 tetrachord is a smaller yet relative image of the lower 1-#4 tetrachord. Looking at the tetrachords, among other divisors as well, is good for mirroring and comparing/contrasting amongst other geometrical and syntactic issues within musical language. The stretching phenomenon between the lower and higher tetrachord is exemplified in this skewing effect.

30 semantics and semiotics to occur, along with the building of instruments, or we can add to the 20th century techniques of microtonal symbols, viz quarter-tones, eighth-tones etc., thus mimicking the effect of diatonicism filled in from a pentatonic core of the past. Hence diatonics [and chromatics] would be the base for supra-modalities, and microtones will fill in the gaps. Lastly, for a fundamental phase x,56 when a complete phase is halved [2x], the first overtone or partial is sounded. This continues on: for 3x, a third of the original phase [produces the third overtone], 4x, a fourth overtone, and so on. This is the harmonic series. The series can be heard on the , an ancient fretless 7-stringed zither.57 (Henryshoots, 2010) Yasser asserts that just as in Faux-bourdon of the 1200’s, where composers struggled to break away from infra-diatonicism (pentatonic) and infra-, hypothetically taking the root [C, D, F, G, A] combined with the 5th pentachord [G, A, C, D, E] and/or 2nd pentachord [D, E, G, A, B] to form diatonicism [C, D, E, F, G, A, B] (or hexatonics) - yet without any triadic harmonic concepts, and yet employing altered triadic inversions - so too do modern composers helplessly try to break from atonality and 12-tone chromatics and diatonics. Yasser thinks that expanded tonality (supradiatonisism) in the future will require the same functionality as equal-temperament, and thus deems a logical derivative system like 19TET should be adopted, studied and taught, in order to see the full rewards of future endeavors, symphonies, and progressive works.

56 From full stringboard to within the octave: A good visual aid to conceptualize the harmonic series (0-1) is to convert it into a double tetrachord template (1-2). The root fundamental is one single phase. So, for the second harmonic 1/2(x) [of a fundamental frequency in the series], creating two phases, all we need to do is place a 1 before ½ to view the ratio precisely between 1 and 2, thus 2/2+½ = 3/2 = 1.5. From there a conversion to cents is straightforward as log21.5(1200)=700 cents or P5. The second harmonic would be two nodes at 1/3(x) and 2/3(x), creating three phases: 1/3(x) is 3/3+1/3 = 4/3, thus log24/3(1200)=498 cents or P4. 2/3(x) is 3/3+2/3 = 5/ 3, thus th log25/3(1200)=884 cents or major 6th. The P4 and major 6 fall exactly on each side of the 700 cent halfway point of a P5, and this process continues on up the harmonics in the series and can be practicably translated in this fashion. One may wonder why 700 cents is half-way along 1200 cents, when 600 cents, the symmetry pivotal point, or #4, would be the logical choice. 700, or 3/2, marks the start of the second tetrachord and is the second occurring overtone (third harmonic) in the harmonic series. This illusion is due to the fact that relative distance and wave length becomes shorter as pitch gets higher. varies between instruments, and even thickness of strings, occurring progressively more, higher up the [harmonic] series, and generally overshooting the theoretical notes. (Inharmonicity - sound due to natural laws is not fully compatible, only indicative, of pure mathematical, physical, and geometric concepts. In 2:1 scales, a point of interest is that the phi ratio falls at 1200/1.618033 or 741.641239 cents, which is 9 cents short of the quarter-tone between the 5th and ♭6 (in the key of C this would be G‡, and in the key of E♭ a B ). The 833 cents scale is also attributed to phi.) 57 Called ‘the instrument of the sages’. 31 Darmstadt, neotonality, dodecophony, Stockhausen, Boulez

Darmstadt’s shadow created by Stockhausen & Boulez dissipated by 1984, yet is still stylistically diverse. (Dominick, 1984) At Darmstadt in 1984 Halbreich lectured that direction is essential, as too is tension and harmony, and that stasis and colour are contained in modality: yet stasis occurs in dodecaphony as the human ear cannot make sense of tension and resolution and direction at complex levels. In microtonal composition and practice this is a prime consideration. Halbreich also postulated a ‘neotonality’ where spectral harmony extends to the idea of a richer complexity of harmony considered consonant at higher levels. Classical hallmarks may be considered to differentiate past and present minimalist Western practices: 1. A strong tension/relaxation technique (expectancy, fulfillment), 2. Minimalist motifs are functionally triadic based melodies in question-answer format and similar to classical technique, 3. ‘Periodicity’, 4. Diatonic triad based, 5. Simplicity, 6. bass motif recurrence, much like Baroque driven pulses, and aural pleasure derived unfettered by emotionalism. Banquart lectured that too many pitches is an overload and only works with ‘defective’ tone rows. (Dominick, 1984) Stockhausen’s ideas incorporated transition and transformation not only of musical languages, rhythms, time signatures and pitches, but extended to transition of process that can expand and contract, moving non-linearly.58 Pitch, rhythm and time, and timbre are illusively separate. The fundamental pitch that produces harmonics/overtones is not needed for humans to perceive it, as long as some notes of the harmonic series are contained within it – timbre and characteristics of any physical sound phenomena are simply sets of partials or harmonics.

58 Stockhausen states that at one point he tried to contract a national anthem into the pitch-space of a major third – dividing the pitches into microtonal equivalents.

32 22TET, A Just 12 tone-scale built on powers of 3 and 5, diminished 7th blue note, 1960s Rio de Janiero Jazz, Bossa Nova, US jazz, flattened 5th and hexatonics in the Blues, New Orleans resurgence, Copacabana

22TET divides the octave into equivalent ratio parts of 22, or the twenty-second root of 2, 22√2, or 54.55 cents. It is thought to have come from theorist RHM Bosanquet, and inspired by the music theory of India, had noted how compatible it was with 5-limit tuning (Just intonation). The small ratios that form harmonic intervals involving prime numbers 2, 3, and 5 are considered 5-limit intonation. The following chart for Just intonation shows the primes used in all but the 2nd and 7th dissonant intervals.

Note C D E F G A B C Ratio 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 Decimal 1 1.125 1.25 1.3333 1.5 1.6666 1.875 2 Cents 0 204 386 498 702 884 1088 1200 Name T T S T T T S Ratio 9/8 10/9 16/15 9/8 10/9 9/8 16/15 Cents 204 182 112 204 182 204 112

16:15 S semitone 1.06666 10:9 T minor tone 1.11111 9:8 major tone 1.125

Which combine to make-up 6:5 Ts minor third 1.2 5:4 Tt major third 1.25 4:3 Tts 1.33333r 3:2 TTts 1.5 2:1 TTTttss Octave 2

Note A B C D E F G A Ratio 1/1 9/8 6/5 4/3 3/2 8/5 9/5 2/1 Cents 0 204 316 498 702 814 1018 1200 Name T S T T s T T Cents 204 112 182 204 112 204 182

A Just 12 tone scale built on powers of 3 and 5 (i.e. 1/9 = 3−2)

Factor 1/9 1/3 1 3 9

33 Note D− A E B F♯+ 5 ratio 10/9 5/3 5/4 15/8 45/32 cents 182 884 386 1088 590 Note F C G D B♭− 1 ratio 4/3 1 3/2 9/8 16/9 cents 498 0 702 204 996 Note G♭− D♭− A♭ E♭ B♭ 1/5 ratio 64/45 16/15 8/5 6/5 9/5 cents 610 112 814 316 1018

The 7/4 (factor 1.75) interval (968.826 cents), or septimal minor or harmonic 7th, is 31 cents lower than its equal tempered counterpart. It is linked with blue notes in jazz, and has been a contentious issue throughout music history. In context it is slightly ‘sweeter’ then a conventional diminished 7th (or minor 7th in jazz). It is derived from the harmonic series, the interval between the 7th harmonic and 4th harmonic. Most often in horns it is corrected to 16:9 Just Pythagorean, yet the pure diminished 7th harmonic was used in Serenade for tenor, and strings, by Britten. The late 1950s and early 1960s Rio de Janiero Jazz scene had a deep Blues influence (Delta blues, North Mississippi Hill Country Blues) during the Bossa Nova explosion. US jazz musicians caught on to bossa nova and although seen as whitened samba, the Brazilian Jazz musicians viewed it as exciting new territory. Popularized by Luiz Gonzaga in the 1940s the baiāo is the most similar Brazilian music to the blues, complete with microtonal shading, flattened 5th and string bending - although the is prevalent over the blues C-E♭-F-G♭-G-B♭-C, which was not in Brazilian genres prior to bossa nova, and continued unchanged throughout the 1960s New Orleans resurgence and innovation as well as in Copacabana. (McCann, 2007) In the Blues any inflection microtonally upon any of the 12 chromatic notes is used in composition, and it is the aesthetic style, feel, attack and gesture which makes a composition unique according to B.B. King. In his book Blues Method music making is compared to singing, in that one must take time with the notes and that every note should mean something. A distinctive player may be known for his distinctive characteristics or style of bending into certain notes or use of vibrato. This idea of ‘musemes’ sets particular players apart. Jeff Titon addresses

34 the question of blue notes and concludes from early recordings of downhome Blues that ‘pitch complexes’ are used - these quarter-tones are used consistently from line to line, stanza to stanza. (Weisethaunet, 2001)

Pitch and cognitive acculturation, development of musical thought and thought in sound, schematic and veridical expectancy, mistuning perception

With regard to microtonal past and present practices it is important to mention the harmonic function of notational systems, time representation, and microtonal function. As music is like a language, with tonal systems and microtonal inflections that can impart meaning (semiotics, semantics and context),59 its artifacts are important in cultural, traditional and practical aspects of music making, thinking, and expression. Musical thought may include timbral information as well as pitch, duration and ornamental embellishment which may be linked to socio-cultural heritability, where music and other types of passed knowledge are linked and may involve microtonal information. For example with the Xavante of Brazil a tradition of ceremonial wailing, called microtonal rising, is practiced by senior age groups during grief, though not by youths. (Graham, 1994) Birdsong is microtonal - birdsong pitch and timbre variety are remarkably complex, as are their structures.60 The phi ratio 833 cents scale (Heinz Bohlen) is based on the golden section, or Fibonacci sequence. The convergence of any interval and its closest combination tone approximate the phi ratio (833 cents). The scale has 12 steps of .8333 and is close to 36TET.

Interval Base Closest Combination Ratio Tone Cents 2:1 3:2 701.955000865387418000 3:2 5:3 884.358712999447403000 5:3 8:5 813.686286135165183000 8:5 13:8 840.527661769310592000 13:8 21:13 830.253245565201749000 21:13 34.21 834.174502165894946000

59 Contextual, geometrical and mathematical. 60 Ornithological writers like Thorpe, Armstrong, and Hartshorne often compellingly viewed birdsong as a form of music. (Preston, 2004) Things to consider from sonographs are structure, dynamics, timbre, and rhythm. For the Oriole, most of the pitch takes place between 3 and 9 khz. (Oehlkers, 2009) Many rhythms in nature are hypnotic and microtonal, from cricket noises to the sound of translated cymatics from the cosmos, stars and planets - signals shifted into the audio domain, as well as the sound from the microcosm – the natural world contains microtonality. 35 34:21 55:34 832.676246729184233000 55:34 89:55 833.248460930085779000 89:55 144:89 833.029884571097529000 144:89 233:144 833.113371854361454000 233:144 377:233 833.081482337260849000 377.233 610:377 833.093663017901213000 In human audition Just intonation is the easiest on the human ear and it avoids ‘beating’, whereby vibrations are in interference. There is another problem to consider when examining any patterns that may emerge from past musical practices and their tonal systems,61 usually with some degree of microtonal implications, and that is this: to what degree is internal musical thinking influenced by real-world experience before it is burned into the mind and ready to use imaginatively? In a study by scientists at Beth Israel Deaconess Medical Centre and Harvard Medical School findings showed that after testing subjects to pitches and asking if the last or second to last were the same, the supramarginal gyrus and dorsolateral cerebellum were ‘significantly correlated with good task performance.’ The SMG and dorsolateral cerebellum could play a critically responsible role in storage of short-term pitch [information] and unfolding pitch discernment in pitch memory tasks. (Gaab, Gaser, Zaehle, Jancke, Schlaug, 2003) This at least is a start to understanding the nature of memory and microtoal pitch classes.62 In another study, mistunings by Western listeners were swayed by past acculturation and musical sophistication. Whilst non-musicians showed a different threshold for mistunings for the culturally-familiar and culturally-unfamiliar, musicians’ thresholds across Western and Javanese did not differ, suggesting that musical skills can be applied.63 The Bohlen-Pierce tritave 3:1 ET scale was studied on trained and untrained musicians as well. (Pierce and Mathews, 1987) These studies are important factors in determining true understanding of pitch relation, and further microtonal pitch relation in past and current practices. Arab and Western listeners have had responses recorded to improvised modal music () – heptatonic Arabic (maqam) systems of 24 quarter steps (50 cents) to the octave. Intervals in the

61 In order to practice music, much like language, a system and practice needs to be in place, or devised. 62 Volume (in itself a paradoxical term) did not seem to correlate: a study for pitch versus (Clement, Demany, Semal, 1999) suggested that pitch and loudness were processed in separate ‘modules of auditory memory.’ 63 To put interval and modal acculturation into further perspective, Lynch and Eilers (Lynch, Eilers, 1991) tested 6- month-old and 1-year-old Western infants using an operant-head-turn procedure. In a melody, the infants detected randomly placed mistunings in the Western major, Western augmented, or Javanese , recording a performance pattern similar to adults. The older 1-year-olds performed better in the Western major over the Western augmented and Javanese pelog. 6-month-olds did better in the major and augmented over the pelog. The conclusion is that culturally specific perception and reorganizing of starts to affect perception between six and 12 months. This is concordant with studies that indicate reorganization of speech takes place by the end the first year. This is also interesting in light of the Chinese lingua-tonal-inflections to elevated incidence of . 36 scales are usually 2, 3, 4, or 6 quarter steps, 6 being quite rare. Participants were asked to identify elements, segments, and use verbal descriptions and performed reductions (generative simplifications). Common to Arab practice is detection of emblematic melodic figures, and differences in segmentation identification were found between European and Arabic participants. Both registered pauses and register changes, whilst the noted segmentation of modal changes (subtle) that went unnoticed to the Europeans. The segments show that Arabic modes go beyond a tuning system incorporating essential rhythmic and melodic configurations signifying the maqam. (Ayari, McAdams, 2003) Experimental studies in the last few decades have investigated expectancy in encoding, organizing and reacting to melodic content and tones. Meyer postulated that a piece of music in a given genre will evoke and generate expectancies – the violation of these expectancies is significant emotionally. The results showed that these musical expectancies are molded by rhythmic patterns, tonal and harmonic structures as well as melodic structures. (Meyer, 1956) This exemplifies why it can take time for artwork to become socially validated. This begs the question why, to an extent, a creation out of any cultural context may not be deemed valid to begin with, as social meaning is ingrained in the repetitions of life-long decoding of cultural 1) tuning/tonality systems 2) tonal-melodic-harmonic relation and 3) language/dialectic reinforcement. The lay-musician or casual listener identifies these patterns too, although perhaps to a lesser extent, and certainly this forms a large basis of understanding even for the professional musician in practice. Barucha furthers a distinction of schematic and veridical expectancy. Schematic is automatic expectancy generic from one’s culture, veridical musical expectancy hinges upon one’s cumulative musical experience. Barucha and Todd noted that listeners would often remain surprised by sequences of music already very familiar to them – knowledge of outcome did not seem to affect re-experience. (Ram, Moorman, 1999)

37 Just, Bohlen-Pierce scale, Wusta-Zalzal, Masonic ratios, 22 tone system of India, Ragas, Messiaen, Babbitt, Cage, Young, French Spectralists, 53TET, 19TET, Bagpipe tuning

The Bohlen-Pierce scale uses the 3:1 ratio (tritave, or octave + fifth) instead of 2:1, with 146.3 cents per step in the equal tempered (non-Just) temperament. From a 2:1 ratio perspective this scale is in 8.202087TET, and avoids octaves. ste Interv Cents Fundamental Just p al 0 30/13 0√3 0 1 1/1 = 1 1 31/13 13√3 146.3038434999154360 1.088182 27/25 = 1.08 2 32/13 6.5√3 292.6084616715978560 1.184140594988857 25/21 = 1.190476190476190480 3 33/13 13/3√3 438.9126925073971200 1.2885607692309613 9/7 = 1.285714285714285710 4 34/13 13/4√3 585.2169233431959990 1.4021889487005645 7/5 = 1.4 5 35/13 13/5√3 731.5211541789951190 1.5258371159564499 75/49 = 1.530612244897959180 6 36/13 13/6√3 877.8253850147942380 1.6603888560010867 5/3 = 1.6666666666666666 7 37/13 13/7√3 1,024.129615850593190 1.8068056703447524 9/5 = 1.8 8 38/13 13/8√3 1,170.433846686392260 1.9661338478579946 49/25 = 1.96 9 39/13 13/9√3 1,316.738077522191110 2.1395119415112758 15/7 = 2.142857142857142860 10 310/13 13/10√3 1,463.042308357990210 2.3281789044302967 7/3 = 2.33333333333333333 11 311/13 13/11√3 1,609.346539193789480 2.5334829434069275 63/25 = 2.52 12 312/13 13/12√3 1,755.650770029588340 2.7568911531325972 25/9 = 2.7777777777777777 13 313/13 13/13√3 1,901.955000865387420 3 2/1

Just and notables table:

Interv Ratio Cents Ratio Cents 12- Pythag Pythagore C e n t s f o r Notables al for For Just fundamen TET to orean an Pythagorean Just tal Just fundamen Just tal Uniso 1/1 0 1.0000 0 0 1/1 1.0000 0 n Min 25/24 70.67242 or 1.0416666 100 +11.73 256/24 1.0534979 Diatonic Chromatic semitone = 2nd or 111.731285 6 7 o r 3 o r 4 2 3 9 o r semitone / 113.685 16/15 26 1.0666666 2187/2 1.0678710 Limma (limit 7 048 9375 =90.2249956 5) 7 8 2 7 o r 113.6850060 5771 Maj 9/8 203.910001 1.125000 200 -3.91 9/8 Just 203.9100017 8/7 or 7/6 (limit 7) 2nd (limit 73 3 3) Min 6/5 315.641287 1.2000 300 -15.64 32/27 1.1851851 294.1349974 7/6 septimal min 3rd 3rd (limit 00 85 0384 OR 266.87090560374, 5) Wusta-Zalzal = 27/22 @ 354 cents, 16/13 in limit 13 38 Maj 5/4 386.313713 1.2500000 400 +13.68 81/64 1.265625 407.8200034 & 9/7 septimal maj 3rd (limit 86 0 628614 6155 3rd , 14/11 in limit 11, 5) 9/7 in limit 7 P 4 4/3 498.044999 1.3333333 500 +1.955 4/3 Just 498.0449991 11/8 in limit 11 or (limit 13 3 00087 3 551.31794236476 3) cents Triton 45/32 590.223715 1.4062500 600 +9.776 729/51 1.4238281 611.7300051 25/18 asymmetric Just e/dim or 7/5 5 9 o r 0 or 1.4 28441 2 25 9232 a n d 7 / 5 & 1 0 / 7 5 (limit 582.512192 or Septimal in 7) 60429 +17.49 l i m i t 7 , 1 0 / 7 = 617.48780739398 cents P 5 3/2 701.955000 1.5 700 - 3/2 Just 701.9650008 Wolf 5th = 678.49, (limit 86 1.9550 6 16/11 in limit 11 = 3) 0086 648.68205763524 cents Min 6 8/5 813.686286 1.60000 800 - 128/81 1.5802469 792.1799965 13/8 tridecimal 6th in (limit 13 13.686 or 1 3 5 8 o r 3 8 1 8 o r limit 13, 14/9 in limit 7 5) 28613 6561/4 1.6018066 815.6400069 = 764.91590473835 096 4063 285 cents, 11/7 in limit 11 Maj 6 5/3 884.358712 1.66667 900 +15.64 27/16 1.6875 905.8650025 18/11 undecimal 6th, or (limit 99 128701 9616 852.59205936602 5) cents Min 7 9/5 or 1017.59628 1.80000 1000 17.596 16/9 1.7777777 996.0899982 7/4 Septimal min 7th or 16/9 786594 or or 2878 or 77777777 6923 968.82590646912, (limit 996.089998 1.7777777 +3.910 16/9 symmetric Just , 3) 26923 78 00173 12/7 in limit 7 = 933.12909440059 cents, & 7/4 in limit 7 Maj 7 15/8 1088.26871 1.875 1100 +11.73 243/12 1.8984375 1109.775004 (limit 4 1286 8 32694 5) Octav 2/1 1200 1200 0 1200 e

21/1200, or the 1200th root of 2 is roughly 1 cent, or 1.0005777895. If n = cents then n = 1200 ·

n/1200 log2 (b/a). Further if a and cents n are known then b may be calculated: b = a x 2 . The human ear can discern a difference of 1Hz for sustained notes. A common major 6 th of C in equal temperament is 440.00 hz. (also 441hz) The wolf 5th is almost a ¼ tone flatter than a P5 and thus placing it between a tritone and P5. The Wusta-Zalzal is 27/22 or 1.22727272727272 or 354.54706023141 cents putting it between a minor 3rd and major 3rd. If limits 3, 5, 7, 11, and 13 are graphed against any equal temperament it can be seen that rarely do all 12 chromatic equal tempered notes fall very near limit tuning, while falling nearer ET the higher the equal tempered divisions are, as in 53-TET and 72-TET - which are still

39 slightly out by a few cents. Limit 3 and 5 forms Just intonation. The most common equal temperaments are: 5, 7, 12, 19, 22, 24, 31, 34, 41, 53, 72.64 The differences of the old Masonic ratios are as follows, and can be viewed as d/t = speed. (Sfakianakis, n.d.)65 Re/do = 9/8: 1 = 9/8 9/8=1.125 Mi/re = 10/8 : 9/8 =10/9 10/8=1.25 1.25/1.125=1.1111 or 10/9 Fa/mi = 4/3 : 10/8 = 16/15 4/3=1.33333 1.33333/1.25=1.06666 or 16/15 So/fa = 3/2 : 4/3 = 9/8 3/2=1.5 1.5/1.33333=1.125 or 9/8 La/sol = 5/3 : 3/2 = 10/9 5/3=1.66666 1.66666/1.5=1.11111 or 10/9 Si/la = 15/8 : 5/3 = 9/8 15/8=1.875 5/3=1.66666 1.875/1.66666=1.125 or 9/8 Do/si = 16/8 : 15/8 = 16/15 16/8=2 2/1.875=1.06666 or 16/15

Comparative Table 1:

Interval 12-TET 12- Just Pythagorean 19-TET 53-TET 53-TET Scottish Indian TET Unison 20/12=1 0 0 0 0 20/53= 1 0 0 0 Min 21/12=12√2 100 7 0 . 6 7 2 4 2 o r 90.22499567827 63.158 24/53= 53/4√2 99.99957691 29.850 9 0 o r 2nd 111.73128526 or 0310416400 112 113.68500605771 Maj 22/12=6√2 200 203.91000173 203.91000173 189.474 29/53= 63/9√2 203.7735345 187.682 203 2nd 7914678100 Min 3rd 23/12=4√2 300 315.64128700 294.13499740384 315.789 213/53= 294.3394160 256.597 294 or 53/13√2 6292929500 316 Maj 3rd 24/12=3√2 400 386.31371386 407.82000346155 378.947 217/53= 384.9055263 343.091 386 or 53/17√2 5548759900 407 P 4th 25/12=12√32 500 498.04499913 498.04499913 505.263 222/53= 498.1128243 493.957 498 53/22√2 0692445500 Aug 4th 26/12=√2 600 590.22371559 611.73000519232 568.421 226/53= 588.6791264 548.649 590 or or 53/26√2 9928285400 612 582.512192604 29 P 5 27/12=12√12 700 701.95500086 701.95500086538 694.737 231/53= 701.8866215 684.729 702 8 7418000 53/31√2 7910072000 Min 6th 28/12=3√2 800 813.68628613 792.17999653818 757.895 235/53= 792.4528009 729.879 792 or 53/35√2 3970148200 814 Maj 6th 29/12=4√8 900 884.35871299 905.86500259616 884.211 239/53= 883.0187369 871.949 884 or 53/39√2 7003403600 906

64 Purity of tritones (25/18 and 36/25) is controversial in 5-limit tuning, and 7-limit tuning gives the septimal tritone (7/5 and 10/7), 582.512 cents and 617.488 cents respectively. These two ratios are considered more consonant than 17/12 (603.000 cents) and 24/17 (597.000 cents) in 17-limit tuning, and closer to an equal-tempered value of 600.000 cents. The undecimal neutral 6th (18/11, 852.59 cents) and tridecimal nuetral 6th (13/8, 840.53 cents) are two of the three neutral 6ths – the last is the equal tempered (18/11, 850 cents). They are approximately a quarter-tone flat of 12-ET minor 6ths and a quarter-tone sharp of major 6ths. 65 Here a 2nd/root is similar to 5th/4th and 7th/6th @ 9/8. Similarly the 3rd/2nd and 6th/5th are @ 10/9 and 4th/3rd and 8ve/7th are @ 16/15. Two ratios are harmonic inverses of each other if they combine to make an octave. For example 3/2 x 4/3 = 2. (Enevoldsen, 2010)

40 Min 7th 210/12=6√32 1000 1017.59628786 996.08999826923 1010.526 244/53= 996.2263076 985.799 996 or 5 9 4 o r 53/44√2 2672999600 1017 996.089998269 23 Maj 7th 211/12=12√2 1100 1088.268714 1109.7750043269 1073.684 248/53= 1,086.79218 1049.363 1088 or 048 4 53/48√2 0595960150 1110 Octave 212/12=2 1200 1200 1200 1200 253/53=2 1200 1200 1200

The powers (of ) show the exact figures of 12TET. This chart shows the Indian and Pythagorean ratios to be the same, whilst the next chart shows the added 53TET notes for the full 22 shrutis. The 22 tone system of śrutis (‘tones’/microtones) used predominantly in heptatonic sets described by Bharata and Dattila, comparable to Western 12TET and 53TET makes a lot of sense in that if looked at from the perspective of 7 note modes based in a 12TET system, each note would have one of two inflections with the exception of the root and 5th. The table below illustrates the 10 notes with slight inflection (20 notes in all) plus the root and 5th, summing to 22 in total.66

22 tone system of India: Shrutis 12-TET 53-TET Name Ratio Cents Frequency Name Frequency Note Cents Frequency (Hz) Ksobhinī 1 0 261.6256 C 261.6256 0 261.6256 Tīvrā 256/243 90 275.6220 C# 277.1826 4 90.566037735849019100 223.44424 Kumudvatī 16/15 111.73 279.0673 5 113.207547169811002000 279.3053 Mandā 10/9 182 290.6951 D 293.6648 8 181.132075471698153000 290.4816 Chandovatī 9/8 203 294.3288 9 203.773584905660637000 294.3056 Dayāvatī 32/27 294 310.0747 D# 311.1270 13 294.339622641509454000 310.1114 Ranjanī 6/5 316 313.9507 14 311.111111111111024000 314.1937 Raktikā 5/4 386 327.0319 E 329.6275 17 384.905660377358421000 326.7661 Raudrī 81/64 407 331.1198 18 407.547169811320710000 331.0677 Krodhā 4/3 498 348.8341 F 349.2282 22 498.113207547169641000 348.8478 Vajrikā 27/20 519 353.1945 23 520.754716981132149000 353.4401 Prasāriṇī 45/32 590 367.9109 F# 369.9944 26 588.679245283018988000 367.5829

Prīti 729/512 612 372.5098 27 611.320754716981092000 372.4218

66 In , where there are two different ratios on the same note there is a difference of 81:80, the syntonic comma (21.51 cent diesis), which is one explanation of India’s 22-Śruti tonal system. The 13th swarasthana results in an octave: or x12 = 2. As x is the twelfth root of 2 we obtain a figure of 1.06, and Pa is a ratio of 1.498 instead of 1.5, and the trained musician is able to hear the difference. Carnatic music is based on rational division. (Sriram, 1990) Higher degrees of harmony are associated with ratios with powers of 2 (2:1, 4:1, 8:1…) as well as small integers (like 3:2 which is easily identified by the ear).

41 Mārjanī 3/2 702 392.4383 G 391.9954 31 701.886792452830232000 392.4229 Ksiti 128/81 792 413.4330 G# 415.3047 35 792.452830188679375000 413.4982 Raktā 8/5 814 418.6009 36 815.094339622641527000 418.9415 Sandīpanī 5/3 884 436.0426 A 440.0000 39 883.018867924528173000 435.7053 Ālāpinī 27/16 906 441.4931 40 905.660377358490696000 441.441 Madantī 16/9 996 465.1121 A# 466.1638 44 996.226415094339526000 465.1488 Rohinī 9/5 1017 470.9260 45 1,018.86792452830176000 471.2721 0 Ramyā 15/8 1088 490.5479 B 493.8833 48 1,086.79245283018860000 490.1298 0 Ugrā 243/128 1110 496.6798 49 1,109.43396226415078000 496.582 0 Ksobhinī 2 1200 523.2511 C 523.2511 53 1200 523.2512

Ragas may be comparable to 12-tone technique in the sense that ragas use re-ordering of motifs instead of partitioning of pitch classes as in serialism, the main difference is in transposition. The sage Matanga defines swara (tone) as ‘that which shines by itself.’ Individual tones are embellished using Gamakas, which translates as ornaments which are melodically more involved than simple ornamental devices external to melody, having values which are assigned to specific notes for example, and have ‘structural relationship with the , with volume, pitch and timbral inflection and structural functionality foreign to Schoenberg’s tonal world-view. The tala indicates the timing - employment of rhythmic stresses, and influenced Messiaen. However, ’s use of operators to influence rhythmic structure after the late 1940’s is unrelated to the tala and is independently a part of Western music. (Wen-chung, 1971) Gamaka comes from the Sanskrit gam, to move, leading through the spaces between scale tones and illuminating the microtones. Gjerdingen described Seeger’s melographs of Carnatic music thus: ‘if we conceive of movement as a primary phenomenon, then the notes and rhythms become secondary phenomena.’ (Battey, 2004) This idea corresponds to modernist coherence and to Romantic gestalten (shape, form) as the sum over parts. Amelia Cuni performs vocal microtones with precision and emotion on Amelia Cuni – John Cage Solo For Voice 58: 18 Microtonal Ragas. Cage employs stochastic elements to generate chance for the ragas. Cuni uses 20 years of study and performance of dhrupad vocalism in a new context enabling her to ‘step back’ from traditional raga, and connect with her Western origins, broadening musical vocabulary. In Cuni’s opinion, Cage connected the 18 microtonal ragas to ‘their original meaning, without relying on traditional only, but providing strategies to free their innate generative power…effective even in a de-contextualised framework…that is an

42 eclectic compendium of compositional techniques relating to music and theatre as well . . .’. 67,68 (Cuni, 2011)

The 53TET frequencies69 are very close to the Shruti (22) system. 53TET is compatible with syntonic and schismatic temperaments, and is arguably close to Just tuning in limit 5. The 53√2=1.0131641430249148. intervals 53TET power Fundamental cents 1 1 0 2 53√2 1.0131641430249148 22.641509433962421300 3 53/2√2 1.0265015807114097 45.283018867924314500 4 53/3√2 1.040014594335196 67.924528301887034400 5 53/4√2 1.053705495203023 90.566037735849019100 6 53/5√2 1.067576625048014 113.207547169811002000 7 53/6√2 1.081630356430202 135.849056603773589000 8 53/7√2 1.0958690931423387 158.490566037735927000 9 53/8√2 1.110295270621048 181.132075471698153000 10 53/9√2 1.12491135636339 203.773584905660637000

11 53/10√2 1.1397198503489083 226.415094339622652000 12 53/11√2 1.1547232854672358 249.056603773585042000 13 53/12√2 1.1699242279513258 271.698113207547147000 14 53/13√2 1.18532527781639 294.339622641509454000 15 53/14√2 1.19686402614609 311.111111111111024000 16 53/15√2 1.2167382713357153 339.622641509433932000

17 53/16√2 1.2327555879634662 362.264150943396286000 18 53/17√2 1.24898375883818 384.905660377358421000 19 53/18√2 1.2654255596753214 407.547169811320710000

67 Legend goes that the first singer of Indian antiquity, Tumburu, tonally expanded the Samaveda chant from a pentatonic chord to six or seven pitches. Knowledge of that style suggests it was originally a pre-filled pentachord and not pentatonic collection, and excavations in the Indus valley recovered lyre-type seven string instruments validating the description of the archaic vina. Historian William Hunter estimates that pitch names (swaras) of the set (Sa Ri Ga Ma Pa Dha Ni) were already prevalent during the time of the Sanskrit grammarian Pānini in the 4th century B.C. Concrete evidence occurs later around A.D. 100-500 in the Nātyaśāstra, yet passages contained therein refer to more ancient practice. (Gauldin, 1983) This system differs from Western 22-TET. 68 Cage thought that a recording ‘destroys one’s need for real music. It substitutes artificial music for real music, and it makes people think that they’re engaging in a musical activity…’ (Haskins, 2010) This is an interesting point to note in terms of what music and musical practices are, how they are created (performed/composed), and heard (as noise, veridical expression or schematic frameworks) – and perhaps listening to recordings do not engage but reflect, as in watching a television program or looking at a picture. Reflection may be a form of after-engagement – although after-engagements before technological mediums were committed to memory and notation, aiding musical memory and language, etymologies, semantics, and contextual bases culturally, imaginatively, and scientifically. Music itself encompasses vastly different genres under performance (composition), from hypnotic to meditative, scientific to cultural, synthetic to organic, calculated to aesthetical. A picture can be a personal memory, like a performance, or a connection with schematic and veridical history and cultural identity – but the concept of a remembrance (recording) being part of a new experience (veridical) is also considerable. These are important factors to address in the practice of musical arts, including microtonal practices. 69 It is further believed that 53TET may be used pivotally in temperament modulation, known as dynamic tonality, as in for example shifting maqamat, or in Western terms micro-tonal modal interchange. 43 20 53/19√2 1.2820838027302701 430.188679245283011000 21 53/20√2 1.298961337279338 452.830188679245396000 22 53/21√2 1.3160610501071177 475.471698113207688000 23 53/22√2 1.333385866000247 498.113207547169641000 24 53/23√2 1.3509387482476742 520.754716981132149000 25 53/24√2 1.3687226991475057 543.396226415094253000 26 53/25√2 1.3867407605205309 566.037735849056680000 27 53/26√2 1.4049960142305022 588.679245283018988000 28 53/27√2 1.4234915827112675 611.320754716981092000 29 53/28√2 1.442230629500841 633.962264150943560000 30 53/29√2 1.4612163597825027 656.603773584905652000 31 53/30√2 1.4804520209330247 679.245283018867807000 32 53/31√2 1.4999409030781112 701.886792452830232000 33 53/32√2 1.5196863396551512 724.528301886792513000 34 53/33√2 1.5396917079833807 747.169811320754752000 35 53/34√2 1.559960429841549 769.811320754716866000 36 53/35√2 1.5804959720531908 792.452830188679375000 37 53/36√2 1.6013018470796005 815.094339622641527000 38 53/37√2 1.6223816136206164 837.735849056603726000 39 53/38√2 1.6437388772233101 860.377358490565983000 40 53/39√2 1.6653772908986904 883.018867924528173000 41 53/40√2 1.687300555746526 905.660377358490696000 42 53/41√2 1.7095124215883912 928.301886792452818000 43 53/42√2 1.732016687609049 950.943396226415010000 44 53/43√2 1.7548172030062736 973.584905660377334000 45 53/44√2 1.7779178676492289 996.226415094339526000 46 53/45√2 1.8013226327455147 1,018.867924528301760000 47 53/46√2 1.8250355015169928 1,041.509433962264250000 48 53/47√2 1.8490605298845093 1,064.150943396226390000 49 53/48√2 1.8734018271616335 1,086.792452830188600000 50 53/49√2 1.8980635567575257 1,109.433962264150780000 51 53/50√2 1.9230499368890601 1,132.075471698113060000 52 53/51√2 1.948365241302321 1,154.716981132075420000 53 53/52√2 1.9740138000035974 1,177.358490566037850000 54 53/53√2 2 1200

19 Tone Equal Temperament:70 Degree Interval Cents Fundamental Note Closes Difference Name to Just to Just in interva cents l 1 0 1 A 1/1 0 Unison 2 19√2 63.15789473684 1.0371550444 A# 36/35 +14.388 1/4-tone, septimal diesis 1961400 461919 3 19/2√2 126.3157894736 1.0756905862 Bb 15/14 +6.873 major diatonic semitone 84091000 201824

70 19 Tone Equal Temperament makes sense as it contains a ¼-tone (septimal diesis), major diatonic semitone, a minor whole tone, septimal minor third, a minor third, major third, septimal major third, perfect fourth, a septimal and Euler’s tritone, a perfect fifth, septimal , minor sixth, , septimal major sixth, Just , classic , and septimal diesis – octave; which are approximate to Just intonation in cents by roughly +/-0.148 to +/-14.585. 44 4 19/3√2 189.4736842105 1.1156579177 B 10/9 +7.070 minor whole tone 26522000 615438 5 19/4√2 252.6315789473 1.1571102372 B#//Cb 7/6 -14.239 septimal minor third 68383000 827198 6 19/5√2 315.7894736842 1.2001027195 C 6/5 +0.148 minor third 10474000 78103 7 19/6√2 378.9473684210 1.2446925894 C# 5/4 -7.367 major third 52587000 640233 8 19/7√2 442.1052631578 1.2909391979 Db 9/7 +7.021 septimal major third 94853000 47405 9 19/8√2 505.2631578947 1.3389041012 D 4/3 +7.376 perfect fourth 36871000 244722 10 19/9√2 568.4210526315 1.3886511426 D# 7/5 -14.092 septimal tritone 78978000 146562 11 19/10√2 631.5789473684 1.4402465375 Eb 10/7 -14.091 Euler's tritone 21038000 38759 12 19/11√2 694.7368421052 1.4937589616 E 3/2 -7.218 perfect fifth 63137000 544857 13 19/12√2 757.8947368421 1.5492596422 E#/Fb 14/9 -7.021 septimal minor sixth 05346000 666558 14 19/13√2 821.0526315789 1.6068224531 F 8/5 +7.366 minor sixth 47567000 33765 15 19/14√2 884.2105263157 1.6665240127 F# 5/3 -0.148 major sixth 89383000 97089 16 19/15√2 947.3684210526 1.7284437865 Gb 12/7 +14.238 septimal major sixth 31625000 632112 17 19/16√2 1,010.52631578 1.7926641922 G 9/5 -7.070 Just minor seventh 9473650000 757116 18 19/17√2 1,073.68421052 1.8592707100 G# 15/8 -14.585 classic major seventh 6315920000 168127 19 19/18√2 1,136.84210526 1.9283519958 Ab 35/18 -14.388 octave - septimal diesis 3157930000 849902

Degree 20 would be note A, completing 1200 cents. The intervals in 19TET ascend in pitch by 63 cents.71 Lindström and Wifstrand created a program that could write in 19TET and import from 12TET, finding that people preferred 12TET over 19TET with the exception that the minor 3rd was preferred in 19TET. (Lindström and Wifstrand, 2012)

Bagpipe tuning gives very interesting ratios: Degree Interval Cents 1 1/1 0 2 117/115 29.850 3 146/131 187.682 71Joseph Yasser and have written music in 19EDO. Mandelbaum’s doctoral thesis explains why he thinks 19TET is the really only practically viable system between 12 and 24, and that the next one on is 31 equal temperament. 45 4 196/169 256.597 5 89/73 343.091 6 141/106 493.957 7 81/59 548.649 8 150/101 684.729 9 125/82 729.879 10 139/84 871.949 11 205/116 985.799 12 11/672 1049.363

Joe Heaney uses a ‘waver’ on certain notes, a device like an appogiatura or unstable flutter and not as fast as vibrato yet faster than a roll, which he places on 4 th and 7th degrees on ascending and with a technique of variation. Notation simply marks their place and does not signify what they sound like.73 (Williams, 2004) In Ferneyhough’s Renvoi/ Shards for quarter-tone guitar and quarter-tone vibraphone, which incorporates microtonal techniques in the pitch and time domain,74 there is atonality, change of time signatures cycling throughout, glissandi, dynamic change, artificial harmonics, half sharps/flats which seem aleotoric – which is in stark contrast to tonality and tonal systems in Western styles in previous centuries. If anything, it would be similar aesthetically to some Chinese musics or certain Nile (Egypt) or Tibetan musics.75 (Incipitsify, 2012) Somewhat akin to , the French Spectralists, or starting in the 1970’s, used of sounds and expanded them out over a symphonic composition that employed microtonality. The French serialists expanded into 24TET and microtonal serialism. Franco-American composer Rudhyar’s ideas are similar to Varèse’s of psychic power, indeed Varèse’s ideas that music was ‘organized sound’ and that sound was ‘living matter’ were of historic import, 76 and parallels the Chinese idea that a tone is an entity unto itself, with the further perplexing concept that the meaning lies within the tones: that is, deeper into the music. As a fundamental feature of Asian music this idea involves a vocabulary of articulations, timbre, inflections, and intensity fluctuations. The importance of the single tones themselves is the

72 Note. 11/6 is a 21/4-tone, undecimal neutral seventh. (microtonal-synthesis.com) 73 The glottal stop used by many male sean-nós singers is a throat technique of stopping the air which draws attention to the line, and an echo effect is created of the word just before the break 74 Pitch/time=speed as frequency/time=length, or notes/bar=bpm. Hence, to work out the speed of a song one must divide the amount of notes/pulses in the spectrum of one bar/measure to obtain the ratio or beats per minute (bpm). It is interesting to note the relation between speed and distance, as it is this function that traces the curve between point and wave (rhythm and pitch). This can be useful in music and can have microtonal outcomes in pitch- frequency as well as timing. 75 It is in stark contrast to Tchaikovsky, Rimsky-Korsakov, Copeland, Bernstein or Prokofiev, whose stylistics were directly delineated from post 1730 (or earlier) aesthetics. Minimalism in the 60's, starting with La Monte Young, used microtonality 76 This corresponds with semiotic theory whereby sign and symbols represent the specific (logic) and context and forms represent the generic, allegory (creative). 46 antithesis of Western polyphonic composition, whereby multi-linear harmony and equal temperament undermine these values to an extent - these ideas are subordinate. Since Varèse this idea is now common and a hallmark of .77 Varèse was more concerned with complex structures of developing sound (tones) over single line development. There are striking similarities in his works to Asian musics, for example in the opening of Intègrales and the ha movement of tagaku (Japanese court) style composition: the ryuteki (transverse flute) and hichiriki (double reed) is similar to the E-flat and and conveys the nuclear ideas linearly. The sho (mouth organ) is similar to the B-flat clarinet and piccolos contributing to upper registers. The koto (movable-bridged zither) and () use lower sonorities as do the . Both Togaku and Varèse use a adding a fourth dimensional texture and moving with specific timbre, register and function related to the material. (Wen-Chung,78 1971)

Midi, scale perception, semiotics, notation, re-creation, Turkish, Eskimo, Indonesian Slendro in 5TET (Salendro), Thai 7TET

Midi tuning and Western instruments are dominated by equal temperament (except fretless strings, voice and harps/zithers), where tuning is slightly out to accommodate the ability to play in all 12 keys. Real-time processing, in today’s systems for pitch related functions, including the ability to extend into other tuning systems, is becoming more widespread. Keyboards are well suited to and historically based microtonal keyboards may serves as models. Midi keyboards in live performance, using arbitrary tuning systems, and free from the restrictions of the studio, would have the exciting intricacies and nuances of live human performance. (Keislar, 1987) Perception lies at the heart of music, and paradoxes remain central to music, art and literature. In 1986, in Music Perception, Dr. Diana Deutsch described her tritone paradox she discovered regarding two notes linked by a tritone. When successively played one after the other some will hear an ascending pattern, whilst others hear it descending – an experience which can be

77 Some of Varèse’s work, like Arcana, use the idée fix, made well known by Berlioz’s Symphonie fantastique, and usually not transposed. Lietmotiv, used by Wagner, however, is transposable. 78 Wen-Chung, as well as Tenney, McPhee and others, was a student of Varèse. 47 ‘particularly astonishing’ to experienced musicians. Tonally, tritones play an important part in evolving music.79 Another paradox described by Dr. Deutch in Musical Illusions and Paradoxes (1995) is the glissando illusion.80 Scale pattern: two lines, left ear and right ear, played simultaneously,

&=Y=S=W=U,===U=W=S=Y! &=R=X=T=V,===V=T=X=R!  and the perceived scale81, left and right ears.

&=R=S=T=U=V=W=X=Y! &=Y=X=W=V=U=T=S=R=! 

Semiotics and a plethora of signs and communicative symbology may be utilized in composition. The Phoenicians had managed the semiotic transition from syllabic to alphabetic c.1500 BC, and possibly may have advanced by the Common Era. There is

79 A listener may hear C followed by F# as descending, and as a different tone pair is played, for example G# then D, it seems to ascend – while another listener may hear them the other way about. This is due to the timbre, partials, artifacts and inflections that make up the sound structure, just as one may sometimes hear a singer seem to sing up an octave for some moments and realize the illusion.This idea of how we perceive information is akin to Ingo Swann’s idea that there are levels of senses that can access information ‘achieving perception appropriate to them’. Anthropologists estimate that pre-modern human societies did not ‘think in terms of senses’ as Swann puts it. (Swann, 1994) 80 Glissando’s are a facet of microtonality and thus will be given a brief mention here. An plays a tone and a sine wave ‘glides’ up and down in frequency (pitch), and these are switched (panned) left to right repeatedly in a manner that whenever the oboe is on the left, for example, a portion of the glissando is on the opposite right, and vice versa. On stereophonically separate speakers some illusions are produced. The oboe is rightly heard jumping from left to right ear, whereas the glissando seems ‘joined’ together, and the human ear will localize the glissando in ‘a variety of ways.’ Right-handers often hear it going left to right as the pitch goes from low to high, and right to left as the pitch goes from high to low. Yet, lefthanders often gain completely different illusions altogether. Dr. Deutch describes other paradoxes and illusions. The last I shall mention which would be a good setting in a microtonal context for future purposes is the Scale illusion (1973). The top is on the right speaker/ear and bottom is on the left. What effect would be produced if there were glissando marks in between notes in the following passages? Might it not accentuate the paradox more clearly? 81 Microtonal music would require more musical thinking, though certainly 24-TET for example should be a natural extension of 12-TET, and any other systems would use the same parts of the brain to recognize pitch and remember pitch group sequences, making it commonly practicable, especially with cultural support. The notation of half sharps and flats may also approximate other tonal systems well, as chromatic 12TET notation may approximate Just intonation. 48 great similarity in the Jewish cantillation (pitch marks to speech) notational system and Ethiopian – the link extends to musical symbols in Syrian and Armenian, whilst the Egyptian has faded to oral tradition. Fellasha communities in Ethiopa still practice ecumenical vocal chants in Hebrew with melismatic vibratos and microtonal slides before and after main tonal syllables. (Kebede, 1980) Pining for systematic efficiency in communicative symbol logistics in the deep array of microtonal notational stylistics, Read states that the notation of Penderecki is ‘commendable’ and Hàba is ’guilty of using different symbology for the same microtonal intervals in several of his works.’ Read’s cataloging in this regard exemplifies the stylistic aesthetical logic that bridges inspired creativity with communicable scoring. (Polansky, 1991) Polansky argues that many composers feel bound by the12-tone canon and the generic use of the ‘microtonal’ in which say a septimal major 2nd (8/7) which is larger than the12-equal-tempered 2nd is simply not microtonal per se, but are part of ratio systems implemented into the divisibility of the octave. Pioneer microtonalists like Partch, Carillo and Hàba82 were as diverse as they were stubborn – composers tend to cling to a personal developed style of notation and there is some contention over what the field should be called at all. Polanski argues that the 150-200 year tenor of 12-tone equal temperament is microtonal as much as any other system since the Greeks, and that it is tenuous as an absolute since its short inception and life, with suspect respectability in European and American art musics. Ben Johnston goes so far as to assert that 12-tone equal temperament is a lie – that the human ear does not naturally hear these ratios, and whatever advantages of 12-TET may be it has also seduced us into believing it the only way.83 There is also a link between microtonalism and indeterminacy in Johnston’s works. (Rapoport, 1988) Schenkerian note-to-note analysis can predict shape for non-Western musics, although the criticism from the ethnomusicology bloc is that Schenkerian notation cannot cope with timbral variations and non-Western temperaments, microtones or slides which may be key musically. (Stock, 1993) Influenced by geo- and politico-historicity, west coast America served as locale for microtonists including Cowell, Cage, McPhee, Harrison, and Hovhaness. It includes an Asian

82 Hàba commissioned specialized quarter- and sixth-tone instruments (trumpets, pianos, ). 83 For over 40 years Johnston investigated rational pitch structures and tried to forward its practice in performance. The St. Louis Symphony’s antagonism for Johnston’s Quintet for Groups stemmed from a performance fiasco, yet performers investing time achieve good results as in the Fine Arts Quartet’s recording of his Fourth String Quartet. Johnston had some quirks such as foreshadowing of microtones by double flats in one early work – somewhat akin to the triple sharp in Alkan’s Qausi-Foust. 49 and African population with a history of commerce unbound by politico-acculturation with rising ethnomusicological study (Asian composers and musicians). Prior to this, Carpenter and Griffes leaned toward orientalism via . Rudyar’s idea of a note as a ‘living entity’ was comparable to the idea that in Asian music one is ‘confronted with living tones’.84

Indonesian Slendro in 5TET (Salendro) Interva 1 2 3 4 5 6 l Cents 0 240 480 720 960 1200

Thai 7TET Interva 1 2 3 4 5 6 7 8 l Cents 0 171.428571 342.857142 514.285714 685.714285 857.142857 1,028.57142 1200 428571429 857142858 285714287 714285716 142857145 857142857

Murman-Hall, Ozgen and Lux Musica performed works by the 17th century Moldovian Demetrius Cantemir who lived in Istanbul from 1687-1710.85 Scholars have not attempted to recreate the musical practices from that time, preferring to gain insight into the Ottoman court’s musical life, yet these skillful musicians attempt the former. These cross-cultural performances fuse traditional and non-traditional styles resulting in hybrid styles that have particular emphasis on early music. The performances (recordings) combine Turkish and non-Turkish with historic European-type renderings of that period’s Ottoman music. The musicians also perform new works reflective of Cantemir’s compositions and improvisations, experimentally placing monophonic tradition into a polyphonic frame. The musicians are less comfortable interpreting non-Western pieces and there is clash of tonality due to the intonation systems of the instruments, especially in passages where fixed pitch instruments accompany microtonal makam

84 Rudyar, the Scriabin influenced Franco-American, was heavily influenced by Eastern philosophy and mysticism, claiming that Western composers were not interested in the audible single tones but more on pitch relation. This is consistent with Russolo’s ideas, and throughout minimalism and noise-art. Edward MacDowell and others had surmised earlier an oriental idea of value in texture but, misconstrued it as sound without music, and is still at the heart of misunderstanding Asian music as well as contemporary music today. Eichheim traveled and collected instruments, though insincerity to his endeavors and research in the music field led to only a few crude works. 85 Featuring pieces from all over the Ottoman Empire like Moldovian dances such as syrba and zhok de nante, and Turkish like prsrev and saz semaisi, and stylistics drawn from his treatise Edvar. Using Western instruments (viols, , flutes, keyboards) and adaptation of Turkish instruments (kemence, kudum, tanbor) they however do not utilize for example Western instruments like the d’amore or non-Western’s such as the .A new instrument called the kemence is used and the classical tanbor. Lux Musica uses a more usual modal heterophony for harmonization already in high use in Turkish art music, for example the delayed heterophonic patterns combined with pedal tones often in parallel intervals. 50 intervals set apart from equal-temperament, such as makam Bestenigar. However some like Nihavend [close to minor, as Rast is to major] work well due to the close relation in tonality and . (O’connell, 2006) Many of the circumpolar Eskimo musics have been effected over time by the West, for example in Greenland, where ancient complex compositions comprising microtones and subtle inflections and interesting rhythmic structures in 5/8 or 7/8, only practiced by a handful now, have given way to the copying of bland western folk formats.86 American Indian and Paleosiberian elements are found in North and West Greenland. Vocables and a compact song are used in Alaska and Siberia, and in Greenland and East Canada a dual call and response (refrain-chorus) is used. Tetronics and pentatonics are used in Greenland and Alaska, although the Copper Eskimos use chromatics, hexatonics, and heptatonics, and all use microtones.87 Eskimo music abounds with microtonal accents and embellishments connected to certain contexts which affect meaning, and glissandi are also used. Westwards of the Copper Eskimos, abrupt tonal centre change occurs. The melodies are usually arch-shaped, with call and response. In Alaska the 2nd lowest note is repeated or prolonged, and the descent of the arched melody slows. In the West intervals greater than an octave can occur, whilst lesser leaps occur in the East (Siberia) of a 4th or 5th. Melodies often have ascending and descending 4ths.88 (Johnston, 1975)

86 Missionization early on (Moravian, Anglican, Catholic) affected communal musical practice. The acquisition of boats for cod liver oil from shark fishing and the decline in seal hunting effected its associated songs, and later in Alaska socio-politics brought change, for example the need for hunting songs disappeared. In Alaska, where contact between Whites and Eskimos is newer than Greenland, it is thought that musical compartmentalization occurs. 87Pentatonics prevail in Alaska and Siberia. Alaskan and Greenlandic tonal range in song is about a 5th or 6th, except a 10th or 12th in the case of the Copper Eskimos; Alaska and Siberia have a range of about a 5th or 6th. 88Copper music plays between two tonal centres. Ethnic symbols like traditional music were forbidden under the old Soviet regime - the hunters and deer herdsmen of Thule and Angmagssalik in Siberia knew nothing of the more free- style expressive song of the West Eskimo, and Alaskan Eskimo music which was influenced from Siberia and the closer American Indian city civilizations enjoys many exciting prospects such as the pan-Canadian Eskimo Northern Games. 51 Xibeifeng, Xenakis stochastic emulator, fretboards and the 12th root of 2, world Fusion, evolving timbral domain, microtonality and after the fact of performance, societal technological status, cultural and logical outset, and aesthetical artistic nuance

Xibeifeng in the 1980’s blew the lid off things, ‘the North West Wind’ inspired by Shaanxi folk with rough vocals, rock instrumentation and beats, arcane melodies (with microtonal inflections), Turkish instruments, drones and pitch ornaments (arabesques).89 (Huang, 2001) Exploration of microtones in Xenakis' stochastic Metastasi s is explored well in the visual Xenakis-Emulator and a 48 tone system is employed, though it is not clear what the intonation system is. Glissandi within the composition is defined extraordinarily.90 (Kammerbauer, 2009) The divisor of standard equal tempered guitar placement used by all but a vanishing few makers is 17.817152 arrived at from the logarithmic function the 12th root of 2 (1.0594631), resulting in the octave or 12th fret at exactly the center of the total length. (truetemperament.com) The equation in April 2013 of Premier Guitar showed that longer string scale length gives higher tension. Longer scale with greater tension increases upper harmonics, whilst low notes are described as more articulate and defined. (Hoepfinger, 2013) One of the main factors to consider in how practical applications incorporating microtonality will be achieved in the future, in light of past practices, is the growing amount of reliance on technology in problem solving. Past practices are only beginning the process of factoring in from modern technology. Theoretically the limits to practical music making would seem endless aided by technology – yet at the same time as endless without specific technologies.91 Notably, in popular context, the marketplace is bridging genres. These genre- fusions incorporate application of musical understanding and tonality and may be regionally specific. Musics are being made continually with the aid of technological and human innovation which also brings a new lexicon with each generation.92

89The Shaoshu Minzu, minority peoples of the North West are Mongols, Kazaks, Hui, Uighurs, which call to mind the 'exotic other' in Han China – a place of crossings and possibilities. 90 It is based on Xenakis’ strip windows facade design on the monastery La Tourette, and is truly an innovative exploration of microtonal relationship as well as the placement in time of notes. 91 Sonic art, where music is more like a 3D painting than imaginable now, may be a field on the horizon and may have an integral performance factor. However, in many respects most things have not changed drastically in regard to physical performance of music except when the instrument is distinctly from the modern computer age. 92 Due to information efficiency and capital flows we now have such cross-cultural genres as Czech bluegrass, Indonesian rap, Japanese salsa, South Asian reggae and Afropop, as well as American shakuhachi or mrdangam players, Chinese lieder, and performing with Tibetan monks. 52 Schoenberg may have rejected microtonal experimentation because the time was not yet ripe: ‘whenever the ear and imagination have matured enough for such music the scale and the instruments will all at once be available. It is certain that this movement is now afoot, certain that it will lead to something.’ (Perlman, 1994) Many non-Western musics have evolving timbral non-pitch and time domains which Bret Battey calls pitch continuum traditions, outside the musical expression via the scalar and metric pitch lattice. Technology tools today are highly focused on pitch and time musical expression as opposed to pitch continuum, or timbral-shifting, musicality.93 Battey has written prototype noncommercial software for personal composition that uses bezier-spline programming to manipulate the microtonal pitch-time domain that is currently not easily possible to date. In the future this type of powerful programming seen in applications like Photoshop and visual effects software may be incorporated graphically into music software for synthesis.94 (Batty, 2004) Contemporary film musics (e.g. Morricone, Rahman) borrow from past and current tonal systems, sometimes with borrowing from alternate tonal systems in (modulation) passages (i.e. written in multi-cultural styles). It is important to note the amount of microtonality going into the modern production of music.95 Effects use can be like the writing of a symphony and have become very complex: equalization of tracks is microtonal alteration. One difference between past practices with microtonality compared with today’s is that microtonality on recordings can be added after the fact of performance. In the east Levantine, like Turkey and the Nile, music is still written and performed with microtones. In film music, distinct aesthetic world tonalities are becoming more fused. Any patterns emerging from microtonality, including tonal systems and socio-historically rooted aesthetics, carry the trappings of societal technological status, cultural and logical outset, and aesthetical artistic nuance, and is often slowly changing and built on previous works. Ethics, philosophies and values are connected to early performers of music as well as today’s, along with techniques and stylistics despite cultural change by cross-pollination of thought and ideas. The fact that fused- microtonal musics are increasingly more commonplace suggests a departure from standard pitch and rhythmic based musics, and as more emphasis is passed from

93 Pitch continuum may be explored in any musical segment such as the Carnatic alap – an unmetered part where the raag is explored. 94Battey says, ‘Picacs can render pitch, amplitude and spectral centroid bezlists into breakpoints for envelopes.’ The software was created originally to write Hindustani music. 95 Much of this microtonal post-production is subtle, although also a front piece to modern music. As timbre is explored more, pitch and time may become secondary and subliminal.

53 the compositional to production there appears a link to new styles of production as a compositional form in which non-pitch and rhythmic facets are factored in, like timbral elements, via use of sophisticated plug-ins (i.e. the plug-ins may be used like an instrument). Here we have two important links: the first of musical trends out of simpler pitch and time bases via multi and microtonal synthesis or means (e.g. stochastical, non-linear or linear), and second, composition linked to production whereby the two become analogous. On one hand we have , where a musical line is split into several instruments to colour timbre, discussed by Schoenberg as timbre-structures and also called Pointillism, as well as Schoenberg and Webern’s idea of emancipation of dissonance where the ear becomes accustomed to dissonance in context. If we think about noise music we see that these ideas have been brought forth and used microtonally and timbrally through use of sophisticated software and equipment that use many of the same classic principles. The key is context, even if multi-timbral and multi and microtonal systems are in use (e.g. repetition for contexts). Just as triadic music was [debatably] distinct after the 1400s and as the chordal 7 th was to the 1600s, as the chordal 9th was indicative of 1750’s and the whole-tone scale was of 1880, so too is chromaticism, microtonality and twelve-tone technique a feature of the 20th century. However, microtonality is deeply rooted in the past, though not under the same guise of 12TET or 24TET standardization. Today production/compositional softwares96 help define new music through multi-faceted contexts. The exception to the developmental direction may lie in stochastic musics (Xenakis, Cage, where microtonality and multi-timbres take place though are hard to notate for re-creation. However, in the future even this may be possible. Rossolo had defined and performed early noise music as an aesthetically viable art-form.97

96 A main factor between past microtonal practices and modern practices lies in the realm of technology. In a performance of a hundred simultaneous recordings at different speeds it would be hard to discern signals from noise – brief patterns and colours of perceived non-randomness may be attributed and strung together via pitch, timbre and time by the mind. These patterns may be so subtle and compounded amongst other tones and frequencies that imagination may alter the performance for each listener, and pareidolia might occur. Equalization morphs timbral, pitch and perception of rhythmic structures, and new musical dimensions are accessed via technology. Roger Penrose believes there may be quantum computation in human brain microtubules, effectively bringing up the question, can humans achieve sonically what standard computers are able to achieve today by non-technological means? That is to say, could we have achieved similar results to computer aided soundtracks, if computers never existed? With specialized instruments and enough time, I believe we could come close. Perhaps the best composers, conductors and performers can approximate, and even allude to standard sounds from modern genres like Glitch, Drum and Bass, and House. Non-algorithmic processes imply non-computability brain functions that are not random or deterministic. Penrose attributes this idea to thought and consciousness, because of the suggestion that objective reduction and quantum computation might be linked to consciousness. (Hameroff, 1998) 97 2,400 years ago Plato said ‘I would teach children music, physics, and philosophy; but more importantly music; for in the patterns of music and all the arts are the key to learning.’ 54 Conclusion, truth in music, modality of believing, dynamic tonality, Third-stream music, sound painting, new directions

In A Theory of Musical Semiotics there is a chapter entitled On the Truth in Music (or what Schoenberg and Asafiev said about the Modality of Believing). It states that the effect of believing, persuasiveness, and convincingness is imperative to any musical communication as well as the semiotics of spectacles, outlining its role in past music crisis and change. This would hold true in microtonality as well. Michael Foucault, on considering epistemes, thought that quotients of epistemology could alter historical development, whilst stylistic outcome is rooted in the change of aesthetical thinking. (Tarasti, 1994) In Chapter six of Metaphor and Musical Thought Spitzer decrees that allegory (Dionysus) overturns symbol (), an idea first attributed to Goethe (though Todorov’s study points to Schiller, Kant, Moritz, Meyer) that sees allegory as ‘the general through the particular’ and symbol as ‘the general in the particular’. Todorov furthers this exposition thus: symbol is ‘productive, motivated, intransitive’ and allegory, which is the reverse, is ‘transitive, arbitrary, rational.’ (Spitzer, 2004) This demonstrates the link between symbol as musical basis and allegory as stylistic sociocultural semiotics of musical etiquette, akin to grammar vs. linguistics. These musical semiotic and semantic concepts are crucial to microtonal practices, tonality, and language and syntax. Today, new progressions are possible with dynamic tuning bends, which allow modulation between equal temperaments in real time [due to the width of the generator, from meantone temperament, of the 5th and octave]. (Plamondon, 2008) In future microtonal practice, jazz, classical, third stream and world fusions may incorporate stylistics like blue notes, changes that use microtonal maqaamat, Balinese or other obscure ratio intervals like those in Scottish bagpipes, mixing aesthetical cross-genre nuances and expanding tonality aesthetics. Western microtonal practice halted early due to standardization of theory, intonation systems, and instrument making practice, and now lies largely in the electronic domain with exception to some world musics.98 Partch envisaged expanded Just tonality instruments with transpositional ability, whereas Stockhausen saw room for expanded rhythm and pitch, as the two are immediately linked.

98 A large part of music making lies in musical training, practicality and theory. If technology will play a role in future microtonal music, mathematical systems and new concepts will also play a role. (wolfram.com) This may also include new branches of logic and mathematics or physics and computer sciences, or experimental mathematics that will be a distinct part of future culture. One early example of this is Stockhausen’s phase shifting work in Samstag aus , as well as microtonal and micro-time bases. 55 To conclude, although some specialized microtonal instruments have been built, and many new innovative instruments are springing up,99 instrument performance techniques are very similar generally in both the past and present, while composition is experimenting more in the direction of non-standard pitch frequencies and non-pitch and rhythm based aesthetics, including performance utilizing and incorporating recent technologies and stylistic fusing. It is therefore likely that technology for practical performance will catch up with compositional experimenting.100,101 Certain rhythmic and microtonal structures are beyond human performance, and new genres like chill-house, acid-jazz, glitch artists and noise artists, include technology in the human equation. In instrumental teaching and practice one could use 12TET and 24TET as the model, while encouraging the ear towards Just intonation, thus avoiding problems in transposition. Digital music producers have been using plug-ins to fine tune, within a cent, using their ears, which was in the past not generally practicable, although a bulk of theory was known. For the electronic composition iTET for Sampled Piano (originally sketched in 1200TET) I employed passing phrases in many tonal systems. iTET for Sampled Piano uses 24TET, 53TET, 31TET, 17TET, 19TET, 7TET, 5TET, Just ratios and Bohlen-Pierce 8.20208TET with 3:1 (tritave, octave + 5th) ratio, and includes dynamic tonality (temperament modulations). To aid

99Ralph Novak pioneered the multi-scale fanned fret-board for modern electric instruments, a principle used by some of the 16th century lute makers. Multi-scale fan are becoming more common. Tolgahan Çoğulu has a secured microtonal guitar patent with grooves and removable mini frets that can sweep back and forth for the desired tonal system, which is especially useful for mid-Eastern musics. (Çoğulu, 2010) H-Pi Instruments’ Tonal Plexus microtonal keyboard uses 211 keys per octave arranged in 12 columns. 41 regions of 5 keys each = 205, and a further 6 duplicate enharmonic keys. (7 naturals, 7 sharps, 7 flats, 7 double-sharps, 7 double-flats and 6 triple- sharps, 6 triple-flats) (Hunt,2013) The Eigenharp has 120 keys (each one tilts to give a flexible tone), percussion buttons, recording, playback, looping, and running on sampled sounds is played via keyboard like a fretboard, tap- pad and mouthpiece, and can sound like a band. The electric violin has also become enhanced for the digital age and pickup technology can easily convert signals into midi to use sound samples or other desired processes, and is set to play a role in future music, especially tonal/microtonal. The Tenori-on was one of the better new musical gadgets to come out lately. It looks like a game of minesweeper, responds to touch in real time, looping themes intuitively, creating ‘soaring, rippling compositions that mesmerize beginners and experts alike.’ The other gadget that seemed fairly robust is the Hapi Drum, looking slightly like a steel drum and played like a bongo with a hole in the base. The player controls the amount of noise with their lap, and notes are accompanied by a ‘subtle resonant harmony from other musically compatible notes.’ (webUrbanist.com, n.d.) 100 Perhaps in the future there will be colloquial labels like non-standard pitch-time phrases/phrasing, but currently standardization of notational and graphical systems, and technologies, are unraveling. As technology grants the ability to organize and annotate more information, there appears to be departure out of standard pitch and time aesthetics. Sound painting, although live, is inspired by technology related genres, and may incorporate samples. Time is an elusive word, and architectural devices and musical theory [like dominant 7] that can shape time through human expectancies involving consonance and dissonance are part of pitch-class, duration-class, and their relative durations in sequential patterning. 101 Many traditional musics are codified now with the aid of the hypnotic, and often highly microtonal, pulse-driven [grid-locked] programmed backing tracks, whereas in the past this hypnotic affect was produced solely by performance instruments. 56 aestheticism, uncommon and unfamiliar tonalities are at times grouped as discordant and balanced with smaller ratio familiar tonalities for tension and resolution.

Glossary

12TET – 12 tone equal temperament; the system breaks the octave into 12 equivalent parts, resulting in a semitone of non-simple ratio – approximately the 12th root of 2 (12√2 or 21/12) or 1.059.

Chromatic tuning – Traditionally, in 12TET, chromatic tuning consists of all 12 semitones, of 100 cents each. Chromaticism is the expansion of diatony which adds a further 5 notes to the traditional 7 (diatonic).

Cymatics – Study of vibration, sound, and translation through physical mediums and material effects of sound.

Dodecaphony – (dodecaphonous)Twelve-tone technique, serialism.

Diatonicism – (διατονική) Diatonic describes scales, modes, chords, and harmony, that is non- chromatic (χρωματική), non-enharmonic, often heptatonic and built on tetrachords.

Eidos – (εἶδος), from οἶδα, ‘I know’ and Proto-Indo-European weyd- meaning to see or know. In Greek taken to mean essence, species, form, or type.

Enharmonic tuning – Enharmonic, or the equivalent note, in the sense of enharmonic tuning are notes that roughly approximate each other.

Enneachord – 9 note chord, enneotonic (9 tone).

Epistemes – quanta or packets of transmittable and interactive knowledge that may be contrasted with empiricism. In Foucaultian philosophy, the total bounds of knowledge and ideas that define a given epoch’s episteme (idea of true knowledge). 57 Euphonious – sounding pleasant, agreeable.

Hellenic chromaticism – Chromaticism that is not strictly constricted by equal temperament.

Heptatonic – 7 note scale or chord

Hexatonic – 6 note scale or chord

Hypo-mixolydian – 5th up from a mixolydian, the ancient Greek mixolydian however was a lochrian. Thus, a hypomixolydian is a modern dorian. Practicably, the scale extended slightly out horizontally below and above the root and 8th, with rules.

Infra-diatonic – Yasser’s term for tonal systems that fall below the standard heptatonic (7 note) scale base which is expandable to 12 as 7 + 5. This includes pentatonic 5 note bases, expandable to 7 as 5 + 2.

Inharmonicity - varies between instruments, and even thickness of strings, occurring progressively more, higher up the harmonic series.

Just intonation – Notes or frequency ratios that correlate to the harmonic series, generally small ratios to begin and larger ratios higher up the harmonic series (limit tuning).

Log () – log216=4 or 2x2x2x2, where 2 is the base, 4 is the exponent, and 16 is the power.

Melisma – (μέλισμα) or song, recitative form of several notes to a syllable. [melismas, melismatic]

Metonymy (metonym, Greek, μετά “other” + ὄνομα “name”) – use of term that substitutes for a thing, such as The Crown in place of British government, or White House in place of US government.

58 Museme – A small element of music whereby meaning is not further destroyed, broken down from constituent parts in musical semiotics, and analogous to morphemes in linguistics.

Neoclassicism – (νέος κλασσικός) Art, architecture, music, literature and theatre inspired by classical Greece and Rome, mainly during the 18th and early 19th century paralleling Romanticism.

New progressions - new chord progressions that utilize different temperaments (intonation systems).

Pareidolia- Cognitive process whereby real sounds are misconstrued imaginatively by picking out certain frequencies and timbres, and associations via unknown time processes.

Polychordia – many-stringed, classically more than 7, and up to 10, 11, or 12 in ancient Greek and kitharas.

TET – Tone Equal Temperament, the logical division of a string [or other method] into equal parts. (e.g. 22TET, or 22EDO or 22ET, also written 22-tet, 22-edo)

Third stream – synthesis of Classical and Jazz, with the element of improvisation.

Tonos – (τόνος) accent or stress. In modern Greek and Latin typography and orthography it is designated as the symbol ΄ over a vowel.

Schematic – term used to denote implicit acculturated framework of experience and knowledge that is unquestioned or assumed and may be subconscious to a degree, and may not be a true representation of logical modes of thought or experience.

Serialism – Musical processes, originally defined by Schoenberg, where notes are shuffled so that no two notes re-occur in any given phrase.

59 Solfege – (solfeggia, solfege system) spoken syllables for each pitch in a scale or mode.

Solmization – attribution of unique syllables to notes.

Syntonic comma - 81:80, 21.5 cents, German Syntonie, in synergy, harmony.

Ultra-diatonic – Yasser’s term for tonal systems that are beyond standard contemporary chromatic 12 tone diatonicism (7 + 5), and for Yasser the next logical choice was 12 + 7 in 19TET.

Veridical – (veri,or true) term used to describe flexible and creative use of accumulated experiences and knowledge.

Wolf 5th - dissonant form of diminished 6th, 16th and 17th centuries, popularly arising out of the quarter-comma meantone temperament and spanning seven semitones (procrustean/imperfect 5th).

Wusta-zalzal - greater than a tempered minor 3rd and less than a tempered major 3rd, with the ratio 27/22.

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