Isaac Newton's Microtonal Approach to Just Intonation
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Historically Informed Retuning of Polyphonic Vocal Performance
journal of interdisciplinary music studies spring/fall 2008, volume 2, issue 1&2, art. #0821208, pp. 121-139 Historically Informed Retuning of Polyphonic Vocal Performance Jonathan Wild and Peter Schubert Schulich School of Music, McGill University Background in history of music theory. The use of just intonation has generated heated debates ever since the first accounts of the articulation of pitch space in the scientific treatises of Ancient Greece. In the Renaissance, the discussion turned to vocal music as the locus of debate. One of the problems with using just intonation is the incommensurability of pure intervals with one another (e.g., the A four pure fifths above F is not the same pitch as the pure major third above F). Treatises and accounts of tuning systems proliferated, and our present- day understanding of what is at stake is limited by the dearth of sounding examples. Background in performance. On the one hand it is very difficult to verify precisely how modern-day singers tune, and on the other, although recent interest in historical tuning has generated several articles with electronically produced sound examples, the examples do not contribute to a direct understanding of tuning in the vocal context—synthesized sound is simply not “the real thing.” Aims. Our study aims to show how the gap between theories of tuning and the art of vocal performance may be bridged. Main contribution. By producing recordings of precisely tuned audio in rich vocal timbres (with vibrato, consonants and vowels), we make available actual repertoire examples, reliably tuned, in a human-sounding rendition. -
Development of Musical Scales in Europe
RABINDRA BHARATI UNIVERSITY VOCAL MUSIC DEPARTMENT COURSE - B.A. ( Compulsory Course ) (CBCS) 2020 Semester - II , Paper - I Teacher - Sri Partha Pratim Bhowmik History of Western Music Development of musical scales in Europe In the 8th century B.C., The musical atmosphere of ancient Greece introduced its development by the influence of then popular aristocratic music. That music was melody- based and the root of that music was rural folk-songs. In each and every country, the development of music was rooted in the folk-songs. The European Aristocratic Music of the Christian Era had been inspired by the developed Greek music. In the 5th century B.C. the renowned Greek Mathematician Pythagoras had first established a relation between science and music. Before him, the scale of Greek music was pentatonic. Pythagoras changed the scale into hexatonic pattern and later into heptatonic pattern. Greek musicians applied the alphabets to indicate the notes of their music. For the natural notes they used the alphabets in normal position and for the deformed notes, the alphabets turned upside down [deformed notes= Vikrita svaras]. The musical instruments, they had invented are – Aulos, Salpinx, pan-pipes, harp, lyre, syrinx etc. In the western music, the term ‘scale’ is derived from Latin word ‘scala’, ie, the ladder; scale means an ascent or descent formation of the musical notes. Each and every scale has a starting note, called ‘tonic note’ [‘tone - tonic’ not the Health-Tonic]. In the Ancient Greece, the musical scale had been formed with the help of lyre , a string instrument, having normally 5 or 6 or 7 strings. -
Theory Placement Examination (D
SAMPLE Placement Exam for Incoming Grads Name: _______________________ (Compiled by David Bashwiner, University of New Mexico, June 2013) WRITTEN EXAM I. Scales Notate the following scales using accidentals but no key signatures. Write the scale in both ascending and descending forms only if they differ. B major F melodic minor C-sharp harmonic minor II. Key Signatures Notate the following key signatures on both staves. E-flat minor F-sharp major Sample Graduate Theory Placement Examination (D. Bashwiner, UNM, 2013) III. Intervals Identify the specific interval between the given pitches (e.g., m2, M2, d5, P5, A5). Interval: ________ ________ ________ ________ ________ Note: the sharp is on the A, not the G. Interval: ________ ________ ________ ________ ________ IV. Rhythm and Meter Write the following rhythmic series first in 3/4 and then in 6/8. You may have to break larger durations into smaller ones connected by ties. Make sure to use beams and ties to clarify the meter (i.e. divide six-eight bars into two, and divide three-four bars into three). 2 Sample Graduate Theory Placement Examination (D. Bashwiner, UNM, 2013) V. Triads and Seventh Chords A. For each of the following sonorities, indicate the root of the chord, its quality, and its figured bass (being sure to include any necessary accidentals in the figures). For quality of chord use the following abbreviations: M=major, m=minor, d=diminished, A=augmented, MM=major-major (major triad with a major seventh), Mm=major-minor, mm=minor-minor, dm=diminished-minor (half-diminished), dd=fully diminished. Root: Quality: Figured Bass: B. -
3 Manual Microtonal Organ Ruben Sverre Gjertsen 2013
3 Manual Microtonal Organ http://www.bek.no/~ruben/Research/Downloads/software.html Ruben Sverre Gjertsen 2013 An interface to existing software A motivation for creating this instrument has been an interest for gaining experience with a large range of intonation systems. This software instrument is built with Max 61, as an interface to the Fluidsynth object2. Fluidsynth offers possibilities for retuning soundfont banks (Sf2 format) to 12-tone or full-register tunings. Max 6 introduced the dictionary format, which has been useful for creating a tuning database in text format, as well as storing presets. This tuning database can naturally be expanded by users, if tunings are written in the syntax read by this instrument. The freely available Jeux organ soundfont3 has been used as a default soundfont, while any instrument in the sf2 format can be loaded. The organ interface The organ window 3 MIDI Keyboards This instrument contains 3 separate fluidsynth modules, named Manual 1-3. 3 keysliders can be played staccato by the mouse for testing, while the most musically sufficient option is performing from connected MIDI keyboards. Available inputs will be automatically recognized and can be selected from the menus. To keep some of the manuals silent, select the bottom alternative "to 2ManualMicroORGANircamSpat 1", which will not receive MIDI signal, unless another program (for instance Sibelius) is sending them. A separate menu can be used to select a foot trigger. The red toggle must be pressed for this to be active. This has been tested with Behringer FCB1010 triggers. Other devices could possibly require adjustments to the patch. -
MTO 10.1: Wibberley, Syntonic Tuning
Volume 10, Number 1, February 2004 Copyright © 2004 Society for Music Theory Roger Wibberley KEYWORDS: Aristoxenus, comma, Ganassi, Jachet, Josquin, Ptolemy, Rore, tetrachord, Vesper-Psalms, Willaert, Zarlino ABSTRACT: This Essay makes at the outset an important (if somewhat controversial) assumption. This is that Syntonic tuning (Just Intonation) is not—though often presumed to be so—primarily what might be termed “a performer’s art.” On the contrary it is a composer’s art. As with the work of any composer from any period, it is the performer’s duty to render the music according to the composer’s wishes as shown through the evidence. Such evidence may be indirect (perhaps documentary) or it may be explicitly structural (to be revealed through analysis). What will be clear is the fallacy of assuming that Just Intonation can (or should) be applied to any music rather than only to that which was specifically designed by the composer for the purpose. How one can deduce whether a particular composer did, or did not, have the sound world of Just Intonation (henceforward referred to as “JI”) in mind when composing will also be explored together with a supporting analytical rationale. Musical soundscape (especially where voices are concerned) means, of course, incalculably more than mere “accurate intonation of pitches” (which alone is the focus of this essay): its color derives not only from pitch combination, but more importantly from the interplay of vocal timbres. These arise from the diverse vowel sounds and consonants that give life, color and expression. The audio examples provided here are therefore to be regarded as “playbacks” and no claim is being implied or intended that they in any way stand up as “performances.” Some care, nonetheless, has been taken to make them as acceptable as is possible with computer-generated sounds. -
The Lost Harmonic Law of the Bible
The Lost Harmonic Law of the Bible Jay Kappraff New Jersey Institute of Technology Newark, NJ 07102 Email: [email protected] Abstract The ethnomusicologist Ernest McClain has shown that metaphors based on the musical scale appear throughout the great sacred and philosophical works of the ancient world. This paper will present an introduction to McClain’s harmonic system and how it sheds light on the Old Testament. 1. Introduction Forty years ago the ethnomusicologist Ernest McClain began to study musical metaphors that appeared in the great sacred and philosophical works of the ancient world. These included the Rg Veda, the dialogues of Plato, and most recently, the Old and New Testaments. I have described his harmonic system and referred to many of his papers and books in my book, Beyond Measure (World Scientific; 2001). Apart from its value in providing new meaning to ancient texts, McClain’s harmonic analysis provides valuable insight into musical theory and mathematics both ancient and modern. 2. Musical Fundamentals Figure 1. Tone circle as a Single-wheeled Chariot of the Sun (Rg Veda) Figure 2. The piano has 88 keys spanning seven octaves and twelve musical fifths. The chromatic musical scale has twelve tones, or semitone intervals, which may be pictured on the face of a clock or along the zodiac referred to in the Rg Veda as the “Single-wheeled Chariot of the Sun.” shown in Fig. 1, with the fundamental tone placed atop the tone circle and associated in ancient sacred texts with “Deity.” The tones are denoted by the first seven letters of the alphabet augmented and diminished by and sharps ( ) and flats (b). -
Models of Octatonic and Whole-Tone Interaction: George Crumb and His Predecessors
Models of Octatonic and Whole-Tone Interaction: George Crumb and His Predecessors Richard Bass Journal of Music Theory, Vol. 38, No. 2. (Autumn, 1994), pp. 155-186. Stable URL: http://links.jstor.org/sici?sici=0022-2909%28199423%2938%3A2%3C155%3AMOOAWI%3E2.0.CO%3B2-X Journal of Music Theory is currently published by Yale University Department of Music. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/yudm.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact [email protected]. http://www.jstor.org Mon Jul 30 09:19:06 2007 MODELS OF OCTATONIC AND WHOLE-TONE INTERACTION: GEORGE CRUMB AND HIS PREDECESSORS Richard Bass A bifurcated view of pitch structure in early twentieth-century music has become more explicit in recent analytic writings. -
Nora-Louise Müller the Bohlen-Pierce Clarinet An
Nora-Louise Müller The Bohlen-Pierce Clarinet An Introduction to Acoustics and Playing Technique The Bohlen-Pierce scale was discovered in the 1970s and 1980s by Heinz Bohlen and John R. Pierce respectively. Due to a lack of instruments which were able to play the scale, hardly any compositions in Bohlen-Pierce could be found in the past. Just a few composers who work in electronic music used the scale – until the Canadian woodwind maker Stephen Fox created a Bohlen-Pierce clarinet, instigated by Georg Hajdu, professor of multimedia composition at Hochschule für Musik und Theater Hamburg. Hence the number of Bohlen- Pierce compositions using the new instrument is increasing constantly. This article gives a short introduction to the characteristics of the Bohlen-Pierce scale and an overview about Bohlen-Pierce clarinets and their playing technique. The Bohlen-Pierce scale Unlike the scales of most tone systems, it is not the octave that forms the repeating frame of the Bohlen-Pierce scale, but the perfect twelfth (octave plus fifth), dividing it into 13 steps, according to various mathematical considerations. The result is an alternative harmonic system that opens new possibilities to contemporary and future music. Acoustically speaking, the octave's frequency ratio 1:2 is replaced by the ratio 1:3 in the Bohlen-Pierce scale, making the perfect twelfth an analogy to the octave. This interval is defined as the point of reference to which the scale aligns. The perfect twelfth, or as Pierce named it, the tritave (due to the 1:3 ratio) is achieved with 13 tone steps. -
Construction and Verification of the Scale Detection Method for Traditional Japanese Music – a Method Based on Pitch Sequence of Musical Scales –
International Journal of Affective Engineering Vol.12 No.2 pp.309-315 (2013) Special Issue on KEER 2012 ORIGINAL ARTICLE Construction and Verification of the Scale Detection Method for Traditional Japanese Music – A Method Based on Pitch Sequence of Musical Scales – Akihiro KAWASE Department of Corpus Studies, National Institute for Japanese Language and Linguistics, 10-2 Midori-cho, Tachikawa City, Tokyo 190-8561, Japan Abstract: In this study, we propose a method for automatically detecting musical scales from Japanese musical pieces. A scale is a series of musical notes in ascending or descending order, which is an important element for describing the tonal system (Tonesystem) and capturing the characteristics of the music. The study of scale theory has a long history. Many scale theories for Japanese music have been designed up until this point. Out of these, we chose to formulate a scale detection method based on Seiichi Tokawa’s scale theories for traditional Japanese music, because Tokawa’s scale theories provide a versatile system that covers various conventional scale theories. Since Tokawa did not describe any of his scale detection procedures in detail, we started by analyzing his theories and understanding their characteristics. Based on the findings, we constructed the scale detection method and implemented it in the Java Runtime Environment. Specifically, we sampled 1,794 works from the Nihon Min-yo Taikan (Anthology of Japanese Folk Songs, 1944-1993), and performed the method. We compared the detection results with traditional research results in order to verify the detection method. If the various scales of Japanese music can be automatically detected, it will facilitate the work of specifying scales, which promotes the humanities analysis of Japanese music. -
Download the Just Intonation Primer
THE JUST INTONATION PPRIRIMMEERR An introduction to the theory and practice of Just Intonation by David B. Doty Uncommon Practice — a CD of original music in Just Intonation by David B. Doty This CD contains seven compositions in Just Intonation in diverse styles — ranging from short “fractured pop tunes” to extended orchestral movements — realized by means of MIDI technology. My principal objectives in creating this music were twofold: to explore some of the novel possibilities offered by Just Intonation and to make emotionally and intellectually satisfying music. I believe I have achieved both of these goals to a significant degree. ——David B. Doty The selections on this CD process—about synthesis, decisions. This is definitely detected in certain struc- were composed between sampling, and MIDI, about not experimental music, in tures and styles of elabora- approximately 1984 and Just Intonation, and about the Cageian sense—I am tion. More prominent are 1995 and recorded in 1998. what compositional styles more interested in result styles of polyphony from the All of them use some form and techniques are suited (aesthetic response) than Western European Middle of Just Intonation. This to various just tunings. process. Ages and Renaissance, method of tuning is com- Taken collectively, there It is tonal music (with a garage rock from the 1960s, mendable for its inherent is no conventional name lowercase t), music in which Balkan instrumental dance beauty, its variety, and its for the music that resulted hierarchic relations of tones music, the ancient Japanese long history (it is as old from this process, other are important and in which court music gagaku, Greek as civilization). -
Cool in the Kitchen: Radiation, Conduction, and the Newton “Hot Block” Experiment
Cool in the Kitchen: Radiation, Conduction, and the Newton “Hot Block” Experiment Mark P. Silverman and Christopher R. Silverman he rate at which an object cools down Our curiosity was aroused. How good an Tgives valuable information about the approximation to reality is Newton’s law— mechanisms of heat loss and the thermal prop- and what in any event determines whether the erties of the material. In general, heat loss temperature of the hot object is too high? occurs by one or more of the following four Furthermore, although Newton’s name is processes: (a) conduction, (b) convection, (c) readily associated with his laws of motion, evaporation, and (d) radiation. law of gravity, and various optical phenomena In conduction, heat is transferred through a and apparatus, it does not usually appear in medium by the collisional encounters of ther- discussions of thermal phenomena. Indeed, mally excited molecules vibrating about their apart from this one instance, a search through equilibrium positions, or, in the case of met- a score or more of history of science books als, by mobile, unbound electrons; only ener- and thermal physics books at various levels of gy, not bulk matter itself, moves through the instruction produced but one other circum- Mark P. Silverman is material. Convection, by contrast, refers to the stance for noting Newton’s name—and that Professor of Physics at Trinity College and former transfer of heat through the action of a moving was his failure to recognize the adiabatic 3 Joliot Professor of Physics fluid; in free or natural convection, the motion nature of sound propagation in air. -
Consistent Pitch Height Forms: a Commentary on Daniel Muzzulini's Contribution Isaac Newton's Microtonal Approach To
Consistent Pitch Height Forms: A commentary on Daniel Muzzulini’s contribution Isaac Newton’s Microtonal Approach to Just Intonation THOMAS NOLL[1] Escola Superior de Música de Catalunya, Departament de Teoria, Composició i Direcció ABSTRACT: This text revisits selected aspects of Muzzulini’s article and reformulates them on the basis of a three-dimensional interval space E and its dual E*. The pitch height of just intonation is conceived as an element h of the dual space. From octave-fifth-third coordinates it becomes transformed into chromatic coordinates. The dual chromatic basis is spanned by the duals a* of a minor second a and the duals b* and c* of two kinds of augmented primes b and c. Then for every natural number n a modified pitch height form hn is derived from h by augmenting its coordinates with the factor n, followed by rounding to nearest integers. Of particular interest are the octave-consitent forms hn mapping the octave to the value n. The three forms hn for n = 612, 118, 53 (yielding smallest deviations from the respective values of n h) form the Muzzulini basis of E*. The respective transformation matrix T* between the coordinate representations of linear forms in the Muzzulini basis and the dual chromatic basis is unimodular and a Pisot matrix with the dominant eigen-co-vector very close to h. Certain selections of the linear forms hn are displayed in Muzzuli coordinates as ball-like point clouds within a suitable cuboid containing the origin. As an open problem remains the estimation of the musical relevance of Newton’s chromatic mode, and chromatic modes in general.