DOCSLIB.ORG

Les Duresses

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Les Duresses Marc Sabat Les Duresses a book of music in Just Intonation PLAINSOUND MUSIC EDITION Les Duresses (2004–) for violins This work-in-progress is a collection of pieces for violin or violin+instrument, conceived as experimental ‘intonation studies’ in a sense parallel to Conlon Nancarrow’s ‘Studies for Player Piano’. Like Couperin’s books of music for harpsichord, I think of my collection as contemporary house music existing for private playing pleasure which might occasionally double as more formal concert music. ‘Les Duresses’ is dedicated to Natalie Pfeiffer. The first two pieces in the series, titled ‘Intonation after Morton Feldman #1 and #2’, each take as a point of departure a pair of tuned dyads drawn from Morton Feldman’s unfinished ‘Composition’ (1984) for solo violin. The harmonically complex transitions become the respective topics of the new pieces, seeking to make these comprehensible to both player and listener. These pieces may be transposed and played on viola, Partch adapted viola, or cello if desired. The Extended Helmholtz-Ellis JI Pitch Notation microtonal accidentals designed by Marc Sabat and Wolfgang von Schweinitz, 2004 3-LIMIT (PYTHAGOREAN) INTERVALS FUNCTION OF THE ACCIDENTALS notate 35 pitches from the series of untempered perfect fifths (3/2) ! ± 702.0 cents; d k r y Ä perfect fifth (3/2); perfect fourth (4/3); major wholetone (9/8) 5-LIMIT (PTOLEMAIC) INTERVALS notate an alteration by one syntonic comma (81/80) ! ± 21.5 cents; major third (5/4); minor third (6/5); major sixth (5/3); minor sixth (8/5); c j q x ! e l s " Å minor wholetone (10/9) notate an alteration by two syntonic commas (81/80)·(81/80) ! ± 43.0 cents; b i p w # f m t $ % augmented fifth (25/16); diminished fourth (32/25) notate an alteration by three syntonic commas (81/80)·(81/80)·(81/80) ! ± 64.5 cents; a h o v & g n u | É minor diesis (128/125) 7-LIMIT (SEPTIMAL) INTERVALS notate an alteration by one septimal comma (64/63) ! ± 27.3 cents; natural seventh (7/4); septimal wholetone (8/7); septimal diminished fifth (7/5); septimal tritone (10/7); ' ( septimal minor third (7/6); septimal quartertone (36/35) notate an alteration by two septimal commas or or (64/63)·(64/63) ! ± 54.5 cents; ) '' * (( septimal sixthtone (49/48) 11-LIMIT (UNDECIMAL) INTERVALS notate an alteration by one undecimal quartertone (33/32) ! ± 53.3 cents; C B undecimal augmented fourth (11/8); undecimal diminished fifth (16/11) 13-LIMIT (TRIDECIMAL) INTERVALS notate an alteration by one tridecimal thirdtone (27/26) ! ± 65.3 cents; tridecimal neutral sixth (13/8); tridecimal neutral third (16/13) + , PRIMES IN THE HARMONIC SERIES OCTAVE 16 - 32 (5-limit signs are given here relative to “A”) notate an alteration of the 5-limit accidental by one 17-limit schisma (16/17)·(16/15) = (256/255) ! ± 6.8 cents; Galileo’s “equal-tempered” semitone (18/17); -l .x 17-limit diminshed seventh chord 10:12:14:17 notate an alteration by one 19-limit schisma (19/16)·(27/32) = (513/512) ! ± 3.4 cents; /r 0r 19-limit minor third (19/16); 19-limit minor triad 16:19:24 notate an alteration by one 23-limit comma (23/16)·(8/9)·(8/9)·(8/9) ! ± 16.5 cents; 1y 2k raised leading tone (23/12) notate an alteration of the 5-limit accidental by one 29-limit comma (29/16)·(5/9) = (145/144) ! ± 12.0 cents \s ]q notate an alteration of the 11-limit accidental by one 31-limit schisma (32/31)·(32/33) = (1024/1023) ! ± 1.7 cents 3B 4C PRIMES IN THE HARMONIC SERIES OCTAVE 32 - 64 (5-limit signs are given here relative to “A”) notate an alteration of the 11-limit accidental by one 37-limit schisma (36/37)·(33/32) = (297/296) ! ± 5.8 cents 5C 6B notate an alteration of the 5-limit accidental by one 41-limit schisma (32/41)·(81/64)·(81/80) = (6561/6560) ! ± 0.3 cents {"} {j} notate an alteration by one 43-limit comma (43/32)·(3/4) = (129/128) ! ± 13.5 cents 7 8 or or notate an alteration of the 7-limit accidental by one 47-limit schisma (32/47)·(48/49)·(3/2) = (2304/2303) ! ± 0.8 cents 9y :y ;k <k notate an alteration of the 5-limit accidental by one 53-limit comma (32/53)·(5/3) = (160/159) ! ± 10.9 cents =x >l notate an alteration of the 13-limit accidental by one 59-limit schisma (32/59)·(24/13) = (768/767) ! ± 2.3 cents ? @ notate an alteration of the 7-limit accidental by one 61-limit schisma (61/32)·(21/40) = (1281/1280) ! ± 1.4 cents Ax Bl IRRATIONAL AND TEMPERED INTERVALS notate the respective Equal Tempered Semitone; may be combined with a cents indication to notate any pitch C D E F G NOTE ABOUT CENTS INDICATIONS optional cents indications may be placed above or below the respective accidentals and are always understood in reference to Equal Tempered semitones, as implied by the Pythagorean accidentals ‘Les Duresses’ : a book of music in Just Intonation for Natalie Pfeiffer No. 1 : Intonation after Morton Feldman #1 (violin solo) Marc Sabat, 2004 814 ¢ 969 ¢ 498 ¢ 386 ¢ 8/5 7/4 4/3 5/4 2. repeat sign : entire bracket con sordino +155 cents -112 ¢ ° ° 32 : 35 ü ° 16 : 15 ü ü ™ ™ w port. w w port. w ™ ™ w w w w ™ ™ 1. & ¢ ¢ w w w w † ¢ w w w w † † f < < f f f o on on o nas many bown changes andn repetitionsn as accurate intonation requires, proceed continuously through the numbered phrases 653 ¢ ° 35/24 ü ™ w port. w w w w w w ™ 2. & ¢ w w w w w w w † f < < < < < n o o o n n o o ° ü ™ w w w w w ™ w w 3. & ¢ w w w w w † w w f f f f n f f o n n o o o n 590 ¢ 582.5 ¢ 45/32 7/5 1. time only °™ w w w w °™ w w w w ™ ü 4. & ™ w ™ w w ™ ¢ w n n n ¢ n n n n † ff f >u >u f f >u n 224 : 225 +8 ¢ 821 ¢ 45/28 1. time w ° only ü ü & w w ™ w w w w ™ w w ™ n w ¢ w w w w † w w † >u >u >u f f >u >u f n n n n n n n 3 1/1 ° ü w w w w ™ w www ww™ w ww 5. & w ™ w w ™ w w n n n ¢ nn n n † nn ff f >u >u u u n 231 ¢ 8/7 °™ www w ™ ü w 6. & ™ www w ™ w ¢ n n n † w w u u>u >u >u f n n 223 ¢ 256/225 °™ www w w ™ ü 7. & ™ ww ™ ¢ n n w † u uf f n °™ w w w w w w w ™ ü 8. & ™ w w ww ww w ww w w ™ ¢ w n w † f uf uf u>u u>u >u u>u uf uf f n n ° ü ™ w w w w w port. w ™ 9. & ¢™ w w w ™ † < <w <w w f uf f o 64 : 75 o n n n +275 ¢ ° ü ™ w port. w w w w ™ 10. & ¢™ w w w w ™ † w <w < f uf f n n n o o o °™ w w ™ ü 11. & ¢™ w w ™ † f < u o Berlin, 13.01.2004 4 No. 2 : Intonation after Morton Feldman #2 (violin solo) 386 ¢ 814 ¢ 275 ¢ 5/4 8/5 75/64 con sordino w. sempreæ simile wæ ww wæ w & w w w w w næ ggn æ g næ o n o as many bow changeso and repetitionso (at least 3) of each interval as accurateo intonation requires; “loure” stroke with several articulations in one bow; repeat segments under square brackets as desired 498 ¢ 267 ¢ 379 ¢ 4/3 7/6 56:45 w w ww w wæ æ æ & w w æ w w æ gæ gn n æ w w go g >v >v n n 224 : 225 >u >u 225 : o 224 +8 ¢ -8 ¢ wæ ww æ w w ww & w w w n æ w g gæ n æ gg ffæ g g o n 582.5 ¢ 7/5 w æ æ w wæ & w w w w w w gæ <g <gæ gæ g g on o g g o 617.5 ¢ 506 ¢ 590 ¢ 10/7 75/56 45/32 w w w w w w & w w w w w w o æ o æ n æ næ oæ oæ n <g <g n n n 224 : 225 +8 ¢ 884 ¢ 969 ¢ 1018 ¢ 5/3 7/4 9/5 +84.5 ¢ 20æ : 21 w æ w w4 æ & w w w w æ næ n <f w o n æ w w o o o o f 1173 ¢ n n 63/32 wæ w w2 æ æ æ & < æ <w w w w <fw <f æ w w 1 n n n n 1 f f 224 : >u 225 o +8 ¢ 541.5 ¢ 316 ¢ 1200 ¢ 5 175:128 6/5 2/1 æ3 w2 æ w w w w w æ & w < g g æ go æ no æ nw w 1 3 w o 24 : 25 n f +71 ¢ n 1178 ¢ 160/81 æ æ w2 w w w w w æ & w n n æ mæ w nnæ m mmw 3 w f n f n 1067 ¢ 1049 ¢ 547.2 ¢ 612 ¢ 50/27 11/6 1000:729 729:512 -17 ¢ -32 ¢ 100 : 99 55 : 54 wæ wæ wæ w w w w & w w w w w w mæ m n n m 4f g g e æ e æ <f æ f f f 5120 : 5103 -6 ¢ 12/7 w w æ æ2 æ w w w w w w & o o w w w hw <f æ æ g g æ n on 1 o h h 41 ¢ 231 ¢ 546.8 ¢ 128/125 8/7 48/35 ww ww w w w æ æ w w w w & h æ h>h >hæ æ w n g gn >vn æ >v 2 >o 49 ¢ 551.3 ¢ 36/35 11/8 -3 ¢ 540 : 539 wæ ww ww w w wæ & w æ >ow >o æ n>o.w æ .wæ 4gæ w w >v g g w >o 225 : 224 o o -8 ¢ n æ æ æ w w æ æ w æ & w w w w w w n n n w o n n <f <f o o o <f 1045 ¢ 64/35 æ æ w w w w wæ w æ & w 4g w g ggw æ w næ o o n o <f <f o London, 21.01.2004 6 No.
Load more

Recommended publications
  • Generalized Interval System and Its Applications
    Generalized Interval System and Its Applications Minseon Song May 17, 2014 Abstract Transformational theory is a modern branch of music theory developed by David Lewin. This theory focuses on the transformation of musical objects rather than the objects them- selves to find meaningful patterns in both tonal and atonal music. A generalized interval system is an integral part of transformational theory. It takes the concept of an interval, most commonly used with pitches, and through the application of group theory, generalizes beyond pitches. In this paper we examine generalized interval systems, beginning with the definition, then exploring the ways they can be transformed, and finally explaining com- monly used musical transformation techniques with ideas from group theory. We then apply the the tools given to both tonal and atonal music. A basic understanding of group theory and post tonal music theory will be useful in fully understanding this paper. Contents 1 Introduction 2 2 A Crash Course in Music Theory 2 3 Introduction to the Generalized Interval System 8 4 Transforming GISs 11 5 Developmental Techniques in GIS 13 5.1 Transpositions . 14 5.2 Interval Preserving Functions . 16 5.3 Inversion Functions . 18 5.4 Interval Reversing Functions . 23 6 Rhythmic GIS 24 7 Application of GIS 28 7.1 Analysis of Atonal Music . 28 7.1.1 Luigi Dallapiccola: Quaderno Musicale di Annalibera, No. 3 . 29 7.1.2 Karlheinz Stockhausen: Kreuzspiel, Part 1 . 34 7.2 Analysis of Tonal Music: Der Spiegel Duet . 38 8 Conclusion 41 A Just Intonation 44 1 1 Introduction David Lewin(1933 - 2003) is an American music theorist.
    [Show full text]
  • 8.1.4 Intervals in the Equal Temperament The
    8.1 Tonal systems 8-13 8.1.4 Intervals in the equal temperament The interval (inter vallum = space in between) is the distance of two notes; expressed numerically by the relation (ratio) of the frequencies of the corresponding tones. The names of the intervals are derived from the place numbers within the scale – for the C-major-scale, this implies: C = prime, D = second, E = third, F = fourth, G = fifth, A = sixth, B = seventh, C' = octave. Between the 3rd and 4th notes, and between the 7th and 8th notes, we find a half- step, all other notes are a whole-step apart each. In the equal-temperament tuning, a whole- step consists of two equal-size half-step (HS). All intervals can be represented by multiples of a HS: Distance between notes (intervals) in the diatonic scale, represented by half-steps: C-C = 0, C-D = 2, C-E = 4, C-F = 5, C-G = 7, C-A = 9, C-B = 11, C-C' = 12. Intervals are not just definable as HS-multiples in their relation to the root note C of the C- scale, but also between all notes: e.g. D-E = 2 HS, G-H = 4 HS, F-A = 4 HS. By the subdivision of the whole-step into two half-steps, new notes are obtained; they are designated by the chromatic sign relative to their neighbors: C# = C-augmented-by-one-HS, and (in the equal-temperament tuning) identical to the Db = D-diminished-by-one-HS. Corresponding: D# = Eb, F# = Gb, G# = Ab, A# = Bb.
    [Show full text]
  • On the Bimodular Approximation and Equal Temperaments
    On the Bimodular Approximation and Equal Temperaments Martin Gough DRAFT June 8 2014 Abstract The bimodular approximation, which has been known for over 300 years as an accurate means of computing the relative sizes of small (sub-semitone) musical intervals, is shown to provide a remarkably good approximation to the sizes of larger intervals, up to and beyond the size of the octave. If just intervals are approximated by their bimodular approximants (rational numbers defined as frequency difference divided by frequency sum) the ratios between those intervals are also rational, and under certain simply stated conditions can be shown to coincide with the integer ratios which equal temperament imposes on the same intervals. This observation provides a simple explanation for the observed accuracy of certain equal divisions of the octave including 12edo, as well as non-octave equal temperaments such as the fifth-based temperaments of Wendy Carlos. Graphical presentations of the theory provide further insights. The errors in the bimodular approximation can be expressed as bimodular commas, among which are many commas featuring in established temperament theory. Introduction Just musical intervals are characterised by small-integer ratios between frequencies. Equal temperaments, by contrast, are characterised by small-integer ratios between intervals. Since interval is the logarithm of frequency ratio, it follows that an equal temperament which accurately represents just intervals embodies a set of rational approximations to the logarithms (to some suitable base) of simple rational numbers. This paper explores the connection between these rational logarithmic approximations and those obtained from a long-established rational approximation to the logarithm function – the bimodular approximation.
    [Show full text]
  • The Death and Resurrection of Function
    THE DEATH AND RESURRECTION OF FUNCTION A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By John Gabriel Miller, B.A., M.C.M., M.A. ***** The Ohio State University 2008 Doctoral Examination Committee: Approved by Dr. Gregory Proctor, Advisor Dr. Graeme Boone ________________________ Dr. Lora Gingerich Dobos Advisor Graduate Program in Music Copyright by John Gabriel Miller 2008 ABSTRACT Function is one of those words that everyone understands, yet everyone understands a little differently. Although the impact and pervasiveness of function in tonal theory today is undeniable, a single, unambiguous definition of the term has yet to be agreed upon. So many theorists—Daniel Harrison, Joel Lester, Eytan Agmon, Charles Smith, William Caplin, and Gregory Proctor, to name a few—have so many different nuanced understandings of function that it is nearly impossible for conversations on the subject to be completely understood by all parties. This is because function comprises at least four distinct aspects, which, when all called by the same name, function , create ambiguity, confusion, and contradiction. Part I of the dissertation first illuminates this ambiguity in the term function by giving a historical basis for four different aspects of function, three of which are traced to Riemann, and one of which is traced all the way back to Rameau. A solution to the problem of ambiguity is then proposed: the elimination of the term function . In place of function , four new terms—behavior , kinship , province , and quality —are invoked, each uniquely corresponding to one of the four aspects of function identified.
    [Show full text]
  • Shadings in the Chromatic Field: Intonations After Morton Feldman
    Shadings in the Chromatic Field: Intonations after Morton Feldman Marc Sabat ... this could be an element of the aural plane, where I'm trying to balance, a kind of coexistence between the chromatic field and those notes selected from the chromatic field that are not in the chromatic series.1 Harmony, or how pitched sounds combine, implies microtonality, enharmonic variations of tuning. Historically, these came to be reflected in written music by having various ways of spelling pitches. A harmonic series over E leads to the notes B and G#, forming a just major triad. Writing Ab instead of G# implies a different structure, but in what way? How may such differences of notation be realized as differences of sound? The notion of enharmonic "equivalence," which smooths away such shadings, belongs to a 20th century atonal model: twelve-tone equal temperament. This system rasters the frequency glissando by constructing equal steps in the irrational proportion of vibration 1:12√2. Twelve successive steps divide an octave, at which interval the "pitch- classes" repeat their names. Their vertical combinations have been exhaustively demonstrated, most notably in Tom Johnson's Chord Catalogue. However, the actual sounding of pitches, tempered or not, always reveals a microtonally articulated sound continuum. Hearing out the complex tonal relations within it suggests a new exploration of harmony: composing intonations in writing, playing and hearing music. Morton Feldman recognized that this opening for composition is fundamentally a question of rethinking the notational image. In works composed for the most part between 1977 and 1985, inspired by his collaboration with violinist Paul Zukofsky, Feldman chose to distinguish between enharmonically spelled pitches.
    [Show full text]
  • MTO 12.3: Duffin, Just Intonation in Renaissance Theory and Practice
    Volume 12, Number 3, October 2006 Copyright © 2006 Society for Music Theory Ross W. Duffin ABSTRACT: Just intonation has a reputation as a chimerical, theoretical system that simply cannot work in practice. This is based on the assessment of most modern authorities and supported by misgivings expressed during the Renaissance when the practice was supposedly at its height. Looming large among such misgivings are tuning puzzles printed by the 16th-century mathematician, Giovanni Battista Benedetti. However, Renaissance music theorists are so unanimous in advocating the simple acoustical ratios of Just intonation that it seems clear that some reconciliation must have occurred between the theory and practice of it. This article explores the basic theory of Just intonation as well as problematic passages used to deny its practicability, and proposes solutions that attempt to satisfy both the theory and the ear. Ultimately, a resource is offered to help modern performers approach this valuable art. Received June 2006 Introduction | Theoretical Background | Benedetti's Puzzles | Problematic Passages | Is Just Tuning Possible? A New Approach | Problem Spots in the Exercises | Rehearsal Usage | Conclusion Introduction The idea . that one can understand the ratios of musical consonances without experiencing them with the senses is wrong. Nor can one know the theory of music without being versed in its practice. [1] So begins the first of two letters sent by the mathematician Giovanni Battista Benedetti to the composer Cipriano de Rore in 1563. Subsequently publishing the letters in 1585,(1) Benedetti was attempting to demonstrate that adhering to principles of Just intonation, as championed most famously by Gioseffo Zarlino,(2) would, in certain cases, cause the pitch of the ensemble to migrate.
    [Show full text]
  • Intervals Continued Compound Intervals, Inversions MUS 102 Music Fundamentals Mark Nelson, Instructor
    Intervals Continued Compound Intervals, Inversions MUS 102 Music Fundamentals Mark Nelson, Instructor Compound Intervals: These intervals are greater than one octave but they function the same as intervals of an octave or less. One can merely remove the octave and what is left is essentially the interval it functions as. Example 1: This compound interval has D on the bottom and F# on the top. By moving the D up one octave to the next D, the interval can now be identified conventionally: Step 1: count the pitches – D-E-F = 3. The interval is a 3rd. Step 2: count the ½ steps – D-D#, D#-E, E-F, F-F# = 4. The interval is a Major 3rd or M3. You can also lower the F# by one octave and you would get the same interval, just one octave lower. Inversions: An inversion is when the two pitches of an interval are reversed. The total between each of the two intervals always adds up to 9. For example, a P4 and its inversion P5 is 4+5=9. Inversion possibilities: 1. Inverted intervals always invert to their opposite except perfect intervals which invert only to themselves. 2. Inversions are useful to flip pitches to allow different singers or instruments to take the high or low part. 3. Inversions have the following rules: Perfect intervals invert to Perfect intervals Major intervals invert to minor intervals (and vise versa) Diminished intervals invert to augmented intervals (and vice versa) Doubly diminished intervals invert to doubly augmented intervals. Chart of Interval Inversions Perfect, Minor, Major, Diminished and Augmented Perfect Unison Perfect
    [Show full text]
  • The Extended Helmholtz-Ellis JI Pitch Notation PLAINSOUND MUSIC EDITION
    The Extended Helmholtz-Ellis JI Pitch Notation microtonal accidentals designed by / mikrotonale Vorzeichen konzipiert von Marc Sabat & Wolfgang von Schweinitz, 2004 English Text : Marc Sabat, 2005 Deutsche Fassung : Natalie Pfeiffer P L A I N S O U N D M U S I C E D I T I O N The Extended Helmholtz-Ellis JI Pitch Notation microtonal accidentals designed by / mikrotonale Vorzeichen konzipiert von Marc Sabat & Wolfgang von Schweinitz, 2004 English Text : Marc Sabat Deutsche Fassung : Natalie Pfeiffer P L A I N S O U N D M U S I C E D I T I O N „Die Obertonreihe ... enthält noch viele Probleme, die eine Auseinandersetzung nötig machen werden. Und wenn wir diesen Problemen augenblicklich noch entrinnen, so verdanken wir das fast ausschließlich einem Kompromiß zwischen den natürlichen Intervallen und unserer Unfähigkeit sie zu verwenden. Jenem Kompromiß, das sich temperiertes System nennt, das einen auf eine unbestimmte Frist geschlossenen Waffenstillstand darstellt. Diese Reduktion der natürlichen Verhältnisse auf handliche wird aber die Entwicklung auf die Dauer nicht aufhalten können; und das Ohr wird sich mit den Problemen befassen müssen, weil es will. Dann wird unsere Skala ebenso aufgehen in eine höhere Ordnung, wie die Kirchentonarten in der Dur- und Molltonart aufgegangen sind. Ob dann Viertel-, Achtel-, Drittel- oder (wie Busoni meint) Sechsteltöne kommen, oder ob man direkt zu einer 53 tönigen Skala übergehen wird ... läßt sich nicht voraussagen. Vielleicht wird diese neue Teilung der Oktave sogar untemperiert sein und mit unserer Skala nur noch wenig gemeinsam haben.“ Arnold Schoenberg: Harmonielehre, 3. Auflage, S. 22-24 (1922) “The overtone series … still contains many problems that will have to be faced.
    [Show full text]
  • Intervals an Interval Is the Distance Between One Note and Another
    Intervals An interval is the distance between one note and another. It is always measured from the lower note. Working out intervals can be very similar to working out scale degrees. The smallest interval in western notation is a semitone (or half-tone) and there is no real limit (other than the range of human hearing – 20Hz to 20kHz) for the largest interval. Major and minor intervals The distance from C to D is a whole tone. D is the second degree of the scale of C major, so it is known as a ‘ major second ’. The distance from C to E is a ‘major third ’. However: the distance from C to Eb is a ‘ minor third ’, as the note E is lowered by one semitone. 1 to b2 = minor second 1 to 2 = major second 1 to b3 = minor third 1 to 3 = major third 1 to b6 = minor sixth 1 to 6 = major sixth 1 to b7 = minor seventh 1 to 7 = major seventh Perfect intervals You will have noticed that the fourth, fifth and octave are missing from the table above. These intervals are considered ‘perfect ’, and different rules apply to them. For example, instead of ‘major’ the interval between note 1 and note four is known as a ‘perfect’ interval. There are no minor intervals when using the ‘perfect’ intervals – a perfect interval that has been lowered by a semitone is known as ‘diminished’. 1 to b4 = diminished fourth 1 to 4 = perfect fourth 1 to b5 = diminished fifth (the ‘devil’s interval’) 1 to 5 = perfect fifth 1 to b8 = diminished octave 1 to 8 = perfect octave N.B.
    [Show full text]
  • The Helmholtz-Ellis JI Pitch Notation (HEJI) | 2020 | LEGEND
    The Helmholtz-Ellis JI Pitch Notation (HEJI) | 2020 | LEGEND revised by Marc Sabat and Thomas Nicholson | PLAINSOUND MUSIC EDITION | www.plainsound.org in collaboration with Wolfgang von Schweinitz, Catherine Lamb, and M.O. Abbott, building upon the original HEJI notation devised by Marc Sabat and Wolfgang von Schweinitz in the early 2000s PYTHAGOREAN JUST INTONATION | generated by multiplying / dividing an arbitrary reference frequency by PRIMES 2 and 3 only notate a series of perfect fifths above / below a reference — 3/2 ≈ ±702:0 cents (ca. 2c wider than tempered) ::: ::: E e n v V each new accidental therefore represents 7 fifths, altering by one apotome — 2187/2048 ≈ ±113:7 cents Frequency ratios including higher prime numbers (5–47) may be precisely written by adding the following distinct accidental symbols. Custom indications for higher primes or various enharmonic substitutions may be invented as needed by simply defining further symbols representing the relevant ratio alterations. PTOLEMAIC JUST INTONATION | PRIMES up to 5 includes the consonant just major third — 5/4 ≈ ±386:3 cents (ca. 14c narrower than tempered) D d m u U F f o w W alteration by one syntonic comma — 81/80 ≈ ±21:5 cents C c l t T G g p x X alteration by two syntonic commas — 81/80 · 81/80 ≈ ±43:0 cents ~u = e |f = v alteration by one schisma to notate an exact enharmonic substitution — 32805/32768 ≈ ±2:0 cents SEPTIMAL JI | PRIME 7 includes the consonant natural seventh — 7/4 ≈ ±968:8 cents (ca. 31c narrower than tempered) < > alteration by one septimal comma — 64/63 ≈ ±27:3 cents (Giuseppe Tartini) , .
    [Show full text]
  • Just Major Thirds
    Wolfgang von Schweinitz Just Major Thirds INTONATION STUDY for two clarinets in B-flat op. 54 2010 composed for James Sullivan and Brian Walsh and the Machine Project Hammer Museum, Los Angeles PLAINSOUND MUSIC EDITON Performance Notes REHEARSAL PROCEDURE This piece is a tuning study exploring some new playing techniques for microtonal just intonation, namely the employment of non-conventional microtonal fingerings in order to produce the specific sonority of precisely tuned non-tempered intervals. Each fingering must be carefully examined and fine-tuned by embouchure at an extremely slow tempo in the first duo rehearsal(s). This initial phase of experimentation could perhaps start out with checking the fingerings for the major sixths (with a frequency ratio of 5/3) in measure 5, 8, 9, 10 and 18, as the beatings between the third and fifth partials will be particularly noticeable if the major sixths are tempered. Then the tuning of the pure major thirds and perfect fourths (and their octave expansions) should carefully be studied, memorizing the specific timbre of these intervals in the various registers. This procedure will also establish a feeling for the melodic interval of the just diatonic semitone with a size of 112 cents (and a frequency ratio of 16 : 15, which is the difference between a perfect fourth and a pure major third). The small chromatic semitone with a size of only 71 cents (25 : 24) is established as the difference between a pure major and a pure minor third (in measures 12-13, 13-14 and 22-23). When the tuning of all the fingerings used in Part I (“Diatonic Theme”) has been optimized, the additional microtonal fingerings needed in Part II (“Enharmonic Variation”) must be checked, again at an extremely slow tempo.
    [Show full text]
  • The Classical Indian Just Intonation Tuning System
    The Classical Indian Just Intonation Tuning System with 22 SRUTI-s defining the 7 SWARA-s of Hindu Classical Music combining the three different kinds of SRUTI which are understood as PRAMANA ("measuring" or "standard") SRUTI = Syntonic Comma (81/80) = 21.5 cents NYUNA ("deficient") SRUTI = Minor Chroma (25/24) = 70.7 cents Wolfgang von Schweinitz October 20 - 22, 2006 PURNA ("fullfilling") SRUTI = Pythagorean Limma (256/243) = 90.2 cents (where PURNA SRUTI may also, enharmonically, be interpreted as the sum of PRAMANA SRUTI and NYUNA SRUTI = Major Chroma (135/128 = 81/80 * 25/24) = 92.2 cents) purna nyuna purna nyuna purna nyuna purna purna pramana pramana pramana pramana pramana pramana pramana pramana pramana pramana nyuna purna nyuna purna nyuna nyuna # # # # # # " ! # " # # ! # # # <e e f m n >m n # # # # # f # n t e u f m n # # ! # # # <e e# f# m# n# e f m n >m ! n" t <f e u f m n # # # # # # " ! # " # # ! # # # <e e f m n >m n ! # # # # # f # n t e u f m n # # ! # # # <e e# f# m# n# n o u v >u n " t <f e u f m n # # " ! ! # # ! # # # <n n# o# u# v# >u n # # # # f # # n" t e u f m n # # # ! # # # <e e # f # m# n# n o u v >u n " t <f e u f m n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 # # ! # # ! <e e# f# m# n# >m n " # # f n" t e# u f# m# n# $ # ! <e e# f# m# n# n# o# u# v# >u n " t <f e#u f# m# n# Sa ri ri Ri Ri ga ga Ga Ga ma ma Ma Ma Pa dha dha Dha Dha ni ni Ni Ni Sa 1 25 21 256 135 16 10 9 7 32 6 5 81 4 27 45 64 729 10 3 25 128 405 8 5 27 7 16 9 15 243 40 2 Ratio 1 24 20 243 128 15 9 8 6 27 5 4 64 3 20 32 45
    [Show full text]