DOCSLIB.ORG

Chapter 8: Extended Tetrachord Classification

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chapter 8: Extended Tetrachord Classification CHAPTER 8: EXTENDED TETRACHORD CLASSIFICATION Chapter 7 introduced the notion of strange circles: using various circles of musical intervals as equivalence classes to which input pitch-classes are assigned. It illustrated this concept by ana- lyzing the internal structure of a network that was trained to identify four different types of tetra- chords. Chapter 8 provides a more complex example of this concept. It describes additional formulae that can be used to define twelve different types of tetrachords for each of the twelve major musical keys. It then reports the training of a multilayer perceptron that learned to classify an input tetrachord into these different tetrachord types. This is a more complex network, requir- ing seven hidden units to converge on a solution to this classification problem. However, this more complicated network can still have its internal structure interpreted. One reason for this is because it, like the Chapter 7 network, organizes input pitch-classes using strange circles. We provide an interpretation of this network, introducing an additional interpretative technique (exam- ining bands in jittered density plots). We then illustrate how the structure of this extended tetra- chord network provides an elegant example of coarse coding. 8.1 Extended Tetrachords .................................................. 2 8.2 Classifying Extended Tetrachords .............................. 5 8.3 Interpreting the Extended Tetrachord Network .......... 7 8.4 Bands and Coarse Coding ......................................... 22 8.5 References ................................................................... 25 © Michael R. W. Dawson 2014 Chapter 8 Classifying Extended Tetrachords 2 8.1 Extended Tetrachords Figure 7-27. Musical notation for twelve different tetrachord types, each using C as the root note. 8.1.1 Extended Chords Therefore the formula for the C major triad is 1-3-5. Adding the seventh note of the scale, Chapter 7 described training a multilayer B, produces the C major seventh tetrachord, perceptron to classify four different types of which follows the formula 1-3-5-7. This was tetrachords (major 7, minor 7, dominant 7, one of the added note tetrachords that we minor 7 flat 5), and presented a detailed studied earlier in this chapter. analysis of the internal structure of this net- work. The point of that example was to use More chords can be created by manipu- a fairly simple musical problem to illustrate lating formulae like those provided in the how an artificial neural network can organize previous paragraph. For instance, one input pitch-classes in terms of their mem- could flatten the third and the fifth note in the bership in various ‘strange circles’ (i.e. inter- formula 1-3-5-7. This produces the formula val-based equivalence classes). In this 1-♭3-5-♭7; if C is the root this is the set of chapter we turn to a more complicated mu- sical problem, involving a larger set of differ- notes [C, E♭, G, B♭], which defines the C ent types of tetrachords. As this problem is minor seventh tetrachord. Note that the flat- more complex, the multilayer perceptron that tened third and seventh notes do not belong solves it requires more hidden units. How- to the C major scale. ever, these hidden units also organize inputs into a variety of strange circles which assists In jazz one often finds extended chords, the interpretation of the network’s internal which use formulae that add notes that fall structure. beyond the octave range of a major scale. For example, if one adds the D that is an The four tetrachords that we explored in octave higher than the second note in the C Chapter 7 were all examples of added note major scale to the C major triad, then one tetrachords. That is, each tetrachord could produces the Cadd9 tetrachord (C, E, G, D). be described as being constructed from a The formula for this chord is 1-3-5-9. triad based upon different notes that be- longed to a scale, with an fourth note added Figure 8-1 provides the musical notation, on top of this triad (see Figure 7-15). The and the musical chord symbol, for twelve fourth note also belonged to the scale. different types of tetrachords. Each of these example tetrachords uses C as the root note Another general approach to building tet- of the chord. Four of these tetrachord types rachords produces a greater variety of chord were used to train the multilayer perceptron types. One begins with a triad formula. For that was described earlier in this chapter. instance, if one takes the first, third, and fifth The other eight are new; the formula for notes of the C major scale (C, E, G, see each is provided in Table 8-1. Figure 7-15) the result is the C major triad. © Michael R. W. Dawson 2014 Chapter 8 Classifying Extended Tetrachords 3 Tetrachord Type Formula Example Forte Number Diminished Seventh 1-♭3-♭5-♭♭7 C7 4-28(3) Minor Seventh 1-♭3-5-♭7 Cm7 4-26(12) Minor Sixth 1-♭3-5-6 Cm6 4-27 Minor, Major Seventh 1-♭3-5-7 Cm(maj7) 4-19 Minor Added Ninth 1-♭3-5-9 Cm(add9) 4-14 Seventh, Flat Fifth 1-3-♭5-♭7 C7♭5 4-25(6) Augmented Seventh 1-3-♯5-♭7 C+7 4-(24(12) Seventh 1-3-5-♭7 C7 4-27 Sixth 1-3-5-6 C6 4-26(12) Major Seventh 1-3-5-7 Cmaj7 4-20(12) Added Ninth 1-3-5-9 Cadd9 4-22 Seventh, Suspended Fourth 1-4-5-♭7 C7sus4 4-23(12) Table 8-1. The names and formulas for twelve different types of tetrachords. An example of each is provided in Figure 8-1. The formulae that are provided in Table 8-1 are designed to work in the context of When we train a multilayer perceptron to any major scale. The numbers in each for- classify the twelve different types of tetra- mula refer to a note’s position in a particular chords in Table 8-1, we will again be using scale. That is, 1 is the first note in a particu- pitch-class representation. Because of this, lar scale, 3 is the third note in a particular notes in extended chords like the added scale, and so on. This means that there are ninth chord will be moved back into the 12 different versions of each of the chord range of a single octave. As well, when we types listed in Table 8-1: one for each of the interpret the internal structure of the net- twelve possible major scales. work, we will be exploiting the properties of some of the circles of intervals that were When these formulae are used to create introduced in earlier sections of the current tetrachords in different keys, some interest- chapter. ing relationships between chords arise. Consider the 6 chord, whose formula is 1-3- For these reasons it is useful to repre- 5-6. In the context of the C major scale this sent the various tetrachords in another visu- produces the C6 chord whose notes are [C, al format. In particular, we can illustrate a E, G, A]. Now consider applying the formula tetrachord in a circle of pitch-classes (in par- for the minor seventh tetrachord (1-♭3-5-♭7) ticular, a circle of minor seconds) by drawing in four spokes that represent which four in the context of the A major scale. This notes are present in a particular chord. produces the Am7 chord whose notes are Drawing such a diagram will illustrate a par- [A, C, E, G]. Note that these notes are iden- ticular chord in the context of a specific ma- tical to those of C6; musically speaking Am7 jor key. However, this diagram represents is identical to an inversion of C6. Similarly, the structure of a tetrachord type for any the dominant seventh chord is the inversion key: if one rigidly rotates the spokes do a of a minor sixth tetrachord in a different key. different position in the circle, then it will provide the notes for the same type of tetra- In other words, the same set of four chord, but relative to some other musical pitch-classes can have two different chord key. names. If we train a network to identify tet- rachord types, then it must be trained to Pitch-class diagrams of the first six tetra- generate both of these chord names to one chords provided in Figure 8-1 or in Table 8-1 set of four input pitch-classes. Table 7-8 are provided in Figure 8-2. Figure 8-3 pro- also provides the Forte numbers of each of vides similar diagrams for the other six tet- these chord types. Note that tetrachords rachord types. that are related by inversion – or tetrachords that can represent different names for the same set of input pitch-classes – have the same Forte number. © Michael R. W. Dawson 2014 Chapter 8 Classifying Extended Tetrachords 4 Figure 8-2. Pitch-class diagrams of the first Figure 8-3. Pitch-class diagrams of the sec- six tetrachords from the musical score in Fig- ond six tetrachords from the musical score in ure 8-1. Figure 8-1. All of the chords presented in Figures 8-2 and 8-3 are created in the context of the C major scale. The structure of the spokes in the diagrams provides an interesting per- spective on the similarities and differences between various tetrachord types. For in- stance it is immediately apparent that both the diminished tetrachord and the seventh flattened fifth tetrachord include two pairs of notes that belong to the same circle of tri- tones, because both diagrams include two long spokes that bisect the circle.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • MTO 20.2: Wild, Vicentino's 31-Tone Compositional Theory
    Volume 20, Number 2, June 2014 Copyright © 2014 Society for Music Theory Genus, Species and Mode in Vicentino’s 31-tone Compositional Theory Jonathan Wild NOTE: The examples for the (text-only) PDF version of this item are available online at: http://www.mtosmt.org/issues/mto.14.20.2/mto.14.20.2.wild.php KEYWORDS: Vicentino, enharmonicism, chromaticism, sixteenth century, tuning, genus, species, mode ABSTRACT: This article explores the pitch structures developed by Nicola Vicentino in his 1555 treatise L’Antica musica ridotta alla moderna prattica . I examine the rationale for his background gamut of 31 pitch classes, and document the relationships among his accounts of the genera, species, and modes, and between his and earlier accounts. Specially recorded and retuned audio examples illustrate some of the surviving enharmonic and chromatic musical passages. Received February 2014 Table of Contents Introduction [1] Tuning [4] The Archicembalo [8] Genus [10] Enharmonic division of the whole tone [13] Species [15] Mode [28] Composing in the genera [32] Conclusion [35] Introduction [1] In his treatise of 1555, L’Antica musica ridotta alla moderna prattica (henceforth L’Antica musica ), the theorist and composer Nicola Vicentino describes a tuning system comprising thirty-one tones to the octave, and presents several excerpts from compositions intended to be sung in that tuning. (1) The rich compositional theory he develops in the treatise, in concert with the few surviving musical passages, offers a tantalizing glimpse of an alternative pathway for musical development, one whose radically augmented pitch materials make possible a vast range of novel melodic gestures and harmonic successions.
    [Show full text]
  • Major and Minor Scales Half and Whole Steps
    Dr. Barbara Murphy University of Tennessee School of Music MAJOR AND MINOR SCALES HALF AND WHOLE STEPS: half-step - two keys (and therefore notes/pitches) that are adjacent on the piano keyboard whole-step - two keys (and therefore notes/pitches) that have another key in between chromatic half-step -- a half step written as two of the same note with different accidentals (e.g., F-F#) diatonic half-step -- a half step that uses two different note names (e.g., F#-G) chromatic half step diatonic half step SCALES: A scale is a stepwise arrangement of notes/pitches contained within an octave. Major and minor scales contain seven notes or scale degrees. A scale degree is designated by an Arabic numeral with a cap (^) which indicate the position of the note within the scale. Each scale degree has a name and solfege syllable: SCALE DEGREE NAME SOLFEGE 1 tonic do 2 supertonic re 3 mediant mi 4 subdominant fa 5 dominant sol 6 submediant la 7 leading tone ti MAJOR SCALES: A major scale is a scale that has half steps (H) between scale degrees 3-4 and 7-8 and whole steps between all other pairs of notes. 1 2 3 4 5 6 7 8 W W H W W W H TETRACHORDS: A tetrachord is a group of four notes in a scale. There are two tetrachords in the major scale, each with the same order half- and whole-steps (W-W-H). Therefore, a tetrachord consisting of W-W-H can be the top tetrachord or the bottom tetrachord of a major scale.
    [Show full text]
  • Specifying Spectra for Musical Scales William A
    Specifying spectra for musical scales William A. Setharesa) Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706-1691 ~Received 5 July 1996; accepted for publication 3 June 1997! The sensory consonance and dissonance of musical intervals is dependent on the spectrum of the tones. The dissonance curve gives a measure of this perception over a range of intervals, and a musical scale is said to be related to a sound with a given spectrum if minima of the dissonance curve occur at the scale steps. While it is straightforward to calculate the dissonance curve for a given sound, it is not obvious how to find related spectra for a given scale. This paper introduces a ‘‘symbolic method’’ for constructing related spectra that is applicable to scales built from a small number of successive intervals. The method is applied to specify related spectra for several different tetrachordal scales, including the well-known Pythagorean scale. Mathematical properties of the symbolic system are investigated, and the strengths and weaknesses of the approach are discussed. © 1997 Acoustical Society of America. @S0001-4966~97!05509-4# PACS numbers: 43.75.Bc, 43.75.Cd @WJS# INTRODUCTION turn closely related to Helmholtz’8 ‘‘beat theory’’ of disso- nance in which the beating between higher harmonics causes The motion from consonance to dissonance and back a roughness that is perceived as dissonance. again is a standard feature of most Western music, and sev- Nonharmonic sounds can have dissonance curves that eral attempts have been made to explain, define, and quantify differ dramatically from Fig.
    [Show full text]
  • View the Analyses of Webern’S Pieces
    UNIVERSITY OF CINCINNATI Date: May 24, 2005 __________________ I, Hyekyung Park __________________________________________________, hereby submit this work as part of the requirements for the degree of: Master of Music in: Music Theory It is entitled: Transformational Networks and Voice Leadings in the First Movement of Webern’s Cantata No. 1, Op. 29. This work and its defense approved by: Chair: Dr. Steven Cahn Dr. David Berry Dr. Earl Rivers TRANSFORMATIONAL NETWORKS AND VOICE LEADINGS IN THE FIRST MOVEMENT OF WEBERN’S CANTATA No. 1, OP. 29. A thesis submitted to the Division of Graduate Studies and Research of the University of Cincinnati In partial fulfillment of the requirement for the degree of MASTER OF MUSIC In the Division of Composition, Musicology, and Theory of the College-Conservatory of Music 2005 by Hyekyung Park B.M. Ewha Womans Univerisity, S. Korea 2002 Committee Chair: Steven Cahn, Ph.D. Abstract This thesis examines the use of transformation approaches for Anton Webern’s the First Cantata Op.29, No.1. The thesis is divided primarily into two parts: the summary of a theory of transformation and analyses of Op.29, No.1, which is studied in a transformation attitude. After presenting the introduction, Chapter 1 summarizes a theory of transformation based on David Lewin’s analyses about Webern’s works, and it researches three different approaches of voice leading, especially focusing on Joseph Straus’s transformational attitude. Before getting to the analyses, Chapter 2 presents the background of Webern’s Cantatas No.1, Op.29 as a basic for understanding this piece. The main contents of Chapter 2 are Webern’s thought about Op.29 and the reason why he collected three different poems as one work.
    [Show full text]
  • Stravinsky and the Octatonic: a Reconsideration
    Stravinsky and the Octatonic: A Reconsideration Dmitri Tymoczko Recent and not-so-recent studies by Richard Taruskin, Pieter lary, nor that he made explicit, conscious use of the scale in many van den Toorn, and Arthur Berger have called attention to the im- of his compositions. I will, however, argue that the octatonic scale portance of the octatonic scale in Stravinsky’s music.1 What began is less central to Stravinsky’s work than it has been made out to as a trickle has become a torrent, as claims made for the scale be. In particular, I will suggest that many instances of purported have grown more and more sweeping: Berger’s initial 1963 article octatonicism actually result from two other compositional tech- described a few salient octatonic passages in Stravinsky’s music; niques: modal use of non-diatonic minor scales, and superimposi- van den Toorn’s massive 1983 tome attempted to account for a tion of elements belonging to different scales. In Part I, I show vast swath of the composer’s work in terms of the octatonic and that the rst of these techniques links Stravinsky directly to the diatonic scales; while Taruskin’s even more massive two-volume language of French Impressionism: the young Stravinsky, like 1996 opus echoed van den Toorn’s conclusions amid an astonish- Debussy and Ravel, made frequent use of a variety of collections, ing wealth of musicological detail. These efforts aim at nothing including whole-tone, octatonic, and the melodic and harmonic less than a total reevaluation of our image of Stravinsky: the com- minor scales.
    [Show full text]
  • The Consecutive-Semitone Constraint on Scalar Structure: a Link Between Impressionism and Jazz1
    The Consecutive-Semitone Constraint on Scalar Structure: A Link Between Impressionism and Jazz1 Dmitri Tymoczko The diatonic scale, considered as a subset of the twelve chromatic pitch classes, possesses some remarkable mathematical properties. It is, for example, a "deep scale," containing each of the six diatonic intervals a unique number of times; it represents a "maximally even" division of the octave into seven nearly-equal parts; it is capable of participating in a "maximally smooth" cycle of transpositions that differ only by the shift of a single pitch by a single semitone; and it has "Myhill's property," in the sense that every distinct two-note diatonic interval (e.g., a third) comes in exactly two distinct chromatic varieties (e.g., major and minor). Many theorists have used these properties to describe and even explain the role of the diatonic scale in traditional tonal music.2 Tonal music, however, is not exclusively diatonic, and the two nondiatonic minor scales possess none of the properties mentioned above. Thus, to the extent that we emphasize the mathematical uniqueness of the diatonic scale, we must downplay the musical significance of the other scales, for example by treating the melodic and harmonic minor scales merely as modifications of the natural minor. The difficulty is compounded when we consider the music of the late-nineteenth and twentieth centuries, in which composers expanded their musical vocabularies to include new scales (for instance, the whole-tone and the octatonic) which again shared few of the diatonic scale's interesting characteristics. This suggests that many of the features *I would like to thank David Lewin, John Thow, and Robert Wason for their assistance in preparing this article.
    [Show full text]
  • An Explanation of Anomalous Hexachords in Four Serial Works by Igor Stravinsky
    University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 8-2011 An Explanation of Anomalous Hexachords in Four Serial Works by Igor Stravinsky Robert Sivy [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Part of the Musicology Commons, and the Music Theory Commons Recommended Citation Sivy, Robert, "An Explanation of Anomalous Hexachords in Four Serial Works by Igor Stravinsky. " Master's Thesis, University of Tennessee, 2011. https://trace.tennessee.edu/utk_gradthes/1025 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Robert Sivy entitled "An Explanation of Anomalous Hexachords in Four Serial Works by Igor Stravinsky." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Master of Music, with a major in Music. Brendan P. McConville, Major Professor We have read this thesis and recommend its acceptance: Barbara Murphy, Donald Pederson Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) An Explanation of Anomalous Hexachords in Four Serial Works by Igor Stravinsky A Thesis Presented for the Master of Music Degree The University of Tennessee, Knoxville Robert Jacob Sivy August 2011 Copyright © 2011 by Robert Jacob Sivy All rights reserved.
    [Show full text]
  • Divisions of the Tetrachord Are Potentially Infinite in Number
    EDITOR'S INTRODUCTION ''''HEN I WAS A young student in California, Lou Harrison suggested that I send one of my first pieces, Piano Study #5 (forJPR) to a Dr. Chalmers, who might publish it in his journal Xenbarmonikon. Flattered and fascinated, I did, and John did, and thus began what is now my twenty year friendship with this polyglot fungus researcher tuning guru science fiction devotee and general everything expert. Lou first showed me the box of papers, already called Divisions ofthe Tetracbord, in 1975. I liked the idea of this grand, obsessive project, and felt that it needed to be availablein a way that was, likeJohn himself, out of the ordinary. When Jody Diamond, Alexis Alrich, and I founded Frog Peak Music (A Composers' Collective) in the early 80S, Divisions (along with Tenney's then unpublished Meta + Hodos) was in my mind as one of the publishing collective's main reasons for existing, and for calling itself a publisher of"speculative theory." The publication of this book has been a long and arduous process. Re­ vised manuscripts traveled with me from California to Java and Sumatra (John requested we bring him a sample of the local fungi), and finally to our new home in New Hampshire. The process of writing, editing, and pub­ lishing it has taken nearly fifteen years, and spanned various writing tech­ nologies. (When John first started using a word processor, and for the first time his many correspondents could actually read his long complicated letters, my wife and I were a bit sad-we had enjoyed reading his com­ pletely illegible writing aloud as a kind of sound poetry).
    [Show full text]
  • Tetrachords of Turkish Makams: How to Make Sense of Makam Theory
    Tetrachords of Turkish makams: how to make sense of makam theory Jim Garrett April 19, 2019 Contents 1 Introduction 2 2 Tetrachords: What are they, how do they t in? 3 3 Specic tetrachords 4 3.1 3 tetrachords with which we're already familiar . 4 3.2 Three microtonal tetrachords . 6 3.3 Hicaz and Nikriz . 7 3.4 Additional tetrachords based on U³³ak . 8 3.4.1 Hüseyni . 8 3.4.2 Saba . 9 3.5 Additional tetrachords based on Segâh . 9 3.5.1 Müstear . 9 3.5.2 Hüzzam . 10 3.5.3 Eksik Segâh . 10 3.6 Pençgâh . 10 3.7 Summary of tetrachords . 10 3.7.1 Modulations . 11 4 What is a makam? 12 5 Additional resources 12 1 6 Additional context 13 6.1 Cultural context . 13 6.2 A plea for attention to tonality . 14 6.3 Makam theory is not really theory . 16 7 Acknowledgements 16 1 Introduction You're probably reading this because you're wondering what makam theory is all about. Probably you've visited several web sites, but it hasn't quite clicked. You've gotten information but you're not sure what it means, or how it ts together. You've seen musical snippets that look like scales, but then you've read that makams are not scales. Maybe you're wondering if this body of knowledge is accessible at all. If this describes your experience, then this essay is written just for you! I believe most introductory resources try to make analogies to scales, because scales are what Western musicians are familiar with.
    [Show full text]
  • On Chords Generating Scales; Three Compositions for Orchestra
    INFORMATION TO USERS This reproduction was made from a copy of a document sent to us for microfilming. While the most advanced technology has been used to photograph and reproduce this document, the quality of the reproduction is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help clarify markings or notations which may appear on this reproduction. 1. The sign or “target” for pages apparently lacking from the document photographed is “Missing Page(s)”. If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure complete continuity. 2. When an image on the film is obliterated with a round black mark, it is an indication of either blurred copy because of movement during exposure, duplicate copy, or copyrighted materials that should not have been filmed. For blurred pages, a good image of the page can be found in the adjacent frame. If copyrighted materials were deleted, a target note will appear listing the pages in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photographed, a definite method of “sectioning” the material has been followed. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete.
    [Show full text]