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Topic: Diatonic set theory

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	Diatonic scale - Wikipedia, the free encyclopedia
		The modern major and minor scales are diatonic, as are all of the so-called 'church' modes.
		Technically speaking, diatonic scales are obtained from a chain of six successive fifths in some version of meantone temperament, and resulting in two tetrachords separated by intervals of a whole tone.
		The scales are the diatonic scale, the ascending minor scale, the harmonic minor scale, the harmonic major scale, and the locrian major scale; of these, all but the last are well-known and in fact consitute the backbone of diatonic practice when taken together.
	en.wikipedia.org /wiki/Diatonic (1238 words)

	Diatonic scale (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-11-03)
		In music theory, a diatonic scale is a scale whose notes are built on the natural staff positions of lines and spaces, with no accidentals, with or without a key signature.
		Diatonic music is written primarily using the notes from a diatonic scale; similarly, diatonic chords and diatonic intervals use notes from such a scale.
		Diatonic set theory describes the following properties: maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity.
	www.mp3.fm.cob-web.org:8888 /Diatonic_scale.htm (503 words)

	Diatonic
		Diatonic music is written primarily using the notes from a diatonic scale; similarly, diatonic
		These unique relationships are as follows: Only certain divisions of the octave, 12 and 20 included, allow uniqueness, coherence, and transpositional simplicity, and that only the diatonic and pentatonic subsets of the 12 tone chromatic set follow these constraints (Balzano, 1980, 1982).
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	www.mp3.fm /Diatonic.htm (320 words)

	Pitch Class Sets
		For example, if the interval vector of the PC Set is: <324222> (6-Z13), and if you transpose the PC Set by a minor third, you will have 4 common tones between the original PC Set and the transposed PC Set.
		If any entry of the interval vector is equal to the number of pitch classes in the set, then the PC Set can be transposed to itself with all pitch classes in common.
		A PC Set which can invert to itself (on some axis of inversion) is said to be "Inversionally Symmetric".
	composertools.com /Theory/PCSets/PCSets8.htm (809 words)

	SET THEORY, Part 2
		Set Class A set class includes a pitch set of a particular type, its inversion, the notes in any ordered combination, in all eleven transpositions.
		In the table that follows, notice that six possible set classes are listed for the dyad, a two-note set of pitches.
		As illustrated in the next example, the major triad 047 is not included in the basic list of trichord set classes because the prime form of this pattern is 037.
	jan.ucc.nau.edu /~krr2/settheory/settheory2.html (1680 words)

	Music: Theory, etc.
		In diatonic or tonal theory, intervals are labelled according to their diatonic function and according to the number of members or degrees they span in a diatonic scale.
		Post-tonal or atonal theory, originally developed for equal tempered European classical music written using the twelve tone technique or serialism, integer notation is often used, most prominently in musical set theory.
		In atonal or musical set theory there are numerous types of intervals, the first being ordered pitch interval, the distance between two pitches upward or downward.
	google.com /notebook/public/09934432889036235243/BDTZ3LAoQx7bCt7gh (5868 words)

	John Hawks Anthropology Weblog : 2006 07
		Pitch-class set theory (3), the study of a discrete 12-note quotient space, was developed as a means of confronting the analytical challenges posed by "post-tonal" music of the 20th century, whose harmonic materials are more varied and complex than those in most earlier music.
		Diatonic set theory (4, 5) investigates the subtle and beautiful relationship between the 12-note chromatic scale and diatonic scales such as the C major scale, with seven unequally spaced notes per octave (a scale type of great importance in many styles of music).
		Scale theory (6, 7) studies structural properties of scales and their subscales more broadly, allowing variation in both chromatic and diatonic cardinalities and occasionally engaging considerations of tuning and acoustics.
	johnhawks.net /weblog/2006/07/11 (3356 words)

	SET THEORY, Part 1
		Diatonic Sets A set is a collection of like objects, a class of elements.
		This set of sets includes all trichords that contain the intervals m2, M2, and m3.
		Since all of these sets share the same interval content, they and all their permutations are members of a collection of like objects, a set of sets.
	jan.ucc.nau.edu /~krr2/settheory/settheory1.html (807 words)

	[No title]
		This work includes both a version of what we call set theory, arrived at by the author largely independently of American theory, and various compositional theories.
		Vuza's paper, "Supplementary Sets: Theory and Algorithms," traced the development of his work from its genesis in the pitch domain to its complex unfolding in the rhythmic domain, giving a summary of some of his results.
		Items appearing in MTO may be saved and stored in electronic or paper form, and may be shared among individuals for purposes of scholarly research or discussion, but may not be republished in any form, electronic or print, without prior, written permission from the author(s), and advance notification of the editors of MTO.
	mto.societymusictheory.org /issues/mto.95.1.1/mto.95.1.1.clampitt.rev (942 words)

	The Regular Mapping Paradigm (Site not responding. Last check: 2007-11-03)
		When a paradigm has held sway for as long as the do re mi of the diatonic scale it's only to be expected that some people have found it inadequate to contain their ideas.
		A regular temperament class is a set of regular temperaments that have the same pattern of different sized intervals, but different specific sizes.
		In terms of group theory, the mapping is a homomorphism from one group of intervals to another.
	www.microtonal.co.uk /paradigm.html (7663 words)

	The Dana School of Music at Youngstown State University
		Applications of theory of diatonic harmony; development of independent study and research projects in such areas as analysis, aural perception, scoring, and arranging.
		Applied instruction in music theory of chromatic harmony; development of independent study and research projects in such areas as analysis, aural perception, scoring, and arranging.
		Applied instruction in music theory of tonal and/or non-tonal music; development of independent study and research projects in such areas as analysis, aural perception, scoring, and arranging.
	www.fpa.ysu.edu /music/main/mustheor.htm (633 words)

	Harp On! Music Theory II (Site not responding. Last check: 2007-11-03)
		Diatonic scales are constructed of major-seconds (2 halftone steps), and minor-seconds (1 halftone step).
		Diatonic triads are 3-note chords that consist entirely of notes found on the diatonic scale.
		Diatonic short harmonica players can use this scale by playing in second position or third position using a number of bends to achieve the correct notes which in itself adds feeling & a more bluesy quality to the music.
	www.angelfire.com /music/HarpOn/theory2.html (4634 words)

	Timothy Johnson - Ithaca College
		He teaches in all areas of the theory and sightsinging curriculum, ranging from introductory courses for first-year students to upper-level and graduate courses.
		His textbook, Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals (Key College Publishing, 2003), is the first introductory, undergraduate-level book published on diatonic set theory.
		This textbook introduces a strong link between introductory pedagogy and recent scholarship in music theory by relating concepts in diatonic set theory directly to the study of music fundamentals through pedagogical exercises and instructions.
	faculty.ithaca.edu /tjohnson (631 words)

	MTMW 97 - Abstracts
		Hugo Wolf's setting of Eduard Morike's Das verlassene Mägdlein is a remarkable example of the "extended tonality" that characterizes late-nineteenth-century compositional practice.
		The curricular material based on maximally-even sets explores how different collections of notes may be distributed evenly among the 12-note chromatic collection and the 7-note diatonic collection to form many of the principal building blocks of introductory music theory.
		Similarly, Battin's critique of aesthetics education is that it is "for the most part theory driven, not driven to theory." Her proposed remedy is to begin with specific puzzle cases about aesthetic objects which lead to a discovery and discussion of theoretical issues.
	www.wmich.edu /mus-theo/mtmw97/mtmw97_abs.html (4798 words)

	Pitch Class Sets
		The prime forms of abstract complements are listed side-by-side in the PC Set table found in the Appendix (except for the sets of 6 pitch classes).
		The set is "self complementary", that is, the set and it's complement have the same prime form.
		The set and its complement are Z-related: Two sets with the same interval vector but which can not be reduced to the same Prime Form by transposition or inversion.
	composertools.com /Theory/PCSets/PCSets7.htm (664 words)

	Stephen McAdams: Psychological constraints on form-bearing dimensions in music (Contemporary Music Review, 1989). ...
		in the major diatonic scale there are series of two and three major seconds separated by minor seconds), and to the existence of rare or distinctive intervals in the set (e.g.
		What Meyer's theory proposes however is that we recognize these processes as basic categories of melodic structure of which there are a very small number.
		I have tried to set out in this article a number of ideas about constraints of a psychological nature on perceptual dimensions that are either well-known bearers of form, such as pitch and duration, or those that are serious candidates, such as timbre.
	www.zainea.com /mcadams.htm (9160 words)

	Aspects of Early Major-Minor Tonality: Chapter 1 (Site not responding. Last check: 2007-11-03)
		The conflict would seem to be between the desire to create a theory that is all-encompassing versus the willingness to accept a theory limited in scope to a more narrowly defined body of literature and to allow for multiple theories when necessary.
		The diatonic collection (or subsets of it) is frequently said to be the basis for music that is tonal in this general sense.
		According to their formulation of the theory, designated as "Structure and Prolongation," a chord would be determined to be a harmony if it functioned as a member of one of five basic progressions.
	bama.ua.edu /~danderso/diss/chap1.htm (8940 words)

	Harp On! Music Theory I (Site not responding. Last check: 2007-11-03)
		Music theory was formulated by observing repeating patterns in music literature and expressing them as "rules." It seems unlikely that early composers were aware of these "rules" when writing the music from which they are drawn.
		The key signature is a set of # and b symbols that indicate which notes are to be raised or lowered a halftone to produce the diatonic scale of the desired key.
		Music theory comes in a very thick book that is used for four semesters and adds up to 12 units or more of college work.
	www.angelfire.com /music/HarpOn/theory1.html (3527 words)

	Music Theory Course Catalog
		Focuses on diatonic tonal language of the Common Practice period, with emphasis on the phrase as the vehicle for musical motion.
		Theories of musical space and time (rhythm, dimensions, proportion), with attention to diverse musical practices, and to scientific analysis, including computer spectrographs, of sound and time.
		Studies Beethoven’s quartets in light of modern historical research and analytical theory, with attention to their harmonic, contrapuntal, motivic, and structural formation, and the implications of these for understanding and performance.
	www.newenglandconservatory.edu /catalog/music_theory.html (3679 words)

	Welcome to the Music Department
		The Music Theory program at the University at Buffalo is one of the most successful in the U.S., with recent graduates moving on to full-time jobs at Yale, Temple, Swarthmore, Bowling Green, Ithaca College, American University, Arizona State, and many other fine universities and colleges around the world.
		Students are given a thorough grounding in the standard disciplines, such as history of theory, Schenkerian analysis, and set theory, while being expected to master promising new areas of research, such as Neo-Riemannian transformations, diatonic set theory, and intertextuality.
		The Department offers two graduate degrees in Music Theory: the Ph.D. in Music Theory and Historical Musicology (students may specialize in either area), and a Master of Arts in Theory.
	www.music.buffalo.edu /theory/index.shtml (474 words)

	Diatonic set theory - Wikipedia, the free encyclopedia
		Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and insights of discrete mathematics to properties of the diatonic collection such as maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity.
		Music theorists working in diatonic set theory include Eytan Agmon, Gerald J. Balzano, Norman Carey, David Clampitt, John Clough, Jay Rahn, and mathematician Jack Douthett.
		A number of key concepts were first formulated by David Rothenberg, who published in the journal Mathematical Systems Theory, and Erv Wilson, working entirely outside of the academic world.
	en.wikipedia.org /wiki/Diatonic_set_theory (268 words)

	Roman numeral and figured bass 2
		a flat or sharp in front of a figure lowers or raises the diatonic pitch by a half step.
		The case of the numeral accounts for the altered diatonic pitches.
		The sharp symbol in the figure means "raised," not necessarily "sharp." The distinction lies in theory, not notation.
	www.musictheoryresources.com /members/FA_roman_num2.htm (378 words)

	Math Across the Curriculum at Mount Holyoke
		As students study diatonic music theory, they simultaneously deal with the corresponding mathematical properties that describe aspects of and relationships within a diatonic set in a twelve-note universe.
		Through physical simulation and other investigations, students discover the ways in which medieval theories of optimal geometric form shaped the aesthetics of design in general and the plans of churches in particular.
		In moving from the original records to data sets, from hand tabulations to computer-assisted analyses, they learn to identify and interpret patterns in numerical data and to present their results in statistical displays and well-documented essays.
	www.mtholyoke.edu /courses/rschwart/mac (682 words)

	GetGuitarLessons: The diatonic 3 note per string vs. the pentatonic scale
		This scale is also the basis for mode theory, which is very important in music theory and advanced guitar playing.
		This is the root position of the diatonic scale, what I called Version 1 in the manuscript.
		This is the root position of the diatonic scale, what I called Version 2 in the manuscript.
	www.getguitarlessons.com /guitar/intermediate/diatonic_I.php (177 words)

	IU Music Theory Newletter -- 2004
		Professor Hook presented a paper titled “Signature Transformations” at the SMT meeting in Madison in November; this paper is slated to appear in written form in a volume of essays to be published in memory of John Clough.
		She continues to teach large-lecture music theory classes, and will be giving a paper at this fall's College Music Society conference on how to use sound effectively in large lectures.
		Reading music theory journals, European 20th-century history, late 15th- and early 16th-century vernacular Dutch music theory and numerous contemporary writers on Southwestern subjects, fiction and otherwise, are strong interests.
	theory.music.indiana.edu /newsletter/newsletter2004.html (3358 words)

	THE HARTT SCHOOL : MUSIC-DANCE-THEATER (Site not responding. Last check: 2007-11-03)
		The Graduate Music Theory Placement Examination is required for all entering Master's Degree students.
		Entering graduate students are to prepare for the examination by studying the following topics: treble, alto, tenor, and bass clefs; modal, diatonic, and chromatic melodies; simple and compound meters, modulation to closely-related keys.
		The examination consists of performing at the piano: diatonic and chromatic chord progressions, cadences, figured bass, and melody harmonization.
	www.hartford.edu /HARTT/adm-how-grad-mustheory.htm (647 words)

	GMTH 2. Jahrgang 2005, Ausgabe 2 - ISSN 1862-6742 - Neo-Riemannian Theory
		(1) Neo-Riemannian Theory (NRT) denotes a range of speculative and analytical studies concerned with the relation of the mathematical structure of tonal pitch materials (e.g.
		NRT arose in response to the failure of traditional theories of tonality to adequately describe as ‘coherent’ certain chromatic repertoires of the late nineteenth century (music of Wagner, Franck, et al.).
		NRT is a sub-discipline of transformational theory, though it also shares certain perspectives and insights with diatonic set theory.
	www.gmth.de /www/artikel/2005-07-09_08-20-25_7 (741 words)

	MUS T658 8889 Seminar in Music Theory: Musical Spaces and Transformations (Site not responding. Last check: 2007-11-03)
		Within the last two decades, a variety of sophisticated techniques from group theory and other areas of mathematics have been applied to the study of music.
		Our study will cover essential concepts in the areas generally known as transformation theory and neo-Riemannian theory; there will also be some intersections with topics in pitch-class set theory, including diatonic set theory (which explores the remarkably subtle and complex relationships between diatonic and chromatic spaces).
		Prerequisites: Students enrolling in T658 should be familiar with the fundamentals of pitch-class set theory as covered, for instance, in T556, Analysis of Music Since 1900.
	www.indiana.edu /~deanfac/blspr05/mus/mus_t658_8889.html (375 words)

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