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	Hexachord - Wikipedia, the free encyclopedia
		In each hexachord, all adjacent pitches are a whole tone apart, except for the middle two, which are separated by a half tone.
		In musical set theory, a hexachord is a collection of six pitch classes, often one of two (complementary) ordered hexachords in a tone row or set form.
		Hexachords may be used to create invariance and combinatoriality, and often a melody and its accompaniment will be drawn from different hexachords.
	en.wikipedia.org /wiki/Hexachord (409 words)

	Compositional techniques of Milton Babbitt (Site not responding. Last check: 2007-10-08)
		The first trichord is comprised of a transposed version of the 3rd, 4th and 5th notes of the "theme" hexachord, while the second trichord is composed of a transposition of the 2nd, 3rd and 4th notes of the for-mentioned hexachord.
		Hexachord I of the tenor line equals Hexachord II of the bass voice, and Hexachord I of the bass voice is identical to Hexachord II of the tenor voice.
		In particular, they adhere to the one pattern discussed earlier: "the first hexachord of Variation I and III is identical to the retrograde of one of the other voices in that hexachord." The first hexachord in the soprano voice is as follows: B natural, D natural, E flat, G flat, D flat, and E natural.
	homepage.mac.com /coltvalenti/iblog/C631812141/E493713625 (2482 words)

	Smooth experiment
		The order of pitch classes in the first hexachord was determined by randomly choosing a starting (white) pitch class, then randomly picking a direction (clockwise or anticlockwise) and moving round the clock face systematically in that direction, picking out the whites in order.
		This procedure ensured that the second hexachord was a literal pitch transformation of the first (for the nonoctifed materials); that is, the transforms respected normal arithmetic rather than modulo arithmetic.
		The two hexachords were separated by a delay of one second to help draw attention to the hexachord structure of the tone row.
	www.lifesci.sussex.ac.uk /home/Zoltan_Dienes/smooth.html (619 words)

	White Island paper (Site not responding. Last check: 2007-10-08)
		Hexachord iterations give way to tetrachord and trichord partitions, and while the chromatic nature of the texture remains, the pervasiveness of diatonic thirds becomes more pronounced in the voices, such as in the strong G/B-F#/A# motion on “Gen’rall Session” in the voices (m12), and the almost triadic implications throughout mm23-26.
		The most common partitioning of the A Hexachord by Martino is the trichord partitioning of 014 (T0+T3=A Hexachord), and the generation of the 0134 tetrachord as a result of interlocking an 014 with the inversion of 014 at T=4.
		However, while the E Hexachord is structurally a governing agent in the work, it figures less as a surface/melodic element than do the A and C hexachords, and linear, melodic strands based on the E hexachords are rare.
	world.std.com /~breeze/WI.html (2614 words)

	Hexachord -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In (An artistic form of auditory communication incorporating instrumental or vocal tones in a structured and continuous manner) music, a hexachord is a (Several things grouped together or considered as a whole) collection of six (The quality of a person's voice) tones.
		In each hexachord, all adjacent pitches are a (A musical interval of two semitones) whole tone apart, except for the middle two, which are separated by a (Click link for more info and facts about half tone) half tone.
		Hexachords may be used to create (The quality of being resistant to variation) invariance and (Click link for more info and facts about combinatoriality) combinatoriality, and often a melody and its (A subordinate musical part; provides background for more important parts) accompaniment will be drawn from different hexachords.
	www.absoluteastronomy.com /encyclopedia/h/he/hexachord.htm (538 words)

	Twelve Tone Composition Part 2 (Site not responding. Last check: 2007-10-08)
		A hexachord that produces its complement under a transposition is prime combinatorial: the original hexachord and one of its transpositions combine to form an aggregate of all twelve pitch classes.
		The nature of these hexachords was investigated and described in a doctoral dissertation completed by Milton Babbitt in 1947 and subsequently developed in the compositions of Babbitt and his followers.
		According to the table of all-combinatorial hexachords, this class is P, I, R, and RI combinatorial at one transposition level.
	jan.ucc.nau.edu /~krr2/12tone/12tone2.html (2352 words)

	Hexachords - Basic System
		In simplest terms, a hexachord is a set of six notes arranged to form intervals of two whole-tones, a central semitone, and two more whole-tones.
		Hexachords on G (with B-natural) are known as durum or "hard"; hexachords on C as "natural"; and hexachords on F (with Bb) as molle or "soft." Note that both "flavors" of the fluid or mutable step B/Bb - the "hard" flavor B-natural and the "soft" flavor Bb - are integral elements of the system.
		As the hexachord system expands, these mi-signs and fa-signs may apply to other degrees than B/Bb, applications involving transposition of the gamut (Section 1.6) or the "invention" of new accidental steps not part of the basic gamut (Section 2).
	www.medieval.org /emfaq/harmony/hex1.html (2638 words)

	Hexachord - Wikipedia
		Onder hexachord wordt in de muziektheorie verstaan: een deel van de toonladder.
		Het woord is afkomstig uit het oudgrieks en betekent: zes tonen.
		Het hexachord op F werd hexachordum mollum (zacht), dat op C hexachordum naturale en dat op G hexachordum durum (hard) genoemd.
	nl.wikipedia.org /wiki/Hexachord (806 words)

	HEXACHORD FACTS AND INFORMATION
		In each hexachord, all adjacent pitches are a whole_tone apart, except for the middle two, which are separated by a half_tone.
		In musical set theory, a hexachord is a collection of six pitch_classes, often one of two (complementary) ordered hexachords in a tone_row or set form.
		Josef_Matthias_Hauer's twelve_tone_technique uses unordered hexachords he referred to as tropes.
	www.witwib.com /?s=hexachord (383 words)

	Babbitt (Site not responding. Last check: 2007-10-08)
		Some hexachords have structures such that they can be transformed into themselves or their complement by the standard transformations of transposition, inversion, and retrograde inversion.
		The hexachord used as a source of structure in Post-Partitions is an (023457) hexachord.
		This particular hexachord is an all-combinatorial hexachord since there are both inversional and transpositional ways of replicating either the hexachord or its complement.
	www.sinc.sunysb.edu /Class/mus352/notes/babbitt.htm (343 words)

	hexachord -- Encyclopædia Britannica
		The names of the degrees of the hexachord are ut, re, mi, fa, sol, and la (also called solmization [q.v.
		The names of the degrees of the hexachord are ut, re, mi, fa, sol, and la (also called solmization [q.v.] syllables); they were devised by the 11th-century teacher and theorist Guido of Arezzo.
		The hexachord was described in medieval and Renaissance musical theory and...
	www.britannica.com /eb/article-9040330?tocId=9040330 (377 words)

	Electronic musical instrument - Patent 4009633
		Since the hexachord consists of the first six tones of the major mode of the diatonic scale, there is little difficulty in learning the hexachord scale.
		Thus a hexachord scale based on C can be united with another hexachord scale based on G to form a diatonic scale based on C, with seven tones per octave.
		The hexachord has an advantage over the octachord in compatibility with the traditional system of two five-line staves, for hexachord labeling of lines and spaces in the lower five-line staff is identical with that in the upper five-line staff.
	www.freepatentsonline.com /4009633.html (6316 words)

	hexachord -- Britannica Concise Encyclopedia - The online encyclopedia you can trust!
		The hexachord was described in medieval and Renaissance musical theory and was extensively used in the teaching of singing.
		Its value was that it gave the singer a fixed set of pitch relations by which he could orient himself as he sang; as a practical device it proved an effective way to teach the sight-reading of music and to teach individual melodies.
		Ascending the hard hexachord to its fourth note, C fa, the singer would find himself on a level with the first note, C ut, of the natural hexachord.
	www.britannica.com /ebc/article-9040330 (722 words)

	[No title]
		This hexachord (H1) can be traced throughout the movement, both as a whole unit and also in terms of subsets.
		Stravinsky's treatment of this hexachord (H3) is different from the Bransle simple in that the presentation is in vertical blocks.
		The complementary hexachord (H2) is understated by the lower stringed instruments using single pitches.
	www.uh.edu /~tkoozin/projects/Jacobi/6306final.html (2458 words)

	Twelve Tone Composition, Part 2 Problems (Site not responding. Last check: 2007-10-08)
		Under "comments" note if the second hexachord is a transformed version of the first hexachord and which all-combinatorial hexachords are used (if any).
		Hexachords are same class but not on the list of all-combinatorial hexachords.
		The second hexachord is not a variant of the first hexachord.
	jan.ucc.nau.edu /~krr2/12tone/12tone2prob.html (1452 words)

	Palestrina's Late Renaissance Motet Ego sum panis vivus: Formal Order and Motivic Unity
		The soft hexachord begins on F, the hard on G and the soft on C. Each of these hexachords overlap in their range and it may (usually) be necessary for a singer to move amongst the three while singing a particular piece of music.
		It is important to understand that this motet is based on the F hexachord, although it essentially looks like F major and a person without an understanding of modal counterpoint could perhaps understand it and perform it in F major.
		In this piece the descending hexachord begins on scale degree five, which is part of the natural hexachord and falls to its ultimate goal of F, thus establishing a tonal grounding.
	www.humanities.mcmaster.ca /~mus701/macmacvol3/moiny.html (2257 words)

	hexachord - a 6-tone musical scale structure
		This definition of hexachord is not the same as the one of the medieval theorist Guido D'Arrezzo.
		In the system constructed by Guido, hexachords were possible on three pitch-levels, with "ut" on what we would today call "C" (the "natural" hexachord), "F" (the "soft" hexachord), and "G" (the "hard" hexachord).
		Usually, the hexachord pair exhibits similarities of interval structure (i.e., transposition) or other serial properties such as retrograde or inversion, or various combinations of all of them.
	tonalsoft.com /enc/h/hexachord.aspx (618 words)

	Twelve-Tone Techniques (Site not responding. Last check: 2007-10-08)
		The idea that structure could be shaped concretely by the properties of the row allowed composers to develop a structural depth that matched the surface detail afforded by the row.
		Hexachordal combinatoriality - Schoenberg preferred to use rows built from two hexachords related by inversion (the hexachords were not Z-related).
		Hexachords with all four kinds of combinatoriality are all-combinatorial.
	www.cwu.edu /~compose/PostTonal_5.html (304 words)

	MTO 4.3: Mengozzi, Review of Pike, Hexachords in Late-Renaissance Music
		Singers were taught to select the correct hexachord on the ground of the intervals to sing, not of the syllables to pronounce; in other words, reducing the number of mutations was no doubt preferable to maximizing the concordances between the two kinds of syllables--indeed the choice was not even an issue.
		We are told that, because the molle hexachord was "colored" by the B flat, "it was thought of as 'soft' or 'sweet', and so it was particularly appropriate for the illustration of sweetness or similar ideas" (p.
		In other words, it seems that the affective connotations of the "molle hexachord" depend a great deal on whether the mi-fa semitone (A-Bb) falls between the first two pitches of the mode, or rather between the third and fourth pitches--nor is it recommended to disregard the location of the other semitone within the octave.
	www.societymusictheory.org /mto/issues/mto.98.4.3/mto.98.4.3.mengozzi.html (4522 words)

	Medieval Musical Tuning Theory
		The hexachord was primarily conceived to facilitate the teaching of music and according to Guido it enabled a pupil to learn in five months what might previously have taken ten years.
		The lowest note on which a hexachord might start was bass G which was identified by the Greek letter gamma.
		In order to move beyond the six notes of the hexachord it was necessary to transfer to a new hexachord starting on the fourth or fifth degree of the old one.
	www.midicode.com /tunings/medieval.shtml (1851 words)

	Hexachords - Early Alternatives
		The result, as in hexachord solmization, would be a notation for relative interval relations and patterns rather than absolute note positions [126]; compare, for example, the use of hexachord syllables in the early 14th century by Jacobus of Liege to describe two-voice progressions without a need to specify letter note names (Section 2.2).
		Thus Allaire [139] urges us to understand the modes "as interlocking hexachords, rather than as scales in the modern sense." Whatever Allaire's qualifying phrase "in the modern sense" may mean, medieval perspectives focus on the modes both as octave species and as unions of tetrachords or hexachords.
		However, as Allaire suggests, the hexachord system may have the unique virtue of highlighting subtle relationships of the latter type, while the octave-species aspects of modality may be obvious enough under any system of solmization.
	www.medieval.org /emfaq/harmony/hex4.html (4624 words)

	Read about Hexachord at WorldVillage Encyclopedia. Research Hexachord and learn about Hexachord here! (Site not responding. Last check: 2007-10-08)
		pitch relationships in the music of the time by grouping pitches into sets of six, or hexachords.
		complementary) ordered hexachords in a tone row or set form.
		twelve tone technique uses unordered hexachords he referred to as tropes.
	encyclopedia.worldvillage.com /s/b/Hexachord (343 words)

	Hexachords, solmization, and musica ficta - Table of Contents (Site not responding. Last check: 2007-10-08)
		The hexachord system, introduced and developed by Guido d'Arezzo and his colleagues in the 11th century, was a central element of musical practice and culture in medieval Europe, and continued to influence Renaissance and Manneristic practice through the early 17th century.
		While rightly acclaimed as a very successful method for teaching the art of sight-reading, Guido's hexachord system more generally serves as a familiar framework from which to approach many issues of medieval and Renaissance composition and performance.
		This FAQ article will first present the basic hexachord system and its origins; then medieval and Renaissance extensions of the system to permit a fuller set of accidentals; and finally some alternative systems proposed by Bartolomé Ramos (1482) and Johannes Lippius (1610, 1612) based on octaves rather than hexachords.
	www.medieval.org /emfaq/harmony/hex.html (155 words)

	MUSICOLOGY & MUSIC DTP: Musical Information in .. (Site not responding. Last check: 2007-10-08)
		It was common in the sixteenth century to transpose modes, and at this juncture "key" signatures took on the additional role of indicating transpositions.
		This superstructure of relationships was built on the still earlier system of hexachords, which were also transposable.
		Performers of the time were supposed to know, because of their intensive study of the hexachordal system, when to apply sharps and flats to the music.
	www.ccarh.org /publications/reprints/ieee/TYPE54.HTM (419 words)

	Cymatics, Sound Healing, & Music/Harp Therapy
		In England from the late 16th century, the notes of the hexachord were labelled fa-so-la-fa-so-la, which was called, not surprisingly, "fasola".
		The expanded hexachord and its fasola syllables survive in the music of sacred harp singing.
		Vespers hymn for the feast of the Birth of John the Baptist.
	members.tripod.com /~WeThePeople/SoundHealing.htm (1440 words)

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