Tonality flux
Encyclopedia
Tonality flux is Harry Partch
's term for the kinds of subtle harmonic
changes that can occur in a microtonal
context from notes moving from one chord
to another by tiny increments of voice leading
. For instance, within a major third
G-B, there can be a minor third
G 1/4-tone
sharp to B 1/4-tone flat, such that moving from one to the other uses shifts in each line of less than a half-step
. Within a just intonation
scale, this could be represented by
moving to
like so:
One voice slides down from 386 cents to 347, the other slides up from 0 cents to 32, yet the harmonic shift can be dramatic. The best-known example of tonality flux, and one of the two Partch uses as illustration, is the beginning of his composition The Letter, in which the Kithara
alternates between two chords, one major
and one minor
, with the minor third of one nestled inside the major third of the other (given here in Ben Johnston
's pitch notation):
In this notation, which assumes G as the tonic
or 1/1, a 7 lowers a pitch from a just intonation
value by 35/36
, or 48.77 cents; an upside-down 7 raises a pitch by the same amount. The first chord is a major triad and, relative to G, contains the notes 8/7 (231 cents above G), 10/7 (617 cents), and 12/7 (933 cents); the second chord is a minor triad comprising the pitches 7/6
(267 cents), 7/5 (583 cents), and 7/4 (969 cents). Notice that while the outer notes ascend from the first chord to the second, the middle note descends. Such subtle movements were among the attractions that Partch found in an expanded just intonation of more than 12 pitches per octave. Tonality flux is a special instance of the principle of parsimonious voice leading.
Harry Partch
Harry Partch was an American composer and instrument creator. He was one of the first twentieth-century composers to work extensively and systematically with microtonal scales, writing much of his music for custom-made instruments that he built himself, tuned in 11-limit just intonation.-Early...
's term for the kinds of subtle harmonic
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
changes that can occur in a microtonal
Microtonal music
Microtonal music is music using microtones—intervals of less than an equally spaced semitone. Microtonal music can also refer to music which uses intervals not found in the Western system of 12 equal intervals to the octave.-Terminology:...
context from notes moving from one chord
Chord (music)
A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...
to another by tiny increments of voice leading
Voice leading
In musical composition, voice leading is the term used to refer to a decision-making consideration when arranging voices , namely, how each voice should move in advancing from each chord to the next.- Details :...
. For instance, within a major third
Major third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...
G-B, there can be a minor third
Minor third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...
G 1/4-tone
Quarter tone
A quarter tone , is a pitch halfway between the usual notes of a chromatic scale, an interval about half as wide as a semitone, which is half a whole tone....
sharp to B 1/4-tone flat, such that moving from one to the other uses shifts in each line of less than a half-step
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
. Within a just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
scale, this could be represented by
| Note name | ratio | cents | interval name |
|---|---|---|---|
| G | 1/1 | 0 | Just major third |
| B | 5/4 | 386 |
moving to
| Note name | ratio | cents | interval name | name | ratio | cents |
|---|---|---|---|---|---|---|
| G | 55/54 | 32 | Just minor third | G – B | 6/5 | 316 |
| B | 11/9 | 347 |
like so:
| Note name | ratio | cents | name | ratio | cents |
|---|---|---|---|---|---|
| B | 5/4 | 386 | |||
| B | 11/9 | 347 | |||
| G | 55/54 | 32 | |||
| G | 1/1 | 0 |
One voice slides down from 386 cents to 347, the other slides up from 0 cents to 32, yet the harmonic shift can be dramatic. The best-known example of tonality flux, and one of the two Partch uses as illustration, is the beginning of his composition The Letter, in which the Kithara
Kithara
The kithara or cithara was an ancient Greek musical instrument in the lyre or lyra family. In modern Greek the word kithara has come to mean "guitar" ....
alternates between two chords, one major
Major chord
In music theory, a major chord is a chord having a root, a major third, and a perfect fifth. When a chord has these three notes alone, it is called a major triad...
and one minor
Minor chord
In music theory, a minor chord is a chord having a root, a minor third, and a perfect fifth.When a chord has these three notes alone, it is called a minor triad....
, with the minor third of one nestled inside the major third of the other (given here in Ben Johnston
Ben Johnston
Benjamin Burwell Johnston, Jr. is a composer of contemporary music in the just intonation system.-Johnston's music:...
's pitch notation):
Tonic (music)
In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...
or 1/1, a 7 lowers a pitch from a just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
value by 35/36
Septimal quarter tone
A septimal quarter-tone is an interval with the ratio of 36:35 , which is the difference between the septimal minor third and the Just minor third , or about 48.77 cents wide. The name derives from the interval being the 7-limit approximation of a quarter tone...
, or 48.77 cents; an upside-down 7 raises a pitch by the same amount. The first chord is a major triad and, relative to G, contains the notes 8/7 (231 cents above G), 10/7 (617 cents), and 12/7 (933 cents); the second chord is a minor triad comprising the pitches 7/6
Septimal minor third
In music, the septimal minor third , also called the subminor third, is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5...
(267 cents), 7/5 (583 cents), and 7/4 (969 cents). Notice that while the outer notes ascend from the first chord to the second, the middle note descends. Such subtle movements were among the attractions that Partch found in an expanded just intonation of more than 12 pitches per octave. Tonality flux is a special instance of the principle of parsimonious voice leading.