Kite's thoughts on generalizing the term tetrachord: Difference between revisions
Created page with "In the original diatonic sense of the word, ''tetrachord'' means both "has 4 notes" and "spans a diatonic 4th". After all, a 4th is called a 4th because it's 4 notes of the diatonic scale. So it's really just two ways of saying the same thing. But when we go beyond diatonic to microtonal, or even just 12edo chromatic, only one of those two meanings can be kept. There's precedent for both usages (https://en.wikipedia.org/wiki/Tetrachord):<blockquote>The expression "chrom..." |
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In the original diatonic sense of the word, ''tetrachord'' means both "has 4 notes" and "spans a diatonic 4th". After all, a 4th is called a 4th because it's 4 notes of the diatonic scale. So it's really just two ways of saying the same thing. | In the original diatonic sense of the word, ''[[tetrachord]]'' means both "has 4 notes" and "spans a diatonic 4th". After all, a 4th is called a 4th because it's 4 notes of the diatonic scale. So it's really just two ways of saying the same thing. | ||
But when we go beyond diatonic to microtonal, or even just 12edo chromatic, only one of those two meanings can be kept. There's precedent for both usages (https://en.wikipedia.org/wiki/Tetrachord):<blockquote>The expression "chromatic tetrachord" may be used in two different senses: to describe the special case consisting of a four-note segment of the chromatic scale,[13] or, in a more historically oriented context, to refer to the six chromatic notes used to fill the interval of a perfect fourth, usually found in descending bass lines.[14] It may also be used to describe sets of fewer than four notes, when used in scale-like fashion to span the interval of a perfect fourth.[15]</blockquote>Since neither usage is so well established that it's set in stone, the microtonal community is free to choose whichever meaning is more useful. Miicrotonal terminology is a tool, and we want the best tools available for the demanding task of describing the vast multitude of possible microtonal scales. | But when we go beyond diatonic to microtonal, or even just 12edo chromatic, only one of those two meanings can be kept. There's precedent for both usages (https://en.wikipedia.org/wiki/Tetrachord):<blockquote>The expression "chromatic tetrachord" may be used in two different senses: to describe the special case consisting of a four-note segment of the chromatic scale,[13] or, in a more historically oriented context, to refer to the six chromatic notes used to fill the interval of a perfect fourth, usually found in descending bass lines.[14] It may also be used to describe sets of fewer than four notes, when used in scale-like fashion to span the interval of a perfect fourth.[15]</blockquote>Since neither usage is so well established that it's set in stone, the microtonal community is free to choose whichever meaning is more useful. Miicrotonal terminology is a tool, and we want the best tools available for the demanding task of describing the vast multitude of possible microtonal scales. | ||
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So in my opinion, "spans a diatonic 4th" is by far the more useful meaning for tetrachord, and should be the one we use going forward. Likewise, ''pentachord'' should mean not "has 5 notes" but "spans a diatonic 5th". Thus C-Eb-F should be called not a trichord but a 3-note tetrachord. And 41edo's C vvD vEb vE F Gb G should be called a 7-note pentachord. | So in my opinion, "spans a diatonic 4th" is by far the more useful meaning for tetrachord, and should be the one we use going forward. Likewise, ''pentachord'' should mean not "has 5 notes" but "spans a diatonic 5th". Thus C-Eb-F should be called not a trichord but a 3-note tetrachord. And 41edo's C vvD vEb vE F Gb G should be called a 7-note pentachord. | ||
—[[Kite Giedraitis]] | |||
Latest revision as of 02:30, 30 October 2026
In the original diatonic sense of the word, tetrachord means both "has 4 notes" and "spans a diatonic 4th". After all, a 4th is called a 4th because it's 4 notes of the diatonic scale. So it's really just two ways of saying the same thing.
But when we go beyond diatonic to microtonal, or even just 12edo chromatic, only one of those two meanings can be kept. There's precedent for both usages (https://en.wikipedia.org/wiki/Tetrachord):
The expression "chromatic tetrachord" may be used in two different senses: to describe the special case consisting of a four-note segment of the chromatic scale,[13] or, in a more historically oriented context, to refer to the six chromatic notes used to fill the interval of a perfect fourth, usually found in descending bass lines.[14] It may also be used to describe sets of fewer than four notes, when used in scale-like fashion to span the interval of a perfect fourth.[15]
Since neither usage is so well established that it's set in stone, the microtonal community is free to choose whichever meaning is more useful. Miicrotonal terminology is a tool, and we want the best tools available for the demanding task of describing the vast multitude of possible microtonal scales.
So which meaning is more useful? Diatonic tetrachords are discussed much more often than e.g. diatonic trichords (scale fragments spanning a 3rd). And N-note scale segments that span a 4th tend to come up in microtonal conversation more often than 4-note scale segments that span some other interval. Perhaps because 4/3 is a perfect interval, it's a prominent landmark and a natural stopping point in a way that 5/4, 6/5, 81/64, etc. aren't.
So in my opinion, "spans a diatonic 4th" is by far the more useful meaning for tetrachord, and should be the one we use going forward. Likewise, pentachord should mean not "has 5 notes" but "spans a diatonic 5th". Thus C-Eb-F should be called not a trichord but a 3-note tetrachord. And 41edo's C vvD vEb vE F Gb G should be called a 7-note pentachord.