36edo: Difference between revisions

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For people accustomed to 12edo, 36edo is one of the easiest (if not ''the'' easiest) higher edo to become accustomed to. This is because one way to envision it is as an extended 12edo to which [https://en.wikipedia.org/wiki/Blue_note blue notes] (which are a sixth-tone lower than normal) and "red notes" (a sixth-tone higher) have been added.

The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. Unlike [[24edo]], which has genuinely foreign intervals such as 250 cents (halfway between a tone and a third) and 450 cents (halfway between a fourth and a third), the new intervals in 36edo all variations on existing ones. Unlike 24edo, 36edo is also relatively free of what Easley Blackwood called "discordant" intervals.

The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. Unlike [[24edo]], which has genuinely foreign intervals such as 250 cents (halfway between a tone and a third) and 450 cents (halfway between a fourth and a third), the new intervals in 36edo all variations on existing ones. Unlike 24edo, 36edo is also relatively free of what Easley Blackwood called "discordant" intervals. The 5th and 11th harmonics fall almost halfway in between scale degrees of 36edo, and thus intervals containing them can be approximated two different ways, one of which is significantly sharp and the other significantly flat. The 333.333-cent interval (the "red minor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366.667 cents and the flat 6/5 is 300 cents. However, 11/10, 20/11, 15/11, and 22/15 all have accurate and consistent approximations since the errors on the 5th and 11th harmonics cancel out with both tending sharp.

Because of the presence of blue notes, and the closeness with which intervals ~~such as 7/4~~ are matched, 36edo is an ideal scale to use for African-American ~~styles~~ of music such as blues and jazz, in which ~~the 7th harmonic and chords containing 7~~ are frequently ~~used~~. The 5th and 11th harmonics fall almost halfway in between scale degrees of 36edo, and thus intervals containing them can be approximated two different ways, one of which is significantly sharp and the other significantly flat. The 333.333-cent interval (the "red minor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366.667 cents and the flat 6/5 is 300 cents. However, 11/10, 20/11, 15/11, ~~and 22/15 all have accurate and consistent approximations~~ since ~~the errors on the 5th and 11th harmonics cancel out with both tending sharp.~~

36edo is fairly cosmopolitan because many genres of world music can be played in it. Because of the presence of blue notes, and the closeness with which the 7th harmonic and its intervals are matched, 36edo is an ideal scale to use for African-American genres of music such as blues and jazz, in which septimal intervals are frequently encountered. Indonesian gamelan music using pelog easily adapts to it as well, since 9edo is a subset and can be notated as every fourth note, and Slendro can be approximated in several different ways as well. 36edo can therefore function as a "bridge" between these genres and Western music. Arabic and Persian music do not adapt as well, however, since their microtonal intervals consist of mostly quarter tones.

~~36edo~~ is ~~fairly cosmopolitan because many other genres of world music can be played in it too. Because it contains 9edo as~~ a subset, and ~~because 9edo~~ can be notated as every fourth note ~~of 36edo~~, ~~Indonesian gamelan music using pelog (~~and ~~mavila) easily adapts to it. Though~~ Slendro ~~is better represented in [[5edo]], it~~ can ~~also~~ be approximated ~~in 36edo~~ in several different ways. 36edo can therefore function as a "bridge" between these genres and Western music. Arabic and Persian music do not adapt as well, however, since their microtonal intervals consist of mostly quarter tones.

The "red unison" and "blue unison" are in fact the same interval (33.333 cents), which is actually fairly consonant as a result of being so narrow (it is perceived as a unison, albeit noticeably "out of tune", but still not overly unpleasant). In contrast, most people consider 24edo's 50 cent step to sound much more discordant when used as a subminor second.

People with perfect (absolute) pitch often have a difficult time listening to xenharmonic and non-12edo scales, which is due to their ability to memorize and become accustomed to the pitches and intervals of 12edo~~, which results~~ in other pitches and intervals sounding out of tune. This is not as much of a problem with 36edo, due to its similarity to 12. With practice, it might even be possible to extend one's perfect pitch to be able to recognize blue and red notes.

People with perfect (absolute) pitch often have a difficult time listening to xenharmonic and non-12edo scales, which is due to their ability to memorize and become accustomed to the pitches and intervals of 12edo resulting in other pitches and intervals sounding out of tune. This is not as much of a problem with 36edo, due to its similarity to 12. With practice, it might even be possible to extend one's perfect pitch to be able to recognize blue and red notes.

=== "Quark" ===

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 For people accustomed to 12edo, 36edo is one of the easiest (if not ''the'' easiest) higher edo to become accustomed to. This is because one way to envision it is as an extended 12edo to which [https://en.wikipedia.org/wiki/Blue_note blue notes] (which are a sixth-tone lower than normal) and "red notes" (a sixth-tone higher) have been added.
-The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. Unlike [[24edo]], which has genuinely foreign intervals such as 250 cents (halfway between a tone and a third) and 450 cents (halfway between a fourth and a third), the new intervals in 36edo all variations on existing ones. Unlike 24edo, 36edo is also relatively free of what Easley Blackwood called "discordant" intervals.
+The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. Unlike [[24edo]], which has genuinely foreign intervals such as 250 cents (halfway between a tone and a third) and 450 cents (halfway between a fourth and a third), the new intervals in 36edo all variations on existing ones. Unlike 24edo, 36edo is also relatively free of what Easley Blackwood called "discordant" intervals. The 5th and 11th harmonics fall almost halfway in between scale degrees of 36edo, and thus intervals containing them can be approximated two different ways, one of which is significantly sharp and the other significantly flat. The 333.333-cent interval (the "red minor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366.667 cents and the flat 6/5 is 300 cents. However, 11/10, 20/11, 15/11, and 22/15 all have accurate and consistent approximations since the errors on the 5th and 11th harmonics cancel out with both tending sharp.
-Because of the presence of blue notes, and the closeness with which intervals such as 7/4 are matched, 36edo is an ideal scale to use for African-American styles of music such as blues and jazz, in which the 7th harmonic and chords containing 7 are frequently used. The 5th and 11th harmonics fall almost halfway in between scale degrees of 36edo, and thus intervals containing them can be approximated two different ways, one of which is significantly sharp and the other significantly flat. The 333.333-cent interval (the "red minor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366.667 cents and the flat 6/5 is 300 cents. However, 11/10, 20/11, 15/11, and 22/15 all have accurate and consistent approximations since the errors on the 5th and 11th harmonics cancel out with both tending sharp.
+edo is fairly cosmopolitan because many genres of world music can be played in it. Because of the presence of blue notes, and the closeness with which the 7th harmonic and its intervals are matched, 36edo is an ideal scale to use for African-American genres of music such as blues and jazz, in which septimal intervals are frequently encountered. Indonesian gamelan music using pelog easily adapts to it as well, since 9edo is a subset and can be notated as every fourth note, and Slendro can be approximated in several different ways as well. 36edo can therefore function as a "bridge" between these genres and Western music. Arabic and Persian music do not adapt as well, however, since their microtonal intervals consist of mostly quarter tones.
-edo is fairly cosmopolitan because many other genres of world music can be played in it too. Because it contains 9edo as a subset, and because 9edo can be notated as every fourth note of 36edo, Indonesian gamelan music using pelog (and mavila) easily adapts to it. Though Slendro is better represented in [[5edo]], it can also be approximated in 36edo in several different ways. 36edo can therefore function as a "bridge" between these genres and Western music. Arabic and Persian music do not adapt as well, however, since their microtonal intervals consist of mostly quarter tones.
 The "red unison" and "blue unison" are in fact the same interval (33.333 cents), which is actually fairly consonant as a result of being so narrow (it is perceived as a unison, albeit noticeably "out of tune", but still not overly unpleasant). In contrast, most people consider 24edo's 50 cent step to sound much more discordant when used as a subminor second.
-People with perfect (absolute) pitch often have a difficult time listening to xenharmonic and non-12edo scales, which is due to their ability to memorize and become accustomed to the pitches and intervals of 12edo, which results in other pitches and intervals sounding out of tune. This is not as much of a problem with 36edo, due to its similarity to 12. With practice, it might even be possible to extend one's perfect pitch to be able to recognize blue and red notes.
+People with perfect (absolute) pitch often have a difficult time listening to xenharmonic and non-12edo scales, which is due to their ability to memorize and become accustomed to the pitches and intervals of 12edo resulting in other pitches and intervals sounding out of tune. This is not as much of a problem with 36edo, due to its similarity to 12. With practice, it might even be possible to extend one's perfect pitch to be able to recognize blue and red notes.
 === "Quark" ===