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. In [[24edo]], intervals such as 250 ~~cents~~ (halfway between a tone and a third) and 450 ~~cents~~ (halfway between a fourth and a third) tend to sound genuinely foreign, whereas the new intervals in 36edo are 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 33{{frac|1|3}}{{c}} interval (the "red minor third" or "supraminor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366{{frac|2|3}}{{c}} and the flat 6/5 is 300{{c}}. 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.

The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. In [[24edo]], intervals such as 250{{c}} (halfway between a tone and a third) and 450{{c}} (halfway between a fourth and a third) tend to sound genuinely foreign, whereas the new intervals in 36edo are 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 33{{frac|1|3}}{{c}} interval (the "red minor third" or "supraminor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366{{frac|2|3}}{{c}} and the flat 6/5 is 300{{c}}. 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, most notably as a very soft [[1L 4s]] scale. 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.

The "red unison" and "blue unison" are in fact the same interval (33.333{{c}}), 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{{c}} 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,since their ability to memorize and become accustomed to the pitches and intervals of 12edo 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.

=== "Quark" ===

In particle physics, [https://en.wikipedia.org/wiki/Baryon baryons], which are the main building blocks of atomic nuclei, are always comprised of three quarks. One could draw an analogy between baryons and semitones (the main building block of 12edo); the baryon is comprised of three quarks and the semitone of three sixth-tones. The number of quarks in a [https://en.wikipedia.org/wiki/Color_charge colorless] particle is always a multiple of three; similarly, the width of "colorless" intervals (the 12-edo intervals, which are neither red nor blue), expressed in terms of sixth-tones, is always a multiple of three. Because of this amusing coincidence, Mason Green proposes referring to the 33.333~~-cent~~ sixth-tone interval as a "quark".

In particle physics, [https://en.wikipedia.org/wiki/Baryon baryons], which are the main building blocks of atomic nuclei, are always comprised of three quarks. One could draw an analogy between baryons and semitones (the main building block of 12edo); the baryon is comprised of three quarks and the semitone of three sixth-tones. The number of quarks in a [https://en.wikipedia.org/wiki/Color_charge colorless] particle is always a multiple of three; similarly, the width of "colorless" intervals (the 12-edo intervals, which are neither red nor blue), expressed in terms of sixth-tones, is always a multiple of three. Because of this amusing coincidence, Mason Green proposes referring to the 33.333{{c}} sixth-tone interval as a "quark".

== Approximation to JI ==

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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. In [[24edo]], intervals such as 250 cents (halfway between a tone and a third) and 450 cents (halfway between a fourth and a third) tend to sound genuinely foreign, whereas the new intervals in 36edo are 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 33{{frac|1|3}}{{c}} interval (the "red minor third" or "supraminor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366{{frac|2|3}}{{c}} and the flat 6/5 is 300{{c}}. 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.
+The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. In [[24edo]], intervals such as 250{{c}} (halfway between a tone and a third) and 450{{c}} (halfway between a fourth and a third) tend to sound genuinely foreign, whereas the new intervals in 36edo are 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 33{{frac|1|3}}{{c}} interval (the "red minor third" or "supraminor third") sharply approximates 6/5 and flatly approximates 11/9, for instance, whereas the sharp 11/9 is 366{{frac|2|3}}{{c}} and the flat 6/5 is 300{{c}}. 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, most notably as a very soft [[1L&nbsp;4s]] scale. 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.
+The "red unison" and "blue unison" are in fact the same interval (33.333{{c}}), 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{{c}} 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,since their ability to memorize and become accustomed to the pitches and intervals of 12edo 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.
 === "Quark" ===
-In particle physics, [https://en.wikipedia.org/wiki/Baryon baryons], which are the main building blocks of atomic nuclei, are always comprised of three quarks. One could draw an analogy between baryons and semitones (the main building block of 12edo); the baryon is comprised of three quarks and the semitone of three sixth-tones. The number of quarks in a [https://en.wikipedia.org/wiki/Color_charge colorless] particle is always a multiple of three; similarly, the width of "colorless" intervals (the 12-edo intervals, which are neither red nor blue), expressed in terms of sixth-tones, is always a multiple of three. Because of this amusing coincidence, Mason Green proposes referring to the 33.333-cent sixth-tone interval as a "quark".
+In particle physics, [https://en.wikipedia.org/wiki/Baryon baryons], which are the main building blocks of atomic nuclei, are always comprised of three quarks. One could draw an analogy between baryons and semitones (the main building block of 12edo); the baryon is comprised of three quarks and the semitone of three sixth-tones. The number of quarks in a [https://en.wikipedia.org/wiki/Color_charge colorless] particle is always a multiple of three; similarly, the width of "colorless" intervals (the 12-edo intervals, which are neither red nor blue), expressed in terms of sixth-tones, is always a multiple of three. Because of this amusing coincidence, Mason Green proposes referring to the 33.333{{c}} sixth-tone interval as a "quark".
 == Approximation to JI ==