EDO: Difference between revisions

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=== Why would I want to use an EDO? ===

If you are a ~~guitarist~~ (or a player of some other fretted string instrument, like a bass guitar, Appalachian dulcimer, ~~ukelele~~, banjo, mandolin, sitar, saz, pipa, or zhong ruan), an EDO will provide you with the simplest possible fretboard layout, as all of the frets will go straight across the fretboard, regardless of how you want to tune the open strings. Speaking of string instruments fretted for EDOs, since ascending through the EDOs will crowd a fretboard relatively quickly, especially as one approaches the 30-something EDOs, [[ed4|~~Equal~~ divisions of the double octave]] (or higher multiple of the octave) are a relatively tidy compromise solution to the problem of laying out high-EDO fretboards.

If you are a [[guitar]]ist (or a player of some other fretted string instrument, like a bass guitar, Appalachian dulcimer, [[ukulele]], banjo, mandolin, sitar, saz, pipa, or zhong ruan), an EDO will provide you with the simplest possible fretboard layout, as all of the frets will go straight across the fretboard, regardless of how you want to tune the open strings. Speaking of string instruments fretted for EDOs, since ascending through the EDOs will crowd a fretboard relatively quickly, especially as one approaches the 30-something EDOs, [[ed4|equal divisions of the double octave]] (or higher multiple of the octave) are a relatively tidy compromise solution to the problem of laying out high-EDO fretboards.

More generally, EDOs allow for modulation to every single key in the tuning, without any alteration in harmonic properties, thus making transposition totally seamless. This also makes them somewhat easier to learn, as you do not have to memorize the harmonic and melodic variations that appear in various keys (which you would have to learn in JI, an unequal regular temperament, or a well-temperament, especially with smaller numbers of tones). For those accustomed to the "equality" of 12-TET, the equality of the alternative EDOs can be reassuringly familiar.

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Some EDOs, such as {{EDOs| 26, 27, 32, 33, or 37 }} have fifths which are reasonably good but quite audibly not just. Other EDOs, such as {{EDOs| 11, 13, 14, 15, 16, 18, 20, 21, 23, or 25 }}, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.

EDOs can be further subdivided and classified according to the size of the fifth, such as with [[Margo Schulter]]'s [[gentle region]] or the distinction between negative, positive, doubly negative and doubly positive of [[~~RHM~~ Bosanquet]]. [[Kite Giedraitis]] has proposed these six categories, based on the size of the fifth. From narrowest to widest:

EDOs can be further subdivided and classified according to the size of the fifth, such as with [[Margo Schulter]]'s [[gentle region]] or the distinction between negative, positive, doubly negative and doubly positive of [[R. H. M. Bosanquet]]. [[Kite Giedraitis]] has proposed these six categories, based on the size of the fifth. From narrowest to widest:

* '''superflat''' EDOs ({{EDOs| 9, 11, 13b, 16, 18b & 23 }}) have a fifth narrower than four-sevenths of an octave = 4\7 = 686¢

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=== Size of an EDO ===

When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal EDO]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. [[5edo|5]], [[7edo|7]] and [[9edo|9]] have arguably been used in various kinds of musical traditions in different parts of the world. [https://soundcloud.com/scottthompson-3/the-13-edos-of-xmas ''The 13 EDOs of Xmas'' by Scott Thompson] is a humorous demonstration of EDOs 1–13.

When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal EDO]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. [[5edo|5]], [[7edo|7]] and [[9edo|9]] have arguably been used in various kinds of musical traditions in different parts of the world. [https://soundcloud.com/scottthompson-3/the-13-edos-of-xmas ''The 13 EDOs of Xmas''] by [[Scott Thompson]] is a humorous demonstration of EDOs 1–13.

On the other hand, if you use the edo to tune a scale or [[regular temperament]], the size of the edo does not matter so much (at least conceptually), as you don't need to use all of it. Some of the EDOs which can be used to tune various temperaments are listed on the [[optimal patent val]] page. Tuning a scale in just intonation by one of these EDOs can be regarded as automatically tempering it to the corresponding regular temperament.

To practically tune large edos through software tuning, one may take advantage of MIDI channels. See [[Tuning per channel]].

To practically tune large edos through software tuning, one may take advantage of [[MIDI]] channels. See [[Tuning per channel]].

All of these tools are also applicable to equal divisions of other ([[nonoctave]]) intervals as well.

@@ Line 40: / Line 40: @@
 === Why would I want to use an EDO? ===
-If you are a guitarist (or a player of some other fretted string instrument, like a bass guitar, Appalachian dulcimer, ukelele, banjo, mandolin, sitar, saz, pipa, or zhong ruan), an EDO will provide you with the simplest possible fretboard layout, as all of the frets will go straight across the fretboard, regardless of how you want to tune the open strings. Speaking of string instruments fretted for EDOs, since ascending through the EDOs will crowd a fretboard relatively quickly, especially as one approaches the 30-something EDOs, [[ed4|Equal divisions of the double octave]] (or higher multiple of the octave) are a relatively tidy compromise solution to the problem of laying out high-EDO fretboards.
+If you are a [[guitar]]ist (or a player of some other fretted string instrument, like a bass guitar, Appalachian dulcimer, [[ukulele]], banjo, mandolin, sitar, saz, pipa, or zhong ruan), an EDO will provide you with the simplest possible fretboard layout, as all of the frets will go straight across the fretboard, regardless of how you want to tune the open strings. Speaking of string instruments fretted for EDOs, since ascending through the EDOs will crowd a fretboard relatively quickly, especially as one approaches the 30-something EDOs, [[ed4|equal divisions of the double octave]] (or higher multiple of the octave) are a relatively tidy compromise solution to the problem of laying out high-EDO fretboards.
 More generally, EDOs allow for modulation to every single key in the tuning, without any alteration in harmonic properties, thus making transposition totally seamless. This also makes them somewhat easier to learn, as you do not have to memorize the harmonic and melodic variations that appear in various keys (which you would have to learn in JI, an unequal regular temperament, or a well-temperament, especially with smaller numbers of tones). For those accustomed to the "equality" of 12-TET, the equality of the alternative EDOs can be reassuringly familiar.
@@ Line 54: / Line 54: @@
 Some EDOs, such as {{EDOs| 26, 27, 32, 33, or 37 }} have fifths which are reasonably good but quite audibly not just. Other EDOs, such as {{EDOs| 11, 13, 14, 15, 16, 18, 20, 21, 23, or 25 }}, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.
-EDOs can be further subdivided and classified according to the size of the fifth, such as with [[Margo Schulter]]'s [[gentle region]] or the distinction between negative, positive, doubly negative and doubly positive of [[RHM Bosanquet]]. [[Kite Giedraitis]] has proposed these six categories, based on the size of the fifth. From narrowest to widest:
+EDOs can be further subdivided and classified according to the size of the fifth, such as with [[Margo Schulter]]'s [[gentle region]] or the distinction between negative, positive, doubly negative and doubly positive of [[R. H. M. Bosanquet]]. [[Kite Giedraitis]] has proposed these six categories, based on the size of the fifth. From narrowest to widest:
 * '''superflat''' EDOs ({{EDOs| 9, 11, 13b, 16, 18b &amp; 23 }}) have a fifth narrower than four-sevenths of an octave = 4\7 = 686¢
@@ Line 79: / Line 79: @@
 === Size of an EDO ===
-When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal EDO]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. [[5edo|5]], [[7edo|7]] and [[9edo|9]] have arguably been used in various kinds of musical traditions in different parts of the world. [https://soundcloud.com/scottthompson-3/the-13-edos-of-xmas ''The 13 EDOs of Xmas'' by Scott Thompson] is a humorous demonstration of EDOs 1–13.
+When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal EDO]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. [[5edo|5]], [[7edo|7]] and [[9edo|9]] have arguably been used in various kinds of musical traditions in different parts of the world. [https://soundcloud.com/scottthompson-3/the-13-edos-of-xmas ''The 13 EDOs of Xmas''] by [[Scott Thompson]] is a humorous demonstration of EDOs 1–13.
 On the other hand, if you use the edo to tune a scale or [[regular temperament]], the size of the edo does not matter so much (at least conceptually), as you don't need to use all of it. Some of the EDOs which can be used to tune various temperaments are listed on the [[optimal patent val]] page. Tuning a scale in just intonation by one of these EDOs can be regarded as automatically tempering it to the corresponding regular temperament.
-To practically tune large edos through software tuning, one may take advantage of MIDI channels. See [[Tuning per channel]].
+To practically tune large edos through software tuning, one may take advantage of [[MIDI]] channels. See [[Tuning per channel]].
 All of these tools are also applicable to equal divisions of other ([[nonoctave]]) intervals as well.