Mike's EDO impressions: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2013-04-~~26 03~~:43:23 UTC</tt>.

: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2013-05-06 23:30:04 UTC</tt>.

: The original revision id was <tt>~~426598496~~</tt>.

: The original revision id was <tt>429430208</tt>.

: The revision comment was: <tt></tt>

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[[xenharmonic/4edo|4]] - lol

----

[[xenharmonic/5edo|5]] (aka [[xenharmonic/8edt|8edt]]) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: //[[http://www.youtube.com/watch?v=rPmuKUm2kJg]]//

[[xenharmonic/5edo|5]] (aka [[xenharmonic/8edt|8edt]]) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: ////[[http://www.youtube.com/watch?v=rPmuKUm2kJg]]////

----

[[xenharmonic/6edo|6]] - the whole tone scale. But, if you flatten the octaves, you can get almost perfect 4:5:7:11 chords, which is worth noting.

Line 28:

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[[xenharmonic/9edo|9]] (aka [[xenharmonic/14edt|14edt]]) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports [[Pelogic family|mavila]] and [[xenharmonic/Pelogic family|pelogic]] temperament, and the 7-note MOS's are of prime interest here. Because of that, it's the first EDO I know how to create something like "functional harmony" in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: //[[http://www.youtube.com/watch?v=KV_MzdtU2WQ]]//. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: [[@http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/]]. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).

[[xenharmonic/9edo|9]] (aka [[xenharmonic/14edt|14edt]]) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports [[Pelogic family|mavila]] and [[xenharmonic/Pelogic family|pelogic]] temperament, and the 7-note MOS's are of prime interest here. Because of that, it's the first EDO I know how to create something like "functional harmony" in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: ////[[http://www.youtube.com/watch?v=KV_MzdtU2WQ]]////. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: [[@http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/]]. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).

----

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----

[[xenharmonic/11edo|11]] - Amazing and totally underrated EDO. It supports excellent 4:7:9:11 chords, as well as 4:7:9:11:15:17:19 chords if you're into that thing. Was once thought to be mostly "atonal" for lacking 3/2, but revealed as a low-numbered EDO of prime interest after the Great Subgroup Revolution Of 2011. Giving you decently accurate tetradic harmony for only 11 notes is almost a miracle. Supports [[Machine|machine]] temperament, of which the 2 2 1 2 2 2 MOS is of interest for being stable and sounding like a "warped diatonic." Example here that loosely uses it:

//[[http://www.youtube.com/watch?v=AhPjsCoMy-Q]]//. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this:

////[[http://www.youtube.com/watch?v=AhPjsCoMy-Q]]////. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this:

[[@http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/]]. Also, much like 8-EDO supports the excellent and underrated 2.9/7.5/3 version of sensi temperament.

----

[[xenharmonic/12edo|12]] (aka [[xenharmonic/19edt|19edt]], "standard semitones") - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of "hint" at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: //[[http://www.youtube.com/watch?v=CaPeks0H3_s]]//. Our theory places "12-EDO" and "meantone" as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it "has already been done"; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)

[[xenharmonic/12edo|12]] (aka [[xenharmonic/19edt|19edt]], "standard semitones") - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of "hint" at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: ////[[http://www.youtube.com/watch?v=CaPeks0H3_s]]////. Our theory places "12-EDO" and "meantone" as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it "has already been done"; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)

----

[[13]] is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the "octave" now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an "extension" in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called "A-team." Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.

[[13edo|13]] is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the "octave" now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an "extension" in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called "A-team." Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.

----

[[14edo|14-EDO]] has frickin touch tone noises! Holy shit! Just play two 7-EDO chains a b9 apart and you'll hear it! It's also interesting for not having 5/4 or 6/5 in any real capacity, but having 11/9 and 9/7 and a passable 7/6. So if you think about the way a 14-EDO native listener would hear the harmonic series, instead of hearing the sequence of intervals like octave-fifth-fourth-major third-minor third-smaller minor third, they'd probably hear octave-fifth-fourth-large neutral third-small neutral third-large subminor third-small subminor third-etc. Note that they'd probably not use names like "neutral" and "subminor" though, since those are just our names for those things. It also has a really interesting version of hedgehog temperament which makes the 5:6 in 5:6:7 out to be a neutral third; this is great for categories and then when you move into hedgehog[8] in 22-EDO, the scalar structure remains intelligible despite the intonation shifting under it. A great tuning I also wish I knew more about.

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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo">4</a> - lol

<hr />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edt">8edt</a>) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: </span~~><em~~><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=rPmuKUm2kJg" rel="nofollow">http://www.youtube.com/watch?v=rPmuKUm2kJg</a~~></em~~>

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edt">8edt</a>) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=rPmuKUm2kJg" rel="nofollow">http://www.youtube.com/watch?v=rPmuKUm2kJg</a>

<hr />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/6edo">6</a> - the whole tone scale. But, if you flatten the octaves, you can get almost perfect 4:5:7:11 chords, which is worth noting.

Line 88:

<hr />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/9edo">9</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edt">14edt</a>) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct &quot;major&quot; and &quot;minor&quot; chords, as detuned as they may be. This is also the first EDO that supports <a class="wiki_link" href="/Pelogic%20family">mavila</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Pelogic%20family">pelogic</a> temperament, and the 7-note MOS's are of prime interest here. Because of that, it's the first EDO I know how to create something like &quot;functional harmony&quot; in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: </span~~><em~~><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=KV_MzdtU2WQ" rel="nofollow">http://www.youtube.com/watch?v=KV_MzdtU2WQ</a~~></em~~>. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: <a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/" rel="nofollow" target="_blank">http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/</a>. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the &quot;minor thirds&quot; are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/9edo">9</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edt">14edt</a>) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct &quot;major&quot; and &quot;minor&quot; chords, as detuned as they may be. This is also the first EDO that supports <a class="wiki_link" href="/Pelogic%20family">mavila</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Pelogic%20family">pelogic</a> temperament, and the 7-note MOS's are of prime interest here. Because of that, it's the first EDO I know how to create something like &quot;functional harmony&quot; in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=KV_MzdtU2WQ" rel="nofollow">http://www.youtube.com/watch?v=KV_MzdtU2WQ</a>. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: <a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/" rel="nofollow" target="_blank">http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/</a>. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the &quot;minor thirds&quot; are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).

<hr />

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<hr />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edo">11</a> - Amazing and totally underrated EDO. It supports excellent 4:7:9:11 chords, as well as 4:7:9:11:15:17:19 chords if you're into that thing. Was once thought to be mostly &quot;atonal&quot; for lacking 3/2, but revealed as a low-numbered EDO of prime interest after the Great Subgroup Revolution Of 2011. Giving you decently accurate tetradic harmony for only 11 notes is almost a miracle. Supports <a class="wiki_link" href="/Machine">machine</a> temperament, of which the 2 2 1 2 2 2 MOS is of interest for being stable and sounding like a &quot;warped diatonic.&quot; Example here that loosely uses it:

~~~~<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=AhPjsCoMy-Q" rel="nofollow">http://www.youtube.com/watch?v=AhPjsCoMy-Q</a~~></em~~>. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another &quot;warped diatonic&quot; scale. An example of this:

<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=AhPjsCoMy-Q" rel="nofollow">http://www.youtube.com/watch?v=AhPjsCoMy-Q</a>. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another &quot;warped diatonic&quot; scale. An example of this:

<a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/" rel="nofollow" target="_blank">http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/</a>. Also, much like 8-EDO supports the excellent and underrated 2.9/7.5/3 version of sensi temperament.

<hr />

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edt">19edt</a>, &quot;standard semitones&quot;) - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of &quot;hint&quot; at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: </span~~><em~~><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=CaPeks0H3_s" rel="nofollow">http://www.youtube.com/watch?v=CaPeks0H3_s</a~~></em~~>. Our theory places &quot;12-EDO&quot; and &quot;meantone&quot; as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it &quot;has already been done&quot;; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edt">19edt</a>, &quot;standard semitones&quot;) - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of &quot;hint&quot; at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=CaPeks0H3_s" rel="nofollow">http://www.youtube.com/watch?v=CaPeks0H3_s</a>. Our theory places &quot;12-EDO&quot; and &quot;meantone&quot; as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it &quot;has already been done&quot;; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)

<hr />

<a class="wiki_link" href="/13">13</a> is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the &quot;octave&quot; now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an &quot;extension&quot; in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called &quot;A-team.&quot; Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.

<a class="wiki_link" href="/13edo">13</a> is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the &quot;octave&quot; now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an &quot;extension&quot; in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called &quot;A-team.&quot; Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.

<hr />

<a class="wiki_link" href="/14edo">14-EDO</a> has frickin touch tone noises! Holy shit! Just play two 7-EDO chains a b9 apart and you'll hear it! It's also interesting for not having 5/4 or 6/5 in any real capacity, but having 11/9 and 9/7 and a passable 7/6. So if you think about the way a 14-EDO native listener would hear the harmonic series, instead of hearing the sequence of intervals like octave-fifth-fourth-major third-minor third-smaller minor third, they'd probably hear octave-fifth-fourth-large neutral third-small neutral third-large subminor third-small subminor third-etc. Note that they'd probably not use names like &quot;neutral&quot; and &quot;subminor&quot; though, since those are just our names for those things. It also has a really interesting version of hedgehog temperament which makes the 5:6 in 5:6:7 out to be a neutral third; this is great for categories and then when you move into hedgehog[8] in 22-EDO, the scalar structure remains intelligible despite the intonation shifting under it. A great tuning I also wish I knew more about.

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-04-26 03:43:23 UTC</tt>.<br>
+: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2013-05-06 23:30:04 UTC</tt>.<br>
-: The original revision id was <tt>426598496</tt>.<br>
+: The original revision id was <tt>429430208</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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 &lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/4edo|4]] - lol&lt;/span&gt;
 ----
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/5edo|5]] (aka [[xenharmonic/8edt|8edt]]) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: &lt;/span&gt;//[[http://www.youtube.com/watch?v=rPmuKUm2kJg]]//
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/5edo|5]] (aka [[xenharmonic/8edt|8edt]]) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: &lt;/span&gt;////[[http://www.youtube.com/watch?v=rPmuKUm2kJg]]////
 ----
 &lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/6edo|6]] - the whole tone scale. But, if you flatten the octaves, you can get almost perfect 4:5:7:11 chords, which is worth noting.&lt;/span&gt;
@@ Line 28: / Line 28: @@
 ----
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/9edo|9]] (aka [[xenharmonic/14edt|14edt]]) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports [[Pelogic family|mavila]] and [[xenharmonic/Pelogic family|pelogic]]&lt;/span&gt; temperament&lt;span style="background-color: #ffffff;"&gt;, and the 7-note MOS's are of prime interest here. &lt;/span&gt;Because of that, &lt;span style="background-color: #ffffff;"&gt;it's the first EDO I know how to create something like "functional harmony" in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: &lt;/span&gt;//[[http://www.youtube.com/watch?v=KV_MzdtU2WQ]]//. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: [[@http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/]]. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/9edo|9]] (aka [[xenharmonic/14edt|14edt]]) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports [[Pelogic family|mavila]] and [[xenharmonic/Pelogic family|pelogic]]&lt;/span&gt; temperament&lt;span style="background-color: #ffffff;"&gt;, and the 7-note MOS's are of prime interest here. &lt;/span&gt;Because of that, &lt;span style="background-color: #ffffff;"&gt;it's the first EDO I know how to create something like "functional harmony" in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: &lt;/span&gt;////[[http://www.youtube.com/watch?v=KV_MzdtU2WQ]]////. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: [[@http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/]]. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).
 ----
@@ Line 34: / Line 34: @@
 ----
 &lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/11edo|11]] - Amazing and totally underrated EDO. It supports excellent 4:7:9:11 chords, as well as 4:7:9:11:15:17:19 chords if you're into that thing. Was once thought to be mostly "atonal" for lacking 3/2, but revealed as a low-numbered EDO of prime interest after the Great Subgroup Revolution Of 2011. Giving you decently accurate tetradic harmony for only 11 notes is almost a miracle. Supports [[Machine|machine]] temperament, of which the 2 2 1 2 2 2 MOS is of interest for being stable and sounding like a "warped diatonic." Example here that loosely uses it: &lt;/span&gt;
-//[[http://www.youtube.com/watch?v=AhPjsCoMy-Q]]//. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this:
+////[[http://www.youtube.com/watch?v=AhPjsCoMy-Q]]////. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this:
 [[@http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/]]. Also, much like 8-EDO supports the excellent and underrated 2.9/7.5/3 version of sensi temperament.
 ----
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/12edo|12]] (aka [[xenharmonic/19edt|19edt]], "standard semitones") - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of "hint" at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: &lt;/span&gt;//[[http://www.youtube.com/watch?v=CaPeks0H3_s]]//. Our theory places "12-EDO" and "meantone" as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it "has already been done"; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/12edo|12]] (aka [[xenharmonic/19edt|19edt]], "standard semitones") - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of "hint" at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: &lt;/span&gt;////[[http://www.youtube.com/watch?v=CaPeks0H3_s]]////. Our theory places "12-EDO" and "meantone" as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it "has already been done"; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)
 ----
-[[13]] is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the "octave" now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an "extension" in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called "A-team." Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.
+[[13edo|13]] is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the "octave" now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an "extension" in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called "A-team." Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.
 ----
 [[14edo|14-EDO]] has frickin touch tone noises! Holy shit! Just play two 7-EDO chains a b9 apart and you'll hear it! It's also interesting for not having 5/4 or 6/5 in any real capacity, but having 11/9 and 9/7 and a passable 7/6. So if you think about the way a 14-EDO native listener would hear the harmonic series, instead of hearing the sequence of intervals like octave-fifth-fourth-major third-minor third-smaller minor third, they'd probably hear octave-fifth-fourth-large neutral third-small neutral third-large subminor third-small subminor third-etc. Note that they'd probably not use names like "neutral" and "subminor" though, since those are just our names for those things. It also has a really interesting version of hedgehog temperament which makes the 5:6 in 5:6:7 out to be a neutral third; this is great for categories and then when you move into hedgehog[8] in 22-EDO, the scalar structure remains intelligible despite the intonation shifting under it. A great tuning I also wish I knew more about.
@@ Line 79: / Line 79: @@
 &lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo"&gt;4&lt;/a&gt; - lol&lt;/span&gt;&lt;br /&gt;
 &lt;hr /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo"&gt;5&lt;/a&gt; (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edt"&gt;8edt&lt;/a&gt;) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: &lt;/span&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=rPmuKUm2kJg" rel="nofollow"&gt;http://www.youtube.com/watch?v=rPmuKUm2kJg&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo"&gt;5&lt;/a&gt; (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edt"&gt;8edt&lt;/a&gt;) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: &lt;/span&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=rPmuKUm2kJg" rel="nofollow"&gt;http://www.youtube.com/watch?v=rPmuKUm2kJg&lt;/a&gt;&lt;br /&gt;
 &lt;hr /&gt;
 &lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/6edo"&gt;6&lt;/a&gt; - the whole tone scale. But, if you flatten the octaves, you can get almost perfect 4:5:7:11 chords, which is worth noting.&lt;/span&gt;&lt;br /&gt;
@@ Line 88: / Line 88: @@
 &lt;br /&gt;
 &lt;hr /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/9edo"&gt;9&lt;/a&gt; (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edt"&gt;14edt&lt;/a&gt;) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct &amp;quot;major&amp;quot; and &amp;quot;minor&amp;quot; chords, as detuned as they may be. This is also the first EDO that supports &lt;a class="wiki_link" href="/Pelogic%20family"&gt;mavila&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Pelogic%20family"&gt;pelogic&lt;/a&gt;&lt;/span&gt; temperament&lt;span style="background-color: #ffffff;"&gt;, and the 7-note MOS's are of prime interest here. &lt;/span&gt;Because of that, &lt;span style="background-color: #ffffff;"&gt;it's the first EDO I know how to create something like &amp;quot;functional harmony&amp;quot; in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: &lt;/span&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=KV_MzdtU2WQ" rel="nofollow"&gt;http://www.youtube.com/watch?v=KV_MzdtU2WQ&lt;/a&gt;&lt;/em&gt;. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: &lt;a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/" rel="nofollow" target="_blank"&gt;http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/&lt;/a&gt;. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the &amp;quot;minor thirds&amp;quot; are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/9edo"&gt;9&lt;/a&gt; (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edt"&gt;14edt&lt;/a&gt;) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct &amp;quot;major&amp;quot; and &amp;quot;minor&amp;quot; chords, as detuned as they may be. This is also the first EDO that supports &lt;a class="wiki_link" href="/Pelogic%20family"&gt;mavila&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Pelogic%20family"&gt;pelogic&lt;/a&gt;&lt;/span&gt; temperament&lt;span style="background-color: #ffffff;"&gt;, and the 7-note MOS's are of prime interest here. &lt;/span&gt;Because of that, &lt;span style="background-color: #ffffff;"&gt;it's the first EDO I know how to create something like &amp;quot;functional harmony&amp;quot; in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: &lt;/span&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=KV_MzdtU2WQ" rel="nofollow"&gt;http://www.youtube.com/watch?v=KV_MzdtU2WQ&lt;/a&gt;. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: &lt;a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/" rel="nofollow" target="_blank"&gt;http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/&lt;/a&gt;. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the &amp;quot;minor thirds&amp;quot; are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).&lt;br /&gt;
 &lt;br /&gt;
 &lt;hr /&gt;
@@ Line 94: / Line 94: @@
 &lt;hr /&gt;
 &lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edo"&gt;11&lt;/a&gt; - Amazing and totally underrated EDO. It supports excellent 4:7:9:11 chords, as well as 4:7:9:11:15:17:19 chords if you're into that thing. Was once thought to be mostly &amp;quot;atonal&amp;quot; for lacking 3/2, but revealed as a low-numbered EDO of prime interest after the Great Subgroup Revolution Of 2011. Giving you decently accurate tetradic harmony for only 11 notes is almost a miracle. Supports &lt;a class="wiki_link" href="/Machine"&gt;machine&lt;/a&gt; temperament, of which the 2 2 1 2 2 2 MOS is of interest for being stable and sounding like a &amp;quot;warped diatonic.&amp;quot; Example here that loosely uses it: &lt;/span&gt;&lt;br /&gt;
-&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=AhPjsCoMy-Q" rel="nofollow"&gt;http://www.youtube.com/watch?v=AhPjsCoMy-Q&lt;/a&gt;&lt;/em&gt;. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another &amp;quot;warped diatonic&amp;quot; scale. An example of this:&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=AhPjsCoMy-Q" rel="nofollow"&gt;http://www.youtube.com/watch?v=AhPjsCoMy-Q&lt;/a&gt;. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another &amp;quot;warped diatonic&amp;quot; scale. An example of this:&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/" rel="nofollow" target="_blank"&gt;http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/&lt;/a&gt;. Also, much like 8-EDO supports the excellent and underrated 2.9/7.5/3 version of sensi temperament.&lt;br /&gt;
 &lt;hr /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo"&gt;12&lt;/a&gt; (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edt"&gt;19edt&lt;/a&gt;, &amp;quot;standard semitones&amp;quot;) - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of &amp;quot;hint&amp;quot; at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: &lt;/span&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=CaPeks0H3_s" rel="nofollow"&gt;http://www.youtube.com/watch?v=CaPeks0H3_s&lt;/a&gt;&lt;/em&gt;. Our theory places &amp;quot;12-EDO&amp;quot; and &amp;quot;meantone&amp;quot; as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it &amp;quot;has already been done&amp;quot;; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo"&gt;12&lt;/a&gt; (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edt"&gt;19edt&lt;/a&gt;, &amp;quot;standard semitones&amp;quot;) - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of &amp;quot;hint&amp;quot; at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: &lt;/span&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=CaPeks0H3_s" rel="nofollow"&gt;http://www.youtube.com/watch?v=CaPeks0H3_s&lt;/a&gt;. Our theory places &amp;quot;12-EDO&amp;quot; and &amp;quot;meantone&amp;quot; as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it &amp;quot;has already been done&amp;quot;; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)&lt;br /&gt;
 &lt;hr /&gt;
-&lt;a class="wiki_link" href="/13"&gt;13&lt;/a&gt; is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the &amp;quot;octave&amp;quot; now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an &amp;quot;extension&amp;quot; in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called &amp;quot;A-team.&amp;quot; Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.&lt;br /&gt;
+&lt;a class="wiki_link" href="/13edo"&gt;13&lt;/a&gt; is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the &amp;quot;octave&amp;quot; now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an &amp;quot;extension&amp;quot; in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called &amp;quot;A-team.&amp;quot; Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.&lt;br /&gt;
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 &lt;a class="wiki_link" href="/14edo"&gt;14-EDO&lt;/a&gt; has frickin touch tone noises! Holy shit! Just play two 7-EDO chains a b9 apart and you'll hear it! It's also interesting for not having 5/4 or 6/5 in any real capacity, but having 11/9 and 9/7 and a passable 7/6. So if you think about the way a 14-EDO native listener would hear the harmonic series, instead of hearing the sequence of intervals like octave-fifth-fourth-major third-minor third-smaller minor third, they'd probably hear octave-fifth-fourth-large neutral third-small neutral third-large subminor third-small subminor third-etc. Note that they'd probably not use names like &amp;quot;neutral&amp;quot; and &amp;quot;subminor&amp;quot; though, since those are just our names for those things. It also has a really interesting version of hedgehog temperament which makes the 5:6 in 5:6:7 out to be a neutral third; this is great for categories and then when you move into hedgehog[8] in 22-EDO, the scalar structure remains intelligible despite the intonation shifting under it. A great tuning I also wish I knew more about.&lt;br /&gt;