Mike's EDO impressions: Difference between revisions

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(Everyone should make one of these!)

[[xenharmonic/1edo|1]]~~~~ - lol

[[xenharmonic/1edo|1]] - lol

[[xenharmonic/2edo|2]]~~~~ - lol

[[xenharmonic/2edo|2]] - lol

[[xenharmonic/3edo|3]]~~~~ - lol

[[xenharmonic/3edo|3]] - lol

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

[[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.

[[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.

[[xenharmonic/7edo|7]]~~~~ (aka ~~~~[[xenharmonic/11edt|11edt]]~~~~) - next-smallest EDO that has something resembling 3/2. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave [[88cET]], and which can also be thought of as a nonoctave version of [[Tetracot family|tetracot temperament]], with really good 2:3:5 chords.

[[xenharmonic/7edo|7]] (aka [[xenharmonic/11edt|11edt]]) - next-smallest EDO that has something resembling 3/2. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave [[88cET]], and which can also be thought of as a nonoctave version of [[Tetracot family|tetracot temperament]], with really good 2:3:5 chords.

[[xenharmonic/8edo|8]]~~~~ - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 [[sensamagic chords|sensamagic chord]]), made of two 450 cent "supermajor thirds" on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and "evil" sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be exceedingly beautiful: I don't know whether they "approximate 3/2 poorly" or "approximate 14/9 well" or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound "diminished." Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat "spacy" sounding music.

[[xenharmonic/8edo|8]] - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 [[sensamagic chords|sensamagic chord]]), made of two 450 cent "supermajor thirds" on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and "evil" sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be exceedingly beautiful: I don't know whether they "approximate 3/2 poorly" or "approximate 14/9 well" or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound "diminished." Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat "spacy" sounding music.

[[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/mikebattagliamusic/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/mikebattagliamusic/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/10edo|10]]~~~~ (aka ~~~~[[xenharmonic/16edt|16edt]]~~~~, "blackwood semitones") - A neutral triad version of ~~~~[[xenharmonic/Blackwood|blackwood]]~~~~, or a "neutral tetrad" version of [[pajara]], or a neutral [[negri]]~~~~, or a neutral ~~~~[[lemba]]~~~~. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for "diatonic"-style melodies, but haven't explored it as much yet. Also an equalized [[Trienstonic clan|octokaidecal]][10]. Need to play more

[[xenharmonic/10edo|10]] (aka [[xenharmonic/16edt|16edt]], "blackwood semitones") - A neutral triad version of [[xenharmonic/Blackwood|blackwood]], or a "neutral tetrad" version of [[pajara]], or a neutral [[negri]], or a neutral [[lemba]]. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for "diatonic"-style melodies, but haven't explored it as much yet. Also an equalized [[Trienstonic clan|octokaidecal]][10]. Need to play more

[[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:

[[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://soundcloud.com/mikebattagliamusic/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!!)

5-EDO - equipentatonic, which is trippy

7-EDO - equidiatonic, which is trippy

8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff

9-EDO - has a lot of what 16-EDO does but with less notes. However, 3/2 is weaker. comparing 9-EDO to 16-EDO can let you compare less notes + easier categorization vs more notes + better accuracy. Smallest EDO with major and minor chords (unless you count 8-EDO but that's kind of out there)

10-EDO - don't know a lot about it, but 10-note scales are interesting for also being something in which major and minor can share a triad class, which may be of semi-categorical relevance

11-EDO - has machine[6] which is a key warped diatonic scale, and orgone[7]. I'd say 11-EDO is way up there in terms of key things to learn for categories because it's small, has great 4:7:9:11 triads, and has warped diatonic scales.

~~That~~'s it for ~~now~~...</pre></div>

13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves

14-EDO - has the whole "kloog" slash "kleeg" thing going on, and also has touch tone noises as intervals for you to try and categorize

15-EDO - has 5-limit harmony plus a 5 note circle of 3/2's, which is crazy in terms of "tonality," which would seem to be peripherally relevant

16-EDO - is notable for being the first EDO (to me) where the 3 step interval can sound like "a step" instead of "a leap." Example is machine: 3 3 1 3 3 3. Much like 3 3 1 3 3 3 1 in 17-EDO, machine[6] in 16-EDO has L/s = 3/1 but the 3-step interval still sounds like "a second." It sounds like 16-EDO is an "enharmonic" scale for machine[11], which I (sort of) perceive as the true "background" for 331333, much like I perceive 19-EDO as an enharmonic underpinning for meantone[12] or whatever.</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Mike's EDO impressions</title></head><body>Template shamelessly stolen from <a class="wiki_link" href="/Keenan%27s%20EDO%20impressions">Keenan's EDO impressions</a>. I reserve the right to change this at any time if I missed something.

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(Everyone should make one of these!)

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/1edo">1</a> - lol

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/1edo">1</a> - lol

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2</a> - lol

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2</a> - lol

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3edo">3</a> - lol

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/3edo">3</a> - lol

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

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

<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>

<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>

<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.

<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.

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7</a~~> (aka ~~~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edt">11edt</a~~>) - next-smallest EDO that has something resembling 3/2. This sounds like an &quot;equalized&quot; diatonic scale, so that there are no more &quot;major&quot; or &quot;minor&quot; thirds, but just &quot;thirds.&quot; 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave <a class="wiki_link" href="/88cET">88cET</a>, and which can also be thought of as a nonoctave version of <a class="wiki_link" href="/Tetracot%20family">tetracot temperament</a>, with really good 2:3:5 chords.

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edt">11edt</a>) - next-smallest EDO that has something resembling 3/2. This sounds like an &quot;equalized&quot; diatonic scale, so that there are no more &quot;major&quot; or &quot;minor&quot; thirds, but just &quot;thirds.&quot; 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave <a class="wiki_link" href="/88cET">88cET</a>, and which can also be thought of as a nonoctave version of <a class="wiki_link" href="/Tetracot%20family">tetracot temperament</a>, with really good 2:3:5 chords.

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edo">8</a> - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 <a class="wiki_link" href="/sensamagic%20chords">sensamagic chord</a>), made of two 450 cent &quot;supermajor thirds&quot; on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and &quot;evil&quot; sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be exceedingly beautiful: I don't know whether they &quot;approximate 3/2 poorly&quot; or &quot;approximate 14/9 well&quot; or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound &quot;diminished.&quot; Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat &quot;spacy&quot; sounding music.

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edo">8</a> - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 <a class="wiki_link" href="/sensamagic%20chords">sensamagic chord</a>), made of two 450 cent &quot;supermajor thirds&quot; on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and &quot;evil&quot; sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be exceedingly beautiful: I don't know whether they &quot;approximate 3/2 poorly&quot; or &quot;approximate 14/9 well&quot; or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound &quot;diminished.&quot; Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat &quot;spacy&quot; sounding music.

<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/mikebattagliamusic/sets/the-mavila-experiments-9-edo/" rel="nofollow">http://soundcloud.com/mikebattagliamusic/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/mikebattagliamusic/sets/the-mavila-experiments-9-edo/" rel="nofollow">http://soundcloud.com/mikebattagliamusic/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/10edo">10</a~~> (aka ~~~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/16edt">16edt</a~~>, &quot;blackwood semitones&quot;) - A neutral triad version of ~~~~<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Blackwood">blackwood</a~~>, or a &quot;neutral tetrad&quot; version of <a class="wiki_link" href="/pajara">pajara</a>, or a neutral <a class="wiki_link" href="/negri">negri</a~~>, or a neutral ~~~~<a class="wiki_link" href="/lemba">lemba</a>. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for &quot;diatonic&quot;-style melodies, but haven't explored it as much yet. Also an equalized <a class="wiki_link" href="/Trienstonic%20clan">octokaidecal</a>[10]. Need to play more

<a class="wiki_link" href="http://xenharmonic.wikispaces.com/10edo">10</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16edt">16edt</a>, &quot;blackwood semitones&quot;) - A neutral triad version of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Blackwood">blackwood</a>, or a &quot;neutral tetrad&quot; version of <a class="wiki_link" href="/pajara">pajara</a>, or a neutral <a class="wiki_link" href="/negri">negri</a>, or a neutral <a class="wiki_link" href="/lemba">lemba</a>. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for &quot;diatonic&quot;-style melodies, but haven't explored it as much yet. Also an equalized <a class="wiki_link" href="/Trienstonic%20clan">octokaidecal</a>[10]. Need to play more

<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" 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>. 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/mikebattagliamusic/sets/tonal-study-in-orgone-temperament/" rel="nofollow">http://soundcloud.com/mikebattagliamusic/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.

<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!!)

<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!!)

5-EDO - equipentatonic, which is trippy

7-EDO - equidiatonic, which is trippy

8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff

9-EDO - has a lot of what 16-EDO does but with less notes. However, 3/2 is weaker. comparing 9-EDO to 16-EDO can let you compare less notes + easier categorization vs more notes + better accuracy. Smallest EDO with major and minor chords (unless you count 8-EDO but that's kind of out there)

10-EDO - don't know a lot about it, but 10-note scales are interesting for also being something in which major and minor can share a triad class, which may be of semi-categorical relevance

11-EDO - has machine[6] which is a key warped diatonic scale, and orgone[7]. I'd say 11-EDO is way up there in terms of key things to learn for categories because it's small, has great 4:7:9:11 triads, and has warped diatonic scales.

~~That~~'s it for ~~now~~...</body></html></pre></div>

13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves

14-EDO - has the whole &quot;kloog&quot; slash &quot;kleeg&quot; thing going on, and also has touch tone noises as intervals for you to try and categorize

15-EDO - has 5-limit harmony plus a 5 note circle of 3/2's, which is crazy in terms of &quot;tonality,&quot; which would seem to be peripherally relevant

16-EDO - is notable for being the first EDO (to me) where the 3 step interval can sound like &quot;a step&quot; instead of &quot;a leap.&quot; Example is machine: 3 3 1 3 3 3. Much like 3 3 1 3 3 3 1 in 17-EDO, machine[6] in 16-EDO has L/s = 3/1 but the 3-step interval still sounds like &quot;a second.&quot; It sounds like 16-EDO is an &quot;enharmonic&quot; scale for machine[11], which I (sort of) perceive as the true &quot;background&quot; for 331333, much like I perceive 19-EDO as an enharmonic underpinning for meantone[12] or whatever.</body></html></pre></div>

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-: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-03-28 15:00:54 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-06-16 00:02:41 UTC</tt>.<br>
-: The original revision id was <tt>315542442</tt>.<br>
+: The original revision id was <tt>345747814</tt>.<br>
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 (Everyone should make one of these!)
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/1edo|1]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - lol&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/1edo|1]] - lol&lt;/span&gt;
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/2edo|2]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - lol&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/2edo|2]] - lol&lt;/span&gt;
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/3edo|3]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - lol&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/3edo|3]] - lol&lt;/span&gt;
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/4edo|4]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - lol&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/4edo|4]] - lol&lt;/span&gt;
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/5edo|5]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/8edt|8edt]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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;[[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]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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;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;
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/7edo|7]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/11edt|11edt]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;) - next-smallest EDO that has something resembling 3/2. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave [[88cET]], and which can also be thought of as a nonoctave version of [[Tetracot family|tetracot temperament]], with really good 2:3:5 chords.&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/7edo|7]] (aka [[xenharmonic/11edt|11edt]]) - next-smallest EDO that has something resembling 3/2. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave [[88cET]], and which can also be thought of as a nonoctave version of [[Tetracot family|tetracot temperament]], with really good 2:3:5 chords.&lt;/span&gt;
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/8edo|8]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 [[sensamagic chords|sensamagic chord]]), made of two 450 cent "supermajor thirds" on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and "evil" sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be exceedingly beautiful: I don't know whether they "approximate 3/2 poorly" or "approximate 14/9 well" or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound "diminished." Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat "spacy" sounding music.&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/8edo|8]] - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 [[sensamagic chords|sensamagic chord]]), made of two 450 cent "supermajor thirds" on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and "evil" sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be exceedingly beautiful: I don't know whether they "approximate 3/2 poorly" or "approximate 14/9 well" or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound "diminished." Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat "spacy" sounding music.&lt;/span&gt;
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/9edo|9]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/14edt|14edt]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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 "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports [[Pelogic family|mavila]] and &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;[[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/mikebattagliamusic/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/mikebattagliamusic/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/10edo|10]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/16edt|16edt]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;, "blackwood semitones") - A neutral triad version of &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/Blackwood|blackwood]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;, or a "neutral tetrad" version of [[pajara]], or a neutral [[negri]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;, or a neutral &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;[[lemba]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for "diatonic"-style melodies, but haven't explored it as much yet. Also an equalized [[Trienstonic clan|octokaidecal]][10]. Need to play more&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/10edo|10]] (aka [[xenharmonic/16edt|16edt]], "blackwood semitones") - A neutral triad version of [[xenharmonic/Blackwood|blackwood]], or a "neutral tetrad" version of [[pajara]], or a neutral [[negri]], or a neutral [[lemba]]. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for "diatonic"-style melodies, but haven't explored it as much yet. Also an equalized [[Trienstonic clan|octokaidecal]][10]. Need to play more&lt;/span&gt;
-&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/11edo|11]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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 "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;
+&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://soundcloud.com/mikebattagliamusic/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]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;[[xenharmonic/19edt|19edt]]&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;, "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!!)
+&lt;span class="commentBody"&gt;5-EDO - equipentatonic, which is trippy&lt;/span&gt;
+&lt;span class="commentBody"&gt; 7-EDO - equidiatonic, which is trippy&lt;/span&gt;
+&lt;span class="commentBody"&gt; 8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff&lt;/span&gt;
+&lt;span class="commentBody"&gt; 9-EDO - has a lot of what 16-EDO does but with less notes. However, 3/2 is weaker. comparing 9-EDO to 16-EDO can let you compare less notes + easier categorization vs more notes + better accuracy. Smallest EDO with major and minor chords (unless you count 8-EDO but that's kind of out there)&lt;/span&gt;
+&lt;span class="commentBody"&gt; 10-EDO - don't know a lot about it, but 10-note scales are interesting for also being something in which major and minor can share a triad class, which may be of semi-categorical relevance&lt;/span&gt;
+&lt;span class="commentBody"&gt; 11-EDO - has machine[6] which is a key warped diatonic scale, and orgone[7]. I'd say 11-EDO is way up there in terms of key things to learn for categories because it's small, has great 4:7:9:11 triads, and has warped diatonic scales.&lt;/span&gt;
-That's it for now...</pre></div>
+&lt;span class="commentBody"&gt;13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves&lt;/span&gt;
+&lt;span class="commentBody"&gt; 14-EDO - has the whole "kloog" slash "kleeg" thing going on, and also has touch tone noises as intervals for you to try and categorize&lt;/span&gt;
+&lt;span class="commentBody"&gt; 15-EDO - has 5-limit harmony plus a 5 note circle of 3/2's, which is crazy in terms of "tonality," which would seem to be peripherally relevant&lt;/span&gt;
+&lt;span class="commentBody"&gt; 16-EDO - is notable for being the first EDO (to me) where the 3 step interval can sound like "a step" instead of "a leap." Example is machine: 3 3 1 3 3 3. Much like 3 3 1 3 3 3 1 in 17-EDO, machine[6] in 16-EDO has L/s = 3/1 but the 3-step interval still sounds like "a second." It sounds like 16-EDO is an "enharmonic" scale for machine[11], which I (sort of) perceive as the true "background" for 331333, much like I perceive 19-EDO as an enharmonic underpinning for meantone[12] or whatever.&lt;/span&gt;</pre></div>
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 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Mike's EDO impressions&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Template shamelessly stolen from &lt;a class="wiki_link" href="/Keenan%27s%20EDO%20impressions"&gt;Keenan's EDO impressions&lt;/a&gt;. I reserve the right to change this at any time if I missed something.&lt;br /&gt;
@@ Line 45: / Line 54: @@
 (Everyone should make one of these!)&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/1edo"&gt;1&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - lol&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/1edo"&gt;1&lt;/a&gt; - lol&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo"&gt;2&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - lol&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo"&gt;2&lt;/a&gt; - lol&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3edo"&gt;3&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - lol&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3edo"&gt;3&lt;/a&gt; - lol&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo"&gt;4&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - lol&lt;/span&gt;&lt;br /&gt;
+&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;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;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edt"&gt;8edt&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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;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;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/6edo"&gt;6&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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;
+&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;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo"&gt;7&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edt"&gt;11edt&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;) - next-smallest EDO that has something resembling 3/2. This sounds like an &amp;quot;equalized&amp;quot; diatonic scale, so that there are no more &amp;quot;major&amp;quot; or &amp;quot;minor&amp;quot; thirds, but just &amp;quot;thirds.&amp;quot; 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave &lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt;, and which can also be thought of as a nonoctave version of &lt;a class="wiki_link" href="/Tetracot%20family"&gt;tetracot temperament&lt;/a&gt;, with really good 2:3:5 chords.&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo"&gt;7&lt;/a&gt; (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edt"&gt;11edt&lt;/a&gt;) - next-smallest EDO that has something resembling 3/2. This sounds like an &amp;quot;equalized&amp;quot; diatonic scale, so that there are no more &amp;quot;major&amp;quot; or &amp;quot;minor&amp;quot; thirds, but just &amp;quot;thirds.&amp;quot; 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave &lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt;, and which can also be thought of as a nonoctave version of &lt;a class="wiki_link" href="/Tetracot%20family"&gt;tetracot temperament&lt;/a&gt;, with really good 2:3:5 chords.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edo"&gt;8&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 &lt;a class="wiki_link" href="/sensamagic%20chords"&gt;sensamagic chord&lt;/a&gt;), made of two 450 cent &amp;quot;supermajor thirds&amp;quot; on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and &amp;quot;evil&amp;quot; sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be exceedingly beautiful: I don't know whether they &amp;quot;approximate 3/2 poorly&amp;quot; or &amp;quot;approximate 14/9 well&amp;quot; or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound &amp;quot;diminished.&amp;quot; Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat &amp;quot;spacy&amp;quot; sounding music.&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edo"&gt;8&lt;/a&gt; - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 &lt;a class="wiki_link" href="/sensamagic%20chords"&gt;sensamagic chord&lt;/a&gt;), made of two 450 cent &amp;quot;supermajor thirds&amp;quot; on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and &amp;quot;evil&amp;quot; sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be exceedingly beautiful: I don't know whether they &amp;quot;approximate 3/2 poorly&amp;quot; or &amp;quot;approximate 14/9 well&amp;quot; or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound &amp;quot;diminished.&amp;quot; Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat &amp;quot;spacy&amp;quot; sounding music.&lt;/span&gt;&lt;br /&gt;
 &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;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edt"&gt;14edt&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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;/span&gt;&lt;span style="background-color: #ffffff;"&gt;&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/mikebattagliamusic/sets/the-mavila-experiments-9-edo/" rel="nofollow"&gt;http://soundcloud.com/mikebattagliamusic/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/mikebattagliamusic/sets/the-mavila-experiments-9-edo/" rel="nofollow"&gt;http://soundcloud.com/mikebattagliamusic/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;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/10edo"&gt;10&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/16edt"&gt;16edt&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;, &amp;quot;blackwood semitones&amp;quot;) - A neutral triad version of &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Blackwood"&gt;blackwood&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;, or a &amp;quot;neutral tetrad&amp;quot; version of &lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt;, or a neutral &lt;a class="wiki_link" href="/negri"&gt;negri&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;, or a neutral &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="/lemba"&gt;lemba&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for &amp;quot;diatonic&amp;quot;-style melodies, but haven't explored it as much yet. Also an equalized &lt;a class="wiki_link" href="/Trienstonic%20clan"&gt;octokaidecal&lt;/a&gt;[10]. Need to play more&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/10edo"&gt;10&lt;/a&gt; (aka &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/16edt"&gt;16edt&lt;/a&gt;, &amp;quot;blackwood semitones&amp;quot;) - A neutral triad version of &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Blackwood"&gt;blackwood&lt;/a&gt;, or a &amp;quot;neutral tetrad&amp;quot; version of &lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt;, or a neutral &lt;a class="wiki_link" href="/negri"&gt;negri&lt;/a&gt;, or a neutral &lt;a class="wiki_link" href="/lemba"&gt;lemba&lt;/a&gt;. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for &amp;quot;diatonic&amp;quot;-style melodies, but haven't explored it as much yet. Also an equalized &lt;a class="wiki_link" href="/Trienstonic%20clan"&gt;octokaidecal&lt;/a&gt;[10]. Need to play more&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edo"&gt;11&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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;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;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://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/mikebattagliamusic/sets/tonal-study-in-orgone-temperament/" rel="nofollow"&gt;http://soundcloud.com/mikebattagliamusic/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;br /&gt;
 &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;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt; (aka &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edt"&gt;19edt&lt;/a&gt;&lt;/span&gt;&lt;span style="background-color: #ffffff;"&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;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;br /&gt;
+&lt;span class="commentBody"&gt;5-EDO - equipentatonic, which is trippy&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; 7-EDO - equidiatonic, which is trippy&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; 8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; 9-EDO - has a lot of what 16-EDO does but with less notes. However, 3/2 is weaker. comparing 9-EDO to 16-EDO can let you compare less notes + easier categorization vs more notes + better accuracy. Smallest EDO with major and minor chords (unless you count 8-EDO but that's kind of out there)&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; 10-EDO - don't know a lot about it, but 10-note scales are interesting for also being something in which major and minor can share a triad class, which may be of semi-categorical relevance&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; 11-EDO - has machine[6] which is a key warped diatonic scale, and orgone[7]. I'd say 11-EDO is way up there in terms of key things to learn for categories because it's small, has great 4:7:9:11 triads, and has warped diatonic scales.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-That's it for now...&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;span class="commentBody"&gt;13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; 14-EDO - has the whole &amp;quot;kloog&amp;quot; slash &amp;quot;kleeg&amp;quot; thing going on, and also has touch tone noises as intervals for you to try and categorize&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; 15-EDO - has 5-limit harmony plus a 5 note circle of 3/2's, which is crazy in terms of &amp;quot;tonality,&amp;quot; which would seem to be peripherally relevant&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; 16-EDO - is notable for being the first EDO (to me) where the 3 step interval can sound like &amp;quot;a step&amp;quot; instead of &amp;quot;a leap.&amp;quot; Example is machine: 3 3 1 3 3 3. Much like 3 3 1 3 3 3 1 in 17-EDO, machine[6] in 16-EDO has L/s = 3/1 but the 3-step interval still sounds like &amp;quot;a second.&amp;quot; It sounds like 16-EDO is an &amp;quot;enharmonic&amp;quot; scale for machine[11], which I (sort of) perceive as the true &amp;quot;background&amp;quot; for 331333, much like I perceive 19-EDO as an enharmonic underpinning for meantone[12] or whatever.&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>