Mike's EDO impressions: Difference between revisions

Line 1:

<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:~~guest~~|~~guest~~]] and made on <tt>2013-02-~~15 17~~:38:20 UTC</tt>.

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

: The original revision id was <tt>~~407391624~~</tt>.

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

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

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 41:

[[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.

----

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.

[[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.

----

15-EDO is the first EDO in what I call the "Holy Trinity" of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are "outside of" the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.

[[15edo|15-EDO]] is the first EDO in what I call the "Holy Trinity" of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are "outside of" the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.

5-EDO - equipentatonic, which is trippy

Line 101:

<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.

<hr />

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 &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.

<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.

<hr />

15-EDO is the first EDO in what I call the &quot;Holy Trinity&quot; of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are &quot;outside of&quot; the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.

<a class="wiki_link" href="/15edo">15-EDO</a> is the first EDO in what I call the &quot;Holy Trinity&quot; of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are &quot;outside of&quot; the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.

5-EDO - equipentatonic, which is trippy

@@ Line 1: / Line 1: @@
 <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:guest|guest]] and made on <tt>2013-02-15 17:38:20 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-04-26 03:43:23 UTC</tt>.<br>
-: The original revision id was <tt>407391624</tt>.<br>
+: The original revision id was <tt>426598496</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>
@@ Line 41: / Line 41: @@
 [[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.
 ----
--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.
+[[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.
 ----
--EDO is the first EDO in what I call the "Holy Trinity" of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are "outside of" the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.
+[[15edo|15-EDO]] is the first EDO in what I call the "Holy Trinity" of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are "outside of" the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.
 &lt;span class="commentBody"&gt;5-EDO - equipentatonic, which is trippy&lt;/span&gt;
@@ Line 101: / Line 101: @@
 &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;hr /&gt;
--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 &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;
+&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;
 &lt;hr /&gt;
--EDO is the first EDO in what I call the &amp;quot;Holy Trinity&amp;quot; of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are &amp;quot;outside of&amp;quot; the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.&lt;br /&gt;
+&lt;a class="wiki_link" href="/15edo"&gt;15-EDO&lt;/a&gt; is the first EDO in what I call the &amp;quot;Holy Trinity&amp;quot; of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are &amp;quot;outside of&amp;quot; the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.&lt;br /&gt;
 &lt;br /&gt;
 &lt;span class="commentBody"&gt;5-EDO - equipentatonic, which is trippy&lt;/span&gt;&lt;br /&gt;