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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : 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> | : The original revision id was <tt>345747814</tt>.<br> | ||
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(Everyone should make one of these!) | (Everyone should make one of these!) | ||
<span style="background-color: #ffffff;">[[xenharmonic/1edo|1]] | <span style="background-color: #ffffff;">[[xenharmonic/1edo|1]] - lol</span> | ||
<span style="background-color: #ffffff;">[[xenharmonic/2edo|2]] | <span style="background-color: #ffffff;">[[xenharmonic/2edo|2]] - lol</span> | ||
<span style="background-color: #ffffff;">[[xenharmonic/3edo|3]] | <span style="background-color: #ffffff;">[[xenharmonic/3edo|3]] - lol</span> | ||
<span style="background-color: #ffffff;">[[xenharmonic/4edo|4]] | <span style="background-color: #ffffff;">[[xenharmonic/4edo|4]] - lol</span> | ||
<span style="background-color: #ffffff;">[[xenharmonic/5edo|5]] | <span style="background-color: #ffffff;">[[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: </span>[[http://www.youtube.com/watch?v=rPmuKUm2kJg]] | ||
<span style="background-color: #ffffff;">[[xenharmonic/6edo|6]] | <span style="background-color: #ffffff;">[[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.</span> | ||
<span style="background-color: #ffffff;">[[xenharmonic/7edo|7]] | <span style="background-color: #ffffff;">[[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.</span> | ||
<span style="background-color: #ffffff;">[[xenharmonic/8edo|8]] | <span style="background-color: #ffffff;">[[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.</span> | ||
<span style="background-color: #ffffff;">[[xenharmonic/9edo|9]] | <span style="background-color: #ffffff;">[[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]]</span> temperament<span style="background-color: #ffffff;">, and the 7-note MOS's are of prime interest here. </span>Because of that, <span style="background-color: #ffffff;">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: </span>[[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). | ||
<span style="background-color: #ffffff;">[[xenharmonic/10edo|10]] | <span style="background-color: #ffffff;">[[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</span> | ||
<span style="background-color: #ffffff;">[[xenharmonic/11edo|11]] | <span style="background-color: #ffffff;">[[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: </span> | ||
[[http://www.youtube.com/watch?v=AhPjsCoMy-Q]]. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this: | [[http://www.youtube.com/watch?v=AhPjsCoMy-Q]]. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this: | ||
[[http://soundcloud.com/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. | [[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. | ||
<span style="background-color: #ffffff;">[[xenharmonic/12edo|12]] | <span style="background-color: #ffffff;">[[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: </span>[[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!!) | ||
<span class="commentBody">5-EDO - equipentatonic, which is trippy</span> | |||
<span class="commentBody"> 7-EDO - equidiatonic, which is trippy</span> | |||
<span class="commentBody"> 8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff</span> | |||
<span class="commentBody"> 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)</span> | |||
<span class="commentBody"> 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</span> | |||
<span class="commentBody"> 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.</span> | |||
<span class="commentBody">13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves</span> | |||
<span class="commentBody"> 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</span> | |||
<span class="commentBody"> 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</span> | |||
<span class="commentBody"> 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.</span></pre></div> | |||
<h4>Original HTML content:</h4> | <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.<br /> | <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.<br /> | ||
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(Everyone should make one of these!)<br /> | (Everyone should make one of these!)<br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1edo">1</a | <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1edo">1</a> - lol</span><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2</a | <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2</a> - lol</span><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3edo">3</a | <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3edo">3</a> - lol</span><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo">4</a | <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo">4</a> - lol</span><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5</a | <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edt">8edt</a>) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: </span><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=rPmuKUm2kJg" rel="nofollow">http://www.youtube.com/watch?v=rPmuKUm2kJg</a><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/6edo">6</a | <span style="background-color: #ffffff;"><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.</span><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7</a | <span style="background-color: #ffffff;"><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.</span><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edo">8</a | <span style="background-color: #ffffff;"><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.</span><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/9edo">9</a | <span style="background-color: #ffffff;"><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></span> temperament<span style="background-color: #ffffff;">, and the 7-note MOS's are of prime interest here. </span>Because of that, <span style="background-color: #ffffff;">it's the first EDO I know how to create something like &quot;functional harmony&quot; in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: </span><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).<br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/10edo">10</a | <span style="background-color: #ffffff;"><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</span><br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edo">11</a | <span style="background-color: #ffffff;"><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: </span><br /> | ||
<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: <br /> | <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:<br /> | ||
<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.<br /> | <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.<br /> | ||
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<span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12</a | <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edt">19edt</a>, &quot;standard semitones&quot;) - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of &quot;hint&quot; at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: </span><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!!)<br /> | ||
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<span class="commentBody">5-EDO - equipentatonic, which is trippy</span><br /> | |||
<span class="commentBody"> 7-EDO - equidiatonic, which is trippy</span><br /> | |||
<span class="commentBody"> 8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff</span><br /> | |||
<span class="commentBody"> 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)</span><br /> | |||
<span class="commentBody"> 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</span><br /> | |||
<span class="commentBody"> 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.</span><br /> | |||
<br /> | <br /> | ||
<span class="commentBody">13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves</span><br /> | |||
<span class="commentBody"> 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</span><br /> | |||
<span class="commentBody"> 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</span><br /> | |||
<span class="commentBody"> 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.</span></body></html></pre></div> | |||
Revision as of 00:02, 16 June 2012
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Template shamelessly stolen from [[Keenan's EDO impressions]]. I reserve the right to change this at any time if I missed something. (Everyone should make one of these!) <span style="background-color: #ffffff;">[[xenharmonic/1edo|1]] - lol</span> <span style="background-color: #ffffff;">[[xenharmonic/2edo|2]] - lol</span> <span style="background-color: #ffffff;">[[xenharmonic/3edo|3]] - lol</span> <span style="background-color: #ffffff;">[[xenharmonic/4edo|4]] - lol</span> <span style="background-color: #ffffff;">[[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: </span>[[http://www.youtube.com/watch?v=rPmuKUm2kJg]] <span style="background-color: #ffffff;">[[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.</span> <span style="background-color: #ffffff;">[[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.</span> <span style="background-color: #ffffff;">[[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.</span> <span style="background-color: #ffffff;">[[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]]</span> temperament<span style="background-color: #ffffff;">, and the 7-note MOS's are of prime interest here. </span>Because of that, <span style="background-color: #ffffff;">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: </span>[[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). <span style="background-color: #ffffff;">[[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</span> <span style="background-color: #ffffff;">[[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: </span> [[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. <span style="background-color: #ffffff;">[[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: </span>[[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!!) <span class="commentBody">5-EDO - equipentatonic, which is trippy</span> <span class="commentBody"> 7-EDO - equidiatonic, which is trippy</span> <span class="commentBody"> 8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff</span> <span class="commentBody"> 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)</span> <span class="commentBody"> 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</span> <span class="commentBody"> 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.</span> <span class="commentBody">13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves</span> <span class="commentBody"> 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</span> <span class="commentBody"> 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</span> <span class="commentBody"> 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.</span>
Original HTML content:
<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.<br /> <br /> (Everyone should make one of these!)<br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1edo">1</a> - lol</span><br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2</a> - lol</span><br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3edo">3</a> - lol</span><br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo">4</a> - lol</span><br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5</a> (aka <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edt">8edt</a>) - smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: </span><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=rPmuKUm2kJg" rel="nofollow">http://www.youtube.com/watch?v=rPmuKUm2kJg</a><br /> <br /> <br /> <span style="background-color: #ffffff;"><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.</span><br /> <br /> <span style="background-color: #ffffff;"><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 "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 <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.</span><br /> <br /> <span style="background-color: #ffffff;"><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 "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.</span><br /> <br /> <span style="background-color: #ffffff;"><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 "major" and "minor" 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></span> temperament<span style="background-color: #ffffff;">, and the 7-note MOS's are of prime interest here. </span>Because of that, <span style="background-color: #ffffff;">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: </span><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 "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).<br /> <br /> <span style="background-color: #ffffff;"><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>, "blackwood semitones") - A neutral triad version of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Blackwood">blackwood</a>, or a "neutral tetrad" 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 "diatonic"-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</span><br /> <br /> <span style="background-color: #ffffff;"><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 "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 <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 "warped diatonic." Example here that loosely uses it: </span><br /> <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 "warped diatonic" scale. An example of this:<br /> <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.<br /> <br /> <br /> <span style="background-color: #ffffff;"><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>, "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: </span><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 "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!!)<br /> <br /> <span class="commentBody">5-EDO - equipentatonic, which is trippy</span><br /> <span class="commentBody"> 7-EDO - equidiatonic, which is trippy</span><br /> <span class="commentBody"> 8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff</span><br /> <span class="commentBody"> 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)</span><br /> <span class="commentBody"> 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</span><br /> <span class="commentBody"> 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.</span><br /> <br /> <span class="commentBody">13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves</span><br /> <span class="commentBody"> 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</span><br /> <span class="commentBody"> 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</span><br /> <span class="commentBody"> 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.</span></body></html>