Mike's EDO impressions
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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]]</span><span style="background-color: #ffffff;"> - lol</span> <span style="background-color: #ffffff;">[[xenharmonic/2edo|2]]</span><span style="background-color: #ffffff;"> - lol</span> <span style="background-color: #ffffff;">[[xenharmonic/3edo|3]]</span><span style="background-color: #ffffff;"> - lol</span> <span style="background-color: #ffffff;">[[xenharmonic/4edo|4]]</span><span style="background-color: #ffffff;"> - lol</span> <span style="background-color: #ffffff;">[[xenharmonic/5edo|5]]</span><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;">[[xenharmonic/8edt|8edt]]</span><span style="background-color: #ffffff;">) - 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><span style="background-color: #ffffff;"> - 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><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;">[[xenharmonic/11edt|11edt]]</span><span style="background-color: #ffffff;">) - 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><span style="background-color: #ffffff;"> - 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><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;">[[xenharmonic/14edt|14edt]]</span><span style="background-color: #ffffff;">) - 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 </span><span style="background-color: #ffffff;">[[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><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;">[[xenharmonic/16edt|16edt]]</span><span style="background-color: #ffffff;">, "blackwood semitones") - A neutral triad version of </span><span style="background-color: #ffffff;">[[xenharmonic/Blackwood|blackwood]]</span><span style="background-color: #ffffff;">, or a "neutral tetrad" version of [[pajara]], or a neutral [[negri]]</span><span style="background-color: #ffffff;">, or a neutral </span><span style="background-color: #ffffff;">[[lemba]]</span><span style="background-color: #ffffff;">. 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><span style="background-color: #ffffff;"> - 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]]</span><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;">[[xenharmonic/19edt|19edt]]</span><span style="background-color: #ffffff;">, "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!!) That's it for now...
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></span><span style="background-color: #ffffff;"> - lol</span><br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2</a></span><span style="background-color: #ffffff;"> - lol</span><br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3edo">3</a></span><span style="background-color: #ffffff;"> - lol</span><br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo">4</a></span><span style="background-color: #ffffff;"> - lol</span><br /> <br /> <span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5</a></span><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/8edt">8edt</a></span><span style="background-color: #ffffff;">) - 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></span><span style="background-color: #ffffff;"> - 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></span><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/11edt">11edt</a></span><span style="background-color: #ffffff;">) - 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></span><span style="background-color: #ffffff;"> - 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></span><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edt">14edt</a></span><span style="background-color: #ffffff;">) - 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 </span><span style="background-color: #ffffff;"><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></span><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/16edt">16edt</a></span><span style="background-color: #ffffff;">, "blackwood semitones") - A neutral triad version of </span><span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Blackwood">blackwood</a></span><span style="background-color: #ffffff;">, 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></span><span style="background-color: #ffffff;">, or a neutral </span><span style="background-color: #ffffff;"><a class="wiki_link" href="/lemba">lemba</a></span><span style="background-color: #ffffff;">. 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></span><span style="background-color: #ffffff;"> - 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></span><span style="background-color: #ffffff;"> (aka </span><span style="background-color: #ffffff;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/19edt">19edt</a></span><span style="background-color: #ffffff;">, "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 /> <br /> That's it for now...</body></html>