Composing Powerstart: Difference between revisions
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Musicians and composers just getting into the area of microtuning might, in an initial survey of the available resources on tuning around the web, encounter a barrage of intimidating jargon and mathematical concepts. Fortunately, a composer or player need not worry about the math side of things! This article suggests a number of ways to jump right in and start putting the //products// of tuning theory to work. | Musicians and composers just getting into the area of microtuning might, in an initial survey of the available resources on tuning around the web, encounter a barrage of intimidating jargon and mathematical concepts. Fortunately, a composer or player need not worry about the math side of things! This article suggests a number of ways to jump right in and start putting the //products// of tuning theory to work. | ||
Quoted from the Xenharmonic Alliance II, January 21 2013: | Quoted from the Xenharmonic Alliance II, January 21 2013: | ||
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===Math: Use as much or as little as you'd like=== | |||
//Mike Battaglia wrote:// | |||
=====<span class="userContent"> "Tuning math is complex. But, if you're a composer, you don't need to ever worry about it. You don't ever need to know what a val is, or what a wedgie is, or what an epimorphic scale is, if you don't want. You don't need to learn how matrix multiplication works or deal with any of that. Those things are useful mathematical constructions which make it easier to communicate, program, and reason about the topic at hand, but they're not anything that a musician should ever, in general, have to know about to write microtonal music.</span>===== | |||
=====<span class="userContent"> If, on the other hand, you DO want to learn tuning math, a basic undergraduate linear algebra course will enable you to understand about 90% of it if we phrase it a certain way.</span>===== | =====<span class="userContent"> If, on the other hand, you DO want to learn tuning math, a basic undergraduate linear algebra course will enable you to understand about 90% of it if we phrase it a certain way.</span>===== | ||
=====<span class="userContent"> But if you don't, then you don't need to. Just ask here for a tuning system and we'll recommend you like a hundred to use, along with some associated scales, and some suggestions for using them. Then it's up to you to go nuts and write. That's all it requires."</span>===== | =====<span class="userContent"> But if you don't, then you don't need to. Just ask here for a tuning system and we'll recommend you like a hundred to use, along with some associated scales, and some suggestions for using them. Then it's up to you to go nuts and write. That's all it requires."</span>===== | ||
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<span class="userContent">Keenan Pepper wrote:</span> | //<span class="userContent">Keenan Pepper wrote:</span>// | ||
<span class="userContent">"</span>And the way to really understand regular temperaments without bothering with all the math is: | <span class="userContent">"</span>And the way to really understand regular temperaments without bothering with all the math is: | ||
* Learn a reasonable amount about just intonation. Things like "prime limit" and "otonality" shouldn't scare you. Being familiar with the whole 11-limit tonality diamond is a good thing. | * Learn a reasonable amount about just intonation. Things like "prime limit" and "otonality" shouldn't scare you. Being familiar with the whole 11-limit tonality diamond is a good thing. | ||
* For each temperament you're interested in, learn how the different tempered JI intervals relate to each other in that temperament. For example, in porcupine two 11/10s equals one 6/5, and that interval (11/10) also represents 12/11 and 10/9 at the same time. | * For each temperament you're interested in, learn how the different tempered JI intervals relate to each other in that temperament. For example, in porcupine two 11/10s equals one 6/5, and that interval (11/10) also represents 12/11 and 10/9 at the same time. | ||
You can express this in a complicated mathematical way with linear alegbra, but that's completely unnecessary if you understand it in a musical way as relationships between intervals you're already familiar with." | You can express this in a complicated mathematical way with linear alegbra, but that's completely unnecessary if you understand it in a musical way as relationships between intervals you're already familiar with." | ||
---- | |||
Mike Battaglia wrote: | ===Porcupine=== | ||
//Mike Battaglia wrote:// | |||
"For starters, you might want to mess around with what's called "porcupine" temperament in 22-EDO. The base diatonic-sized scale is (as steps out of 22-EDO) 4 3 3 3 3 3 3, and you can chromatically alter anything in that scale you want by 1 step out of 22. For instance, if you flat the 7, you get the scale 4 3 3 3 3 2 4, which is nice because it has a 4:5:6:7:9:11 chord in it. There's another "superdiatonic" scale at 1 3 3 3 3 3 3 3 which you can morph the above into if you want, and a 15-note chromatic scale at 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2; feel free to not stick dogmatically to these exact scales but to change them as you desire. | "For starters, you might want to mess around with what's called "porcupine" temperament in 22-EDO. The base diatonic-sized scale is (as steps out of 22-EDO) 4 3 3 3 3 3 3, and you can chromatically alter anything in that scale you want by 1 step out of 22. For instance, if you flat the 7, you get the scale 4 3 3 3 3 2 4, which is nice because it has a 4:5:6:7:9:11 chord in it. There's another "superdiatonic" scale at 1 3 3 3 3 3 3 3 which you can morph the above into if you want, and a 15-note chromatic scale at 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2; feel free to not stick dogmatically to these exact scales but to change them as you desire. | ||
If you don't mind a bit less accuracy in representing harmonic ratios, the above temperament also exists in 15-EDO, except the diatonic-sized scale is now 3 2 2 2 2 2 2, the superdiatonic is 1 2 2 2 2 2 2 2, and the chromatic scale is all of 15-EDO. 15-EDO also has a really nice "symmetrical diatonic" scale, called the Blackwood-10 scale, which is 2 1 2 1 2 1 2 1 2 1. Play around with major and minor chords in this scale a bit, and transpose them up and down the shape of the scale, and you'll see why it's so magical - the circle of fifths is only five steps long. | If you don't mind a bit less accuracy in representing harmonic ratios, the above temperament also exists in 15-EDO, except the diatonic-sized scale is now 3 2 2 2 2 2 2, the superdiatonic is 1 2 2 2 2 2 2 2, and the chromatic scale is all of 15-EDO. 15-EDO also has a really nice "symmetrical diatonic" scale, called the Blackwood-10 scale, which is 2 1 2 1 2 1 2 1 2 1. Play around with major and minor chords in this scale a bit, and transpose them up and down the shape of the scale, and you'll see why it's so magical - the circle of fifths is only five steps long." | ||
---- | |||
===World Music Scales=== | |||
If you don't care about harmonic ratios at all, but perhaps instead care about world music, then you might enjoy 16-EDO, which contains in it a wonderful extension of both gamelan music and Chopi timbila music; 5 2 2 5 2 is a great pelog and 3 3 3 4 3 works as slendro. | If you don't care about harmonic ratios at all, but perhaps instead care about world music, then you might enjoy 16-EDO, which contains in it a wonderful extension of both gamelan music and Chopi timbila music; 5 2 2 5 2 is a great pelog and 3 3 3 4 3 works as slendro. | ||
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The 3 3 3 4 3 slendro can turn into the 3 3 3 1 3 3 "slendric-6" scale as well, though I prefer the 3 3 1 3 3 3 mode. This scale is nice because it sounds kind of like a "warped diatonic" scale. Chromatically altering things by 2 steps here, instead of 1 step, sounds really nice. | The 3 3 3 4 3 slendro can turn into the 3 3 3 1 3 3 "slendric-6" scale as well, though I prefer the 3 3 1 3 3 3 mode. This scale is nice because it sounds kind of like a "warped diatonic" scale. Chromatically altering things by 2 steps here, instead of 1 step, sounds really nice. | ||
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World music fans might also like 17-EDO, which contains within it a system of scales very similar to the maqamat used in the middle east; 24-EDO and 31-EDO contain the same features but with better intonation, albeit at the cost of more notes, but you can always use smaller 17-note subsets if you want. | World music fans might also like 17-EDO, which contains within it a system of scales very similar to the maqamat used in the middle east; 24-EDO and 31-EDO contain the same features but with better intonation, albeit at the cost of more notes, but you can always use smaller 17-note subsets if you want. | ||
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A really good paper on how 17-EDO offers a sort of bizarro-universe for the diatonic scale, which we might have gone with historically if things were different, can be found at [[@http://www.anaphoria.com/Secor17puzzle.pdf]]. | A really good paper on how 17-EDO offers a sort of bizarro-universe for the diatonic scale, which we might have gone with historically if things were different, can be found at [[@http://www.anaphoria.com/Secor17puzzle.pdf]]. | ||
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===Historical Tunings and Extended Meantone=== | |||
Some people are really interested in historic tunings for meantone, and perhaps extending them in ways that go beyond the 12-EDO "closure" that we ended up going with. So if you really want to get away from the notion that C# has to equal Db, and want to explore extended meantone, there's a number of great options for you. | Some people are really interested in historic tunings for meantone, and perhaps extending them in ways that go beyond the 12-EDO "closure" that we ended up going with. So if you really want to get away from the notion that C# has to equal Db, and want to explore extended meantone, there's a number of great options for you. | ||
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You can do all sorts of amazing stuff with 19-EDO if you want, and make it sound almost exactly like ordinary 12-EDO music too, but then depart from it into some rather mind-blowing stuff if you want. | You can do all sorts of amazing stuff with 19-EDO if you want, and make it sound almost exactly like ordinary 12-EDO music too, but then depart from it into some rather mind-blowing stuff if you want. | ||
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There are also the people who care about none of this, but really just want really well-intoned higher-limit chords. | ===Higher Accuracy=== | ||
There are also the people who care about none of this, but really just want really well-intoned higher-limit chords. <span class="wiki_link_ext">Gene Smith</span> is certainly the person who's explored this style the most, though I also have a few things to say about it. | |||
These people already tend to know a bit of math related to JI, so I'll assume you know what a prime limit is and what ratios are below, as well as having some compositional idea of the sounds you're after. | These people already tend to know a bit of math related to JI, so I'll assume you know what a prime limit is and what ratios are below, as well as having some compositional idea of the sounds you're after. | ||
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If EDOs are what you're after, and you want a medium-sized one with good 11-limit stuff, you should try starting with 22-EDO. 22-EDO isn't perfect for the person who really insist in hyper-JI accuracy, but if you want is the usual crunchy 11-limit sound without requiring a lot of notes, it's pretty hard to beat 22-EDO. 4:5:6:7:9:11 chords can sound pretty spectacular, though you can hear the difference from JI if you look for it (or use a really harsh GM timbre which brings that stuff out). 22-EDO has a few interesting ways of tempering intervals together, which can be either a bug or a feature depending on what you want; 6/5 and 11/9 are equated, as are 7/5 and 10/7. | If EDOs are what you're after, and you want a medium-sized one with good 11-limit stuff, you should try starting with 22-EDO. 22-EDO isn't perfect for the person who really insist in hyper-JI accuracy, but if you want is the usual crunchy 11-limit sound without requiring a lot of notes, it's pretty hard to beat 22-EDO. 4:5:6:7:9:11 chords can sound pretty spectacular, though you can hear the difference from JI if you look for it (or use a really harsh GM timbre which brings that stuff out). 22-EDO has a few interesting ways of tempering intervals together, which can be either a bug or a feature depending on what you want; 6/5 and 11/9 are equated, as are 7/5 and 10/7. | ||
If that's not accurate enough for you, and especially if you want a higher-limit tuning which still works with common practice harmony, it's difficult to beat 31-EDO, as previously mentioned. 31-EDO gives you great 11-limit resources, as well as some decent 13-limit ones as well, it's also very close to the historic 1/4-comma meantone. | If that's not accurate enough for you, and especially if you want a higher-limit tuning which still works with common practice harmony, it's difficult to beat 31-EDO, as previously mentioned. 31-EDO gives you great 11-limit resources, as well as some decent 13-limit ones as well, it's also very close to the historic 1/4-comma meantone. | ||
Somewhere between 22-EDO and 31-EDO in terms of accuracy is 34-EDO; it's like two copies of 17-EDO, and is as accurate in the 13-limit as 17-EDO is, except now you have 5/4 as well. 7/4 isn't perfectly represented here, but if you're happy with it in 17-EDO, you'll be happy here as well. Peter 'Rush' Kosmorsky and Neil Haverstick have both worked extensively with this tuning. 34-EDO also has very nice sounding 5-limit harmony, in some way made nicer by the slight sharpness of the 3/2; I would suggest people to look at it before demanding 41-EDO or 53-EDO, as I describe below. | Somewhere between 22-EDO and 31-EDO in terms of accuracy is 34-EDO; it's like two copies of 17-EDO, and is as accurate in the 13-limit as 17-EDO is, except now you have 5/4 as well. 7/4 isn't perfectly represented here, but if you're happy with it in 17-EDO, you'll be happy here as well. Peter 'Rush' Kosmorsky and Neil Haverstick have both worked extensively with this tuning. 34-EDO also has very nice sounding 5-limit harmony, in some way made nicer by the slight sharpness of the 3/2; I would suggest people to look at it before demanding 41-EDO or 53-EDO, as I describe below. | ||
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If you like the 72-EDO approach but like 17-EDO, you might try 68-EDO as a similar thing. | If you like the 72-EDO approach but like 17-EDO, you might try 68-EDO as a similar thing. | ||
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===More accuracy=== | |||
For people who don't care at all about EDOs, don't mind unequal chromatic scales and just want good harmony, there's a zillion options for you; Gene Smith will no doubt be able to add a lot to this, although I'm quite certain I've scared him off with this Margo-sized post here. | For people who don't care at all about EDOs, don't mind unequal chromatic scales and just want good harmony, there's a zillion options for you; Gene Smith will no doubt be able to add a lot to this, although I'm quite certain I've scared him off with this Margo-sized post here. | ||
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There are so many good unequal 11-limit temperaments that it's almost impossible for me to write about them all here; if this is really what you're after, post more about the things that you want specifically, and I'll answer specific questions. | There are so many good unequal 11-limit temperaments that it's almost impossible for me to write about them all here; if this is really what you're after, post more about the things that you want specifically, and I'll answer specific questions. | ||
---- | |||
===More info pending: Mind-bending tunings, non-octave tunings, subgroup tunings=== | |||
There are two more groups of people I have yet to address: | There are two more groups of people I have yet to address: | ||
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2) The people who do care about some of the above, but don't really care about strict full 11-limit harmony or whatever. They might be happy to play around with the 7-limit, but without any prime 5, or the 11-limit without any prime 7, or maybe just a tuning which has good 4:7:9:11 chords but no good 3/1, etc. EDOs which look totally crappy from other perspectives, like 11-EDO, now look amazing to you once you're shown what resources are in them. You'll also like unequal temperaments such as "slendric," existing in 36-EDO, where three 8/7's makes a 3/2, giving you 4:6:7 chords everywhere with no 5. | 2) The people who do care about some of the above, but don't really care about strict full 11-limit harmony or whatever. They might be happy to play around with the 7-limit, but without any prime 5, or the 11-limit without any prime 7, or maybe just a tuning which has good 4:7:9:11 chords but no good 3/1, etc. EDOs which look totally crappy from other perspectives, like 11-EDO, now look amazing to you once you're shown what resources are in them. You'll also like unequal temperaments such as "slendric," existing in 36-EDO, where three 8/7's makes a 3/2, giving you 4:6:7 chords everywhere with no 5. | ||
I'd like to write something for those people, but I'm beat for now. I'm personally in both of these groups, so I've written something for everyone but me. Till next time...</pre></div> | I'd like to write something for those people, but I'm beat for now. I'm personally in both of these groups, so I've written something for everyone but me. Till next time..."</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>Composing Powerstart</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Composing Powerstart!"></a><!-- ws:end:WikiTextHeadingRule:0 -->Composing Powerstart!</h1> | <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>Composing Powerstart</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Composing Powerstart!"></a><!-- ws:end:WikiTextHeadingRule:0 -->Composing Powerstart!</h1> | ||
<br /> | <br /> | ||
Musicians and composers just getting into the area of microtuning might, in an initial survey of the available resources on tuning around the web, encounter a barrage of intimidating jargon and mathematical concepts. Fortunately, a composer or player need not worry about the math side of things! This article suggests a number of ways to jump right in and start putting the <em>products</em> of tuning theory to work.<br /> | Musicians and composers just getting into the area of microtuning might, in an initial survey of the available resources on tuning around the web, encounter a barrage of intimidating jargon and mathematical concepts. Fortunately, a composer or player need not worry about the math side of things! This article suggests a number of ways to jump right in and start putting the <em>products</em> of tuning theory to work.<br /> | ||
<br /> | |||
<br /> | <br /> | ||
Quoted from the Xenharmonic Alliance II, January 21 2013:<br /> | Quoted from the Xenharmonic Alliance II, January 21 2013:<br /> | ||
< | <hr /> | ||
Mike Battaglia wrote:<br /> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="Composing Powerstart!--Math: Use as much or as little as you'd like"></a><!-- ws:end:WikiTextHeadingRule:2 -->Math: Use as much or as little as you'd like</h3> | ||
<!-- ws:start:WikiTextHeadingRule: | <em>Mike Battaglia wrote:</em><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h5&gt; --><h5 id="toc2"><a name="Composing Powerstart!--Math: Use as much or as little as you'd like--&quot;Tuning math is complex. But, if you're a composer, you don't need to ever worry about it. You don't ever need to know what a val is, or what a wedgie is, or what an epimorphic scale is, if you don't want. You don't need to learn how matrix multiplication works or deal with any of that. Those things are useful mathematical constructions which make it easier to communicate, program, and reason about the topic at hand, but they're not anything that a musician should ever, in general, have to know about to write microtonal music."></a><!-- ws:end:WikiTextHeadingRule:4 --><span class="userContent"> &quot;Tuning math is complex. But, if you're a composer, you don't need to ever worry about it. You don't ever need to know what a val is, or what a wedgie is, or what an epimorphic scale is, if you don't want. You don't need to learn how matrix multiplication works or deal with any of that. Those things are useful mathematical constructions which make it easier to communicate, program, and reason about the topic at hand, but they're not anything that a musician should ever, in general, have to know about to write microtonal music.</span></h5> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h5&gt; --><h5 id="toc3"><a name="Composing Powerstart!--Math: Use as much or as little as you'd like--If, on the other hand, you DO want to learn tuning math, a basic undergraduate linear algebra course will enable you to understand about 90% of it if we phrase it a certain way."></a><!-- ws:end:WikiTextHeadingRule:6 --><span class="userContent"> If, on the other hand, you DO want to learn tuning math, a basic undergraduate linear algebra course will enable you to understand about 90% of it if we phrase it a certain way.</span></h5> | |||
<br /> | <br /> | ||
<span class="userContent">Keenan Pepper wrote:</span><br /> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h5&gt; --><h5 id="toc4"><a name="Composing Powerstart!--Math: Use as much or as little as you'd like--But if you don't, then you don't need to. Just ask here for a tuning system and we'll recommend you like a hundred to use, along with some associated scales, and some suggestions for using them. Then it's up to you to go nuts and write. That's all it requires.&quot;"></a><!-- ws:end:WikiTextHeadingRule:8 --><span class="userContent"> But if you don't, then you don't need to. Just ask here for a tuning system and we'll recommend you like a hundred to use, along with some associated scales, and some suggestions for using them. Then it's up to you to go nuts and write. That's all it requires.&quot;</span></h5> | ||
<hr /> | |||
<em><span class="userContent">Keenan Pepper wrote:</span></em><br /> | |||
<span class="userContent">&quot;</span>And the way to really understand regular temperaments without bothering with all the math is:<br /> | <span class="userContent">&quot;</span>And the way to really understand regular temperaments without bothering with all the math is:<br /> | ||
<ul><li>Learn a reasonable amount about just intonation. Things like &quot;prime limit&quot; and &quot;otonality&quot; shouldn't scare you. Being familiar with the whole 11-limit tonality diamond is a good thing.</li><li>For each temperament you're interested in, learn how the different tempered JI intervals relate to each other in that temperament. For example, in porcupine two 11/10s equals one 6/5, and that interval (11/10) also represents 12/11 and 10/9 at the same time.</li></ul>You can express this in a complicated mathematical way with linear alegbra, but that's completely unnecessary if you understand it in a musical way as relationships between intervals you're already familiar with.&quot;<br /> | <ul><li>Learn a reasonable amount about just intonation. Things like &quot;prime limit&quot; and &quot;otonality&quot; shouldn't scare you. Being familiar with the whole 11-limit tonality diamond is a good thing.</li><li>For each temperament you're interested in, learn how the different tempered JI intervals relate to each other in that temperament. For example, in porcupine two 11/10s equals one 6/5, and that interval (11/10) also represents 12/11 and 10/9 at the same time.</li></ul>You can express this in a complicated mathematical way with linear alegbra, but that's completely unnecessary if you understand it in a musical way as relationships between intervals you're already familiar with.&quot;<br /> | ||
< | <hr /> | ||
Mike Battaglia wrote:<br /> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Composing Powerstart!--Porcupine"></a><!-- ws:end:WikiTextHeadingRule:10 -->Porcupine</h3> | ||
<em>Mike Battaglia wrote:</em><br /> | |||
&quot;For starters, you might want to mess around with what's called &quot;porcupine&quot; temperament in 22-EDO. The base diatonic-sized scale is (as steps out of 22-EDO) 4 3 3 3 3 3 3, and you can chromatically alter anything in that scale you want by 1 step out of 22. For instance, if you flat the 7, you get the scale 4 3 3 3 3 2 4, which is nice because it has a 4:5:6:7:9:11 chord in it. There's another &quot;superdiatonic&quot; scale at 1 3 3 3 3 3 3 3 which you can morph the above into if you want, and a 15-note chromatic scale at 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2; feel free to not stick dogmatically to these exact scales but to change them as you desire.<br /> | &quot;For starters, you might want to mess around with what's called &quot;porcupine&quot; temperament in 22-EDO. The base diatonic-sized scale is (as steps out of 22-EDO) 4 3 3 3 3 3 3, and you can chromatically alter anything in that scale you want by 1 step out of 22. For instance, if you flat the 7, you get the scale 4 3 3 3 3 2 4, which is nice because it has a 4:5:6:7:9:11 chord in it. There's another &quot;superdiatonic&quot; scale at 1 3 3 3 3 3 3 3 which you can morph the above into if you want, and a 15-note chromatic scale at 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2; feel free to not stick dogmatically to these exact scales but to change them as you desire.<br /> | ||
<br /> | <br /> | ||
If you don't mind a bit less accuracy in representing harmonic ratios, the above temperament also exists in 15-EDO, except the diatonic-sized scale is now 3 2 2 2 2 2 2, the superdiatonic is 1 2 2 2 2 2 2 2, and the chromatic scale is all of 15-EDO. 15-EDO also has a really nice &quot;symmetrical diatonic&quot; scale, called the Blackwood-10 scale, which is 2 1 2 1 2 1 2 1 2 1. Play around with major and minor chords in this scale a bit, and transpose them up and down the shape of the scale, and you'll see why it's so magical - the circle of fifths is only five steps long.<br /> | If you don't mind a bit less accuracy in representing harmonic ratios, the above temperament also exists in 15-EDO, except the diatonic-sized scale is now 3 2 2 2 2 2 2, the superdiatonic is 1 2 2 2 2 2 2 2, and the chromatic scale is all of 15-EDO. 15-EDO also has a really nice &quot;symmetrical diatonic&quot; scale, called the Blackwood-10 scale, which is 2 1 2 1 2 1 2 1 2 1. Play around with major and minor chords in this scale a bit, and transpose them up and down the shape of the scale, and you'll see why it's so magical - the circle of fifths is only five steps long.&quot;<br /> | ||
< | <hr /> | ||
If you don't care about harmonic ratios at all, but perhaps instead care about world music, then you might enjoy 16-EDO, which contains in it a wonderful extension of both gamelan music and Chopi timbila music; 5 2 2 5 2 is a great pelog and 3 3 3 4 3 works as slendro.<br /> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Composing Powerstart!--World Music Scales"></a><!-- ws:end:WikiTextHeadingRule:12 -->World Music Scales</h3> | ||
If you don't care about harmonic ratios at all, but perhaps instead care about world music, then you might enjoy 16-EDO, which contains in it a wonderful extension of both gamelan music and Chopi timbila music; 5 2 2 5 2 is a great pelog and 3 3 3 4 3 works as slendro.<br /> | |||
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Both of these scales can be &quot;extended&quot; into &quot;diatonic&quot;-sized versions, such as the 2 3 2 2 3 2 2 mavila-7 scale, named after the Chopi village which used a very similar scale to tune its xylophones. This scale is really nuts because of its &quot;anti-diatonic&quot; structure; the 675 cent fifths are so flat that four of them gives you a 300 cent minor third instead of the more familiar major third. As a result, there's now two large seconds and five small seconds, four major thirds and three minor thirds, etc, which is the complete opposite of what you're used to. There's even a 2 2 2 1 2 2 2 2 1 9-note superdiatonic scale to play with if you want, and of course you should always feel free to chromatically alter things!<br /> | Both of these scales can be &quot;extended&quot; into &quot;diatonic&quot;-sized versions, such as the 2 3 2 2 3 2 2 mavila-7 scale, named after the Chopi village which used a very similar scale to tune its xylophones. This scale is really nuts because of its &quot;anti-diatonic&quot; structure; the 675 cent fifths are so flat that four of them gives you a 300 cent minor third instead of the more familiar major third. As a result, there's now two large seconds and five small seconds, four major thirds and three minor thirds, etc, which is the complete opposite of what you're used to. There's even a 2 2 2 1 2 2 2 2 1 9-note superdiatonic scale to play with if you want, and of course you should always feel free to chromatically alter things!<br /> | ||
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The 3 3 3 4 3 slendro can turn into the 3 3 3 1 3 3 &quot;slendric-6&quot; scale as well, though I prefer the 3 3 1 3 3 3 mode. This scale is nice because it sounds kind of like a &quot;warped diatonic&quot; scale. Chromatically altering things by 2 steps here, instead of 1 step, sounds really nice.<br /> | The 3 3 3 4 3 slendro can turn into the 3 3 3 1 3 3 &quot;slendric-6&quot; scale as well, though I prefer the 3 3 1 3 3 3 mode. This scale is nice because it sounds kind of like a &quot;warped diatonic&quot; scale. Chromatically altering things by 2 steps here, instead of 1 step, sounds really nice.<br /> | ||
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World music fans might also like 17-EDO, which contains within it a system of scales very similar to the maqamat used in the middle east; 24-EDO and 31-EDO contain the same features but with better intonation, albeit at the cost of more notes, but you can always use smaller 17-note subsets if you want.<br /> | World music fans might also like 17-EDO, which contains within it a system of scales very similar to the maqamat used in the middle east; 24-EDO and 31-EDO contain the same features but with better intonation, albeit at the cost of more notes, but you can always use smaller 17-note subsets if you want.<br /> | ||
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A really good paper on how 17-EDO offers a sort of bizarro-universe for the diatonic scale, which we might have gone with historically if things were different, can be found at <a class="wiki_link_ext" href="http://www.anaphoria.com/Secor17puzzle.pdf" rel="nofollow" target="_blank">http://www.anaphoria.com/Secor17puzzle.pdf</a>.<br /> | A really good paper on how 17-EDO offers a sort of bizarro-universe for the diatonic scale, which we might have gone with historically if things were different, can be found at <a class="wiki_link_ext" href="http://www.anaphoria.com/Secor17puzzle.pdf" rel="nofollow" target="_blank">http://www.anaphoria.com/Secor17puzzle.pdf</a>.<br /> | ||
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Some people are really interested in historic tunings for meantone, and perhaps extending them in ways that go beyond the 12-EDO &quot;closure&quot; that we ended up going with. So if you really want to get away from the notion that C# has to equal Db, and want to explore extended meantone, there's a number of great options for you.<br /> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Composing Powerstart!--Historical Tunings and Extended Meantone"></a><!-- ws:end:WikiTextHeadingRule:14 -->Historical Tunings and Extended Meantone</h3> | ||
Some people are really interested in historic tunings for meantone, and perhaps extending them in ways that go beyond the 12-EDO &quot;closure&quot; that we ended up going with. So if you really want to get away from the notion that C# has to equal Db, and want to explore extended meantone, there's a number of great options for you.<br /> | |||
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A particularly well-known historical meantone tuning is 1/4-comma meantone, where the 3/2's are a bit flatter than we're used to, but the major thirds are exactly 5/4. What's particularly interesting is that this same tuning turns the augmented sixth, e.g. C-A#, into an almost exact 7/4 - so you can treat it as a 7-limit tuning.<br /> | A particularly well-known historical meantone tuning is 1/4-comma meantone, where the 3/2's are a bit flatter than we're used to, but the major thirds are exactly 5/4. What's particularly interesting is that this same tuning turns the augmented sixth, e.g. C-A#, into an almost exact 7/4 - so you can treat it as a 7-limit tuning.<br /> | ||
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As mentioned before, all of the &quot;maqamic&quot; stuff from 17-EDO and 24-EDO is also in 31-EDO, but now the major thirds are 5/4. So there's that as well.<br /> | As mentioned before, all of the &quot;maqamic&quot; stuff from 17-EDO and 24-EDO is also in 31-EDO, but now the major thirds are 5/4. So there's that as well.<br /> | ||
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Alternatively, you have 19-EDO, which is very close to 1/3-comma meantone, for which the minor thirds are pure 6/5's. This tuning can also play virtually all common practice music. While 31-EDO does a lot better in the 11-limit, 19-EDO still has an OK 7-limit. However, what you lose in intonation, you gain by having a really badass set of novel enharmonic equivalences: instead of C# <!-- ws:start:WikiTextHeadingRule: | Alternatively, you have 19-EDO, which is very close to 1/3-comma meantone, for which the minor thirds are pure 6/5's. This tuning can also play virtually all common practice music. While 31-EDO does a lot better in the 11-limit, 19-EDO still has an OK 7-limit. However, what you lose in intonation, you gain by having a really badass set of novel enharmonic equivalences: instead of C# <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Db, it's now C#"></a><!-- ws:end:WikiTextHeadingRule:16 --> Db, it's now C# </h1> | ||
Dbb. This leads to a really tight-knit &quot;structure&quot; with tons of enharmonic equivalences everywhere, much like in 12-EDO, and unlike 31-EDO, the enharmonic equivalences are really simple and can be made use of.<br /> | Dbb. This leads to a really tight-knit &quot;structure&quot; with tons of enharmonic equivalences everywhere, much like in 12-EDO, and unlike 31-EDO, the enharmonic equivalences are really simple and can be made use of.<br /> | ||
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You can do all sorts of amazing stuff with 19-EDO if you want, and make it sound almost exactly like ordinary 12-EDO music too, but then depart from it into some rather mind-blowing stuff if you want.<br /> | You can do all sorts of amazing stuff with 19-EDO if you want, and make it sound almost exactly like ordinary 12-EDO music too, but then depart from it into some rather mind-blowing stuff if you want.<br /> | ||
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There are also the people who care about none of this, but really just want really well-intoned higher-limit chords. < | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Db, it's now C#--Higher Accuracy"></a><!-- ws:end:WikiTextHeadingRule:18 -->Higher Accuracy</h3> | ||
There are also the people who care about none of this, but really just want really well-intoned higher-limit chords. <span class="wiki_link_ext">Gene Smith</span> is certainly the person who's explored this style the most, though I also have a few things to say about it.<br /> | |||
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These people already tend to know a bit of math related to JI, so I'll assume you know what a prime limit is and what ratios are below, as well as having some compositional idea of the sounds you're after.<br /> | These people already tend to know a bit of math related to JI, so I'll assume you know what a prime limit is and what ratios are below, as well as having some compositional idea of the sounds you're after.<br /> | ||
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If EDOs are what you're after, and you want a medium-sized one with good 11-limit stuff, you should try starting with 22-EDO. 22-EDO isn't perfect for the person who really insist in hyper-JI accuracy, but if you want is the usual crunchy 11-limit sound without requiring a lot of notes, it's pretty hard to beat 22-EDO. 4:5:6:7:9:11 chords can sound pretty spectacular, though you can hear the difference from JI if you look for it (or use a really harsh GM timbre which brings that stuff out). 22-EDO has a few interesting ways of tempering intervals together, which can be either a bug or a feature depending on what you want; 6/5 and 11/9 are equated, as are 7/5 and 10/7.<br /> | If EDOs are what you're after, and you want a medium-sized one with good 11-limit stuff, you should try starting with 22-EDO. 22-EDO isn't perfect for the person who really insist in hyper-JI accuracy, but if you want is the usual crunchy 11-limit sound without requiring a lot of notes, it's pretty hard to beat 22-EDO. 4:5:6:7:9:11 chords can sound pretty spectacular, though you can hear the difference from JI if you look for it (or use a really harsh GM timbre which brings that stuff out). 22-EDO has a few interesting ways of tempering intervals together, which can be either a bug or a feature depending on what you want; 6/5 and 11/9 are equated, as are 7/5 and 10/7.<br /> | ||
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If that's not accurate enough for you, and especially if you want a higher-limit tuning which still works with common practice harmony, it's difficult to beat 31-EDO, as previously mentioned. 31-EDO gives you great 11-limit resources, as well as some decent 13-limit ones as well, it's also very close to the historic 1/4-comma meantone. <br /> | If that's not accurate enough for you, and especially if you want a higher-limit tuning which still works with common practice harmony, it's difficult to beat 31-EDO, as previously mentioned. 31-EDO gives you great 11-limit resources, as well as some decent 13-limit ones as well, it's also very close to the historic 1/4-comma meantone.<br /> | ||
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Somewhere between 22-EDO and 31-EDO in terms of accuracy is 34-EDO; it's like two copies of 17-EDO, and is as accurate in the 13-limit as 17-EDO is, except now you have 5/4 as well. 7/4 isn't perfectly represented here, but if you're happy with it in 17-EDO, you'll be happy here as well. Peter 'Rush' Kosmorsky and Neil Haverstick have both worked extensively with this tuning. 34-EDO also has very nice sounding 5-limit harmony, in some way made nicer by the slight sharpness of the 3/2; I would suggest people to look at it before demanding 41-EDO or 53-EDO, as I describe below.<br /> | Somewhere between 22-EDO and 31-EDO in terms of accuracy is 34-EDO; it's like two copies of 17-EDO, and is as accurate in the 13-limit as 17-EDO is, except now you have 5/4 as well. 7/4 isn't perfectly represented here, but if you're happy with it in 17-EDO, you'll be happy here as well. Peter 'Rush' Kosmorsky and Neil Haverstick have both worked extensively with this tuning. 34-EDO also has very nice sounding 5-limit harmony, in some way made nicer by the slight sharpness of the 3/2; I would suggest people to look at it before demanding 41-EDO or 53-EDO, as I describe below.<br /> | ||
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If you like the 72-EDO approach but like 17-EDO, you might try 68-EDO as a similar thing.<br /> | If you like the 72-EDO approach but like 17-EDO, you might try 68-EDO as a similar thing.<br /> | ||
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For people who don't care at all about EDOs, don't mind unequal chromatic scales and just want good harmony, there's a zillion options for you; Gene Smith will no doubt be able to add a lot to this, although I'm quite certain I've scared him off with this Margo-sized post here.<br /> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Db, it's now C#--More accuracy"></a><!-- ws:end:WikiTextHeadingRule:20 -->More accuracy</h3> | ||
For people who don't care at all about EDOs, don't mind unequal chromatic scales and just want good harmony, there's a zillion options for you; Gene Smith will no doubt be able to add a lot to this, although I'm quite certain I've scared him off with this Margo-sized post here.<br /> | |||
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You have Miracle temperament, which exists in 31-EDO, 41-EDO and 72-EDO, which is generated by a slightly sharp 16/15, so that two makes 8/7, three makes 11/9, five makes 7/5, and six makes 3/2. There's a really nice 10-note &quot;decimal&quot; scale here, which is sssssssssL, or 7 7 7 7 7 7 7 7 7 9 in 72-EDO. There's also a 21-note chromatic-sized scale to use, often called &quot;blackjack&quot;. So you might enjoy just working within blackjack as the entire tuning, or perhaps the 31-note &quot;canasta&quot; or 41-note &quot;stud loco&quot; scales if that's not enough for you.<br /> | You have Miracle temperament, which exists in 31-EDO, 41-EDO and 72-EDO, which is generated by a slightly sharp 16/15, so that two makes 8/7, three makes 11/9, five makes 7/5, and six makes 3/2. There's a really nice 10-note &quot;decimal&quot; scale here, which is sssssssssL, or 7 7 7 7 7 7 7 7 7 9 in 72-EDO. There's also a 21-note chromatic-sized scale to use, often called &quot;blackjack&quot;. So you might enjoy just working within blackjack as the entire tuning, or perhaps the 31-note &quot;canasta&quot; or 41-note &quot;stud loco&quot; scales if that's not enough for you.<br /> | ||
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There are so many good unequal 11-limit temperaments that it's almost impossible for me to write about them all here; if this is really what you're after, post more about the things that you want specifically, and I'll answer specific questions.<br /> | There are so many good unequal 11-limit temperaments that it's almost impossible for me to write about them all here; if this is really what you're after, post more about the things that you want specifically, and I'll answer specific questions.<br /> | ||
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There are two more groups of people I have yet to address:<br /> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Db, it's now C#--More info pending: Mind-bending tunings, non-octave tunings, subgroup tunings"></a><!-- ws:end:WikiTextHeadingRule:22 -->More info pending: Mind-bending tunings, non-octave tunings, subgroup tunings</h3> | ||
There are two more groups of people I have yet to address:<br /> | |||
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1) The people who don't care about any of the above, but just want to demolish their brains with the most ridiculous mind#$@*&amp;ing sounds possible, which are nothing like 12-EDO. You're probably going to like scales that sound totally different from 12-EDO, regardless of what ratios are in them; you're probably going to find deliberately &quot;inaccurate&quot; tunings, like 13-EDO and 16-EDO, to be really interesting. You're probably also going to be down to experiment with nonoctave scales like Bohlen-Pierce. Ron Sword is all over this stuff.<br /> | 1) The people who don't care about any of the above, but just want to demolish their brains with the most ridiculous mind#$@*&amp;ing sounds possible, which are nothing like 12-EDO. You're probably going to like scales that sound totally different from 12-EDO, regardless of what ratios are in them; you're probably going to find deliberately &quot;inaccurate&quot; tunings, like 13-EDO and 16-EDO, to be really interesting. You're probably also going to be down to experiment with nonoctave scales like Bohlen-Pierce. Ron Sword is all over this stuff.<br /> | ||
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2) The people who do care about some of the above, but don't really care about strict full 11-limit harmony or whatever. They might be happy to play around with the 7-limit, but without any prime 5, or the 11-limit without any prime 7, or maybe just a tuning which has good 4:7:9:11 chords but no good 3/1, etc. EDOs which look totally crappy from other perspectives, like 11-EDO, now look amazing to you once you're shown what resources are in them. You'll also like unequal temperaments such as &quot;slendric,&quot; existing in 36-EDO, where three 8/7's makes a 3/2, giving you 4:6:7 chords everywhere with no 5.<br /> | 2) The people who do care about some of the above, but don't really care about strict full 11-limit harmony or whatever. They might be happy to play around with the 7-limit, but without any prime 5, or the 11-limit without any prime 7, or maybe just a tuning which has good 4:7:9:11 chords but no good 3/1, etc. EDOs which look totally crappy from other perspectives, like 11-EDO, now look amazing to you once you're shown what resources are in them. You'll also like unequal temperaments such as &quot;slendric,&quot; existing in 36-EDO, where three 8/7's makes a 3/2, giving you 4:6:7 chords everywhere with no 5.<br /> | ||
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I'd like to write something for those people, but I'm beat for now. I'm personally in both of these groups, so I've written something for everyone but me. Till next time...</body></html></pre></div> | I'd like to write something for those people, but I'm beat for now. I'm personally in both of these groups, so I've written something for everyone but me. Till next time...&quot;</body></html></pre></div> | ||