Composing Powerstart: Difference between revisions
Wikispaces>d.schallert **Imported revision 400311488 - Original comment: ** |
Wikispaces>d.schallert **Imported revision 400313208 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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:d.schallert|d.schallert]] and made on <tt>2013-01-22 00: | : This revision was by author [[User:d.schallert|d.schallert]] and made on <tt>2013-01-22 00:43:38 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>400313208</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 8: | Line 8: | ||
<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;white-space: pre-wrap ! important" class="old-revision-html">=Composing Powerstart!= | <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;white-space: pre-wrap ! important" class="old-revision-html">=Composing Powerstart!= | ||
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 | 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. | ||
| Line 23: | Line 23: | ||
//<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 "[[Harmonic Limit|prime limit]]" and "[[@http://en.wikipedia.org/wiki/Otonality_and_Utonality|otonality]]" shouldn't scare you. Being familiar with the whole 11-limit [[@http://en.wikipedia.org/wiki/Tonality_diamond|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 [[Regular Temperaments|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." | ||
---- | ---- | ||
===Porcupine=== | ===Porcupine=== | ||
//Mike Battaglia wrote:// | //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 [[22edo|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 [[15edo|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=== | ===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 [[16edo|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. | ||
Both of these scales can be "extended" into "diatonic"-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 "anti-diatonic" 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! | Both of these scales can be "extended" into "diatonic"-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 "anti-diatonic" 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! | ||
| Line 40: | Line 40: | ||
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. | ||
---- | ---- | ||
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 [[17edo|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. | ||
17-EDO is also notable for containing a very interesting diatonic scale, for which the fifths are slightly sharp from what we're used to (and rather pleasantly, I think). As a result, the "major thirds" in the diatonic scale end up being closer to 9/7 than 5/4, and the "minor thirds" end up being closer to 7/6 than 6/5. Major chords are thus a bit less "sweet" than usual, though I don't mind them much, whereas minor chords are now 6:7:9 and have a sort of "subminor" flavor to them. You can also think about ditching "thirds," and instead harmonizing this scale in terms of 4:6:7 chords, of which there are four instead of three. I really like this because it has a very calm, quiet, meditative sound to it. This is called "superpyth" temperament, short for "superpythagorean," because the fifths are a bit sharp of | 17-EDO is also notable for containing a very interesting diatonic scale, for which the fifths are slightly sharp from what we're used to (and rather pleasantly, I think). As a result, the "major thirds" in the diatonic scale end up being closer to 9/7 than 5/4, and the "minor thirds" end up being closer to 7/6 than 6/5. Major chords are thus a bit less "sweet" than usual, though I don't mind them much, whereas minor chords are now 6:7:9 and have a sort of "subminor" flavor to them. You can also think about ditching "thirds," and instead harmonizing this scale in terms of 4:6:7 chords, of which there are four instead of three. I really like this because it has a very calm, quiet, meditative sound to it. This is called "superpyth" temperament, short for "superpythagorean," because the fifths are a bit sharp of [[@http://en.wikipedia.org/wiki/Pythagorean_tuning|Pythagorean]] (instead of a bit flat as usual). | ||
For people looking to mess with higher-limit stuff, 17-EDO is also really notable for giving decent 13-limit harmony, with the caveat that there's no good representation for 5/1 and other ratios containing 5. | For people looking to mess with higher-limit stuff, 17-EDO is also really notable for giving decent 13-limit harmony, with the caveat that there's no good representation for 5/1 and other ratios containing 5. | ||
| Line 49: | Line 49: | ||
---- | ---- | ||
===Historical Tunings and Extended Meantone=== | ===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 [[12edo|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. | ||
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. | 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. | ||
| Line 57: | Line 57: | ||
As mentioned before, all of the "maqamic" 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. | As mentioned before, all of the "maqamic" 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. | ||
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# | 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# equals Db, it's now C# equals Dbb. This leads to a really tight-knit "structure" 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. | ||
For instance, there's now an entire circle of major thirds which doesn't close at the octave after 3 iterations, but which does sync up with the perfect twelfth after 5 iterations. Also, the "diesis" between A# and Bb is now the same as the "chromatic semitone" between A# and Ax, which you can exploit to make some pretty neat musical effects. You've also got some very novel scales, such as the "semaphore-9" scale, which is 3 3 1 3 1 3 1 3 1; subminor and supermajor chords are everywhere here. | For instance, there's now an entire circle of major thirds which doesn't close at the octave after 3 iterations, but which does sync up with the perfect twelfth after 5 iterations. Also, the "diesis" between A# and Bb is now the same as the "chromatic semitone" between A# and Ax, which you can exploit to make some pretty neat musical effects. You've also got some very novel scales, such as the "semaphore-9" scale, which is 3 3 1 3 1 3 1 3 1; subminor and supermajor chords are everywhere here. | ||
| Line 112: | Line 112: | ||
<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 | 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.<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
| Line 127: | Line 127: | ||
<em><span class="userContent">Keenan Pepper wrote:</span></em><br /> | <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 <a class="wiki_link" href="/just%20intonation">just intonation</a>. Things like &quot;<a class="wiki_link" href="/Harmonic%20Limit">prime limit</a>&quot; and &quot;<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Otonality_and_Utonality" rel="nofollow" target="_blank">otonality</a>&quot; shouldn't scare you. Being familiar with the whole 11-limit <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonality_diamond" rel="nofollow" target="_blank">tonality diamond</a> is a good thing.</li><li>For each <a class="wiki_link" href="/Regular%20Temperaments">temperament</a> you're interested in, learn how the different tempered JI intervals relate to each other in that temperament. For example, in <a class="wiki_link" href="/porcupine">porcupine</a>, 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 /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Composing Powerstart!--Porcupine"></a><!-- ws:end:WikiTextHeadingRule:10 -->Porcupine</h3> | <!-- 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 /> | <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;<a class="wiki_link" href="/porcupine">porcupine</a>&quot; temperament in <a class="wiki_link" href="/22edo">22-EDO</a>. 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.&quot;<br /> | If you don't mind a bit less accuracy in representing harmonic ratios, the above temperament also exists in <a class="wiki_link" href="/15edo">15-EDO</a>, 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 /> | <hr /> | ||
<!-- 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> | <!-- 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 /> | If you don't care about harmonic ratios at all, but perhaps instead care about world music, then you might enjoy <a class="wiki_link" href="/16edo">16-EDO</a>, 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 /> | ||
<br /> | <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 /> | 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 /> | ||
| Line 142: | Line 142: | ||
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 /> | ||
<hr /> | <hr /> | ||
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 <a class="wiki_link" href="/17edo">17-EDO</a>, 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 /> | ||
<br /> | <br /> | ||
17-EDO is also notable for containing a very interesting diatonic scale, for which the fifths are slightly sharp from what we're used to (and rather pleasantly, I think). As a result, the &quot;major thirds&quot; in the diatonic scale end up being closer to 9/7 than 5/4, and the &quot;minor thirds&quot; end up being closer to 7/6 than 6/5. Major chords are thus a bit less &quot;sweet&quot; than usual, though I don't mind them much, whereas minor chords are now 6:7:9 and have a sort of &quot;subminor&quot; flavor to them. You can also think about ditching &quot;thirds,&quot; and instead harmonizing this scale in terms of 4:6:7 chords, of which there are four instead of three. I really like this because it has a very calm, quiet, meditative sound to it. This is called &quot;superpyth&quot; temperament, short for &quot;superpythagorean,&quot; because the fifths are a bit sharp of | 17-EDO is also notable for containing a very interesting diatonic scale, for which the fifths are slightly sharp from what we're used to (and rather pleasantly, I think). As a result, the &quot;major thirds&quot; in the diatonic scale end up being closer to 9/7 than 5/4, and the &quot;minor thirds&quot; end up being closer to 7/6 than 6/5. Major chords are thus a bit less &quot;sweet&quot; than usual, though I don't mind them much, whereas minor chords are now 6:7:9 and have a sort of &quot;subminor&quot; flavor to them. You can also think about ditching &quot;thirds,&quot; and instead harmonizing this scale in terms of 4:6:7 chords, of which there are four instead of three. I really like this because it has a very calm, quiet, meditative sound to it. This is called &quot;superpyth&quot; temperament, short for &quot;superpythagorean,&quot; because the fifths are a bit sharp of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Pythagorean_tuning" rel="nofollow" target="_blank">Pythagorean</a> (instead of a bit flat as usual).<br /> | ||
<br /> | <br /> | ||
For people looking to mess with higher-limit stuff, 17-EDO is also really notable for giving decent 13-limit harmony, with the caveat that there's no good representation for 5/1 and other ratios containing 5.<br /> | For people looking to mess with higher-limit stuff, 17-EDO is also really notable for giving decent 13-limit harmony, with the caveat that there's no good representation for 5/1 and other ratios containing 5.<br /> | ||
| Line 151: | Line 151: | ||
<hr /> | <hr /> | ||
<!-- 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> | <!-- 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 /> | Some people are really interested in historic tunings for <a class="wiki_link" href="/meantone">meantone</a>, and perhaps extending them in ways that go beyond the <a class="wiki_link" href="/12edo">12-EDO</a> &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 /> | ||
<br /> | <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 /> | 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 /> | ||
| Line 159: | Line 159: | ||
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 /> | ||
<br /> | <br /> | ||
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# | 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# equals Db, it's now C# equals 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 /> | ||
<br /> | <br /> | ||
For instance, there's now an entire circle of major thirds which doesn't close at the octave after 3 iterations, but which does sync up with the perfect twelfth after 5 iterations. Also, the &quot;diesis&quot; between A# and Bb is now the same as the &quot;chromatic semitone&quot; between A# and Ax, which you can exploit to make some pretty neat musical effects. You've also got some very novel scales, such as the &quot;semaphore-9&quot; scale, which is 3 3 1 3 1 3 1 3 1; subminor and supermajor chords are everywhere here.<br /> | For instance, there's now an entire circle of major thirds which doesn't close at the octave after 3 iterations, but which does sync up with the perfect twelfth after 5 iterations. Also, the &quot;diesis&quot; between A# and Bb is now the same as the &quot;chromatic semitone&quot; between A# and Ax, which you can exploit to make some pretty neat musical effects. You've also got some very novel scales, such as the &quot;semaphore-9&quot; scale, which is 3 3 1 3 1 3 1 3 1; subminor and supermajor chords are everywhere here.<br /> | ||
| Line 166: | Line 165: | ||
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 /> | ||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Composing Powerstart!--Higher Accuracy"></a><!-- ws:end:WikiTextHeadingRule:16 -->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 /> | 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 /> | ||
<br /> | <br /> | ||
| Line 189: | Line 188: | ||
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 /> | ||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Composing Powerstart!--More accuracy"></a><!-- ws:end:WikiTextHeadingRule:18 -->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 /> | 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 /> | ||
<br /> | <br /> | ||
| Line 204: | Line 203: | ||
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 /> | ||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Composing Powerstart!--More info pending: Mind-bending tunings, non-octave tunings, subgroup tunings"></a><!-- ws:end:WikiTextHeadingRule:20 -->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 /> | There are two more groups of people I have yet to address:<br /> | ||
<br /> | <br /> | ||