Whitewood family: Difference between revisions
Wikispaces>guest **Imported revision 190499458 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 190505860 - Original comment: ** |
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<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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-02 15:27:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>190505860</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> | ||
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<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">This family of temperaments tempers out the apotome, 2187/2048. Consequently the fifths are always 4/7 of an octave, a distinctly flat 685.714 cents. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it. | <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">This family of temperaments tempers out the apotome, 2187/2048. Consequently the fifths are always 4/7 of an octave, a distinctly flat 685.714 cents. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it. | ||
The 5-limit version of this temperament is called "whitewood" temperament, to serve in contrast with the "blackwood" temperament which tempers out 256/243, the pythagorean limma. Whereas blackwood temperament can be thought of as a closed chain of 5 fifths and a major third generator, whitewood is a closed chain of 7 fifths and a major third generator. This means that blackwood is generally supported by 5n- | The 5-limit version of this temperament is called "whitewood" temperament, to serve in contrast with the "blackwood" temperament which tempers out 256/243, the pythagorean limma. Whereas blackwood temperament can be thought of as a closed chain of 5 fifths and a major third generator, whitewood is a closed chain of 7 fifths and a major third generator. This means that blackwood is generally supported by 5n-EDOs, and whitewood is supported by 7n-EDOs, and the MOS of both scales follow a similar pattern. | ||
Like blackwood, it shares a number of interesting properties which derive from the relatively small circle of fifths common to both: from any major or minor triad in the scale, one can always move away by ~3/2 or ~4/3 to reach another triad of the same type. This contrasts with the diatonic scale, in which one will eventually "hit a wall" if one moves by perfect fifth for long enough; the chain of fifths will eventually "stop" and make the next fifth a diminished fifth. This means that this scale is, in a sense, "pantonal," since resolutions that work in one key will work in all other keys. | Like blackwood, it shares a number of interesting properties which derive from the relatively small circle of fifths common to both: from any major or minor triad in the scale, one can always move away by ~3/2 or ~4/3 to reach another triad of the same type. This contrasts with the diatonic scale, in which one will eventually "hit a wall" if one moves by perfect fifth for long enough; the chain of fifths will eventually "stop" and make the next fifth a diminished fifth. This means that this scale is, in a sense, "pantonal," since resolutions that work in one key will work in all other keys. | ||
Another interesting property is that it becomes possible to construct "super linked" 5-limit chords. In | Another interesting property is that it becomes possible to construct "super linked" 5-limit chords. In Whitewood[14] (or Blackwood[10]), if one stacks alternating major and minor thirds on top of one another, one will eventually come back to the root without ever hitting a wall, and hence the pattern can continue forever. Since all of the diatonic modes can be thought of as a stacked chain of 7 alternating thirds, placed in inversion, this means that Whitewood[14] and Blackwood[10] also make for excellent "panmodal" scales, in which you can construct "modal" sounding sonorities in one key that will work in all keys. | ||
Lastly, while blackwood fifths are sharp and thus necessitates the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning. | Lastly, while blackwood fifths are sharp and thus necessitates the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning. | ||
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Wedgie: <<7 -7 11 -11 -36|| | Wedgie: <<7 -7 11 -11 -36|| | ||
EDOs: 7, 14, 21, 28, 49 | EDOs: 7, 14, 21, 28, 49 | ||
==Other Whitewood== | ==Other Whitewood== | ||
Commas: 525/512, | Commas: 525/512, 729/700 | ||
[[POTE tuning|POTE generator]]: | [[POTE tuning|POTE generator]]: 378.512 | ||
Map: | Map: [<7 11 0 52|, <0 0 1 -2|] | ||
Wedgie: | Wedgie: <<0 7 -14 11 -22 -52|| | ||
EDOs: 7, 35, 42 | EDOs: 7, 35, 42 | ||
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<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>Apotome family</title></head><body>This family of temperaments tempers out the apotome, 2187/2048. Consequently the fifths are always 4/7 of an octave, a distinctly flat 685.714 cents. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it.<br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Apotome family</title></head><body>This family of temperaments tempers out the apotome, 2187/2048. Consequently the fifths are always 4/7 of an octave, a distinctly flat 685.714 cents. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it.<br /> | ||
<br /> | <br /> | ||
The 5-limit version of this temperament is called &quot;whitewood&quot; temperament, to serve in contrast with the &quot;blackwood&quot; temperament which tempers out 256/243, the pythagorean limma. Whereas blackwood temperament can be thought of as a closed chain of 5 fifths and a major third generator, whitewood is a closed chain of 7 fifths and a major third generator. This means that blackwood is generally supported by 5n- | The 5-limit version of this temperament is called &quot;whitewood&quot; temperament, to serve in contrast with the &quot;blackwood&quot; temperament which tempers out 256/243, the pythagorean limma. Whereas blackwood temperament can be thought of as a closed chain of 5 fifths and a major third generator, whitewood is a closed chain of 7 fifths and a major third generator. This means that blackwood is generally supported by 5n-EDOs, and whitewood is supported by 7n-EDOs, and the MOS of both scales follow a similar pattern.<br /> | ||
<br /> | <br /> | ||
Like blackwood, it shares a number of interesting properties which derive from the relatively small circle of fifths common to both: from any major or minor triad in the scale, one can always move away by ~3/2 or ~4/3 to reach another triad of the same type. This contrasts with the diatonic scale, in which one will eventually &quot;hit a wall&quot; if one moves by perfect fifth for long enough; the chain of fifths will eventually &quot;stop&quot; and make the next fifth a diminished fifth. This means that this scale is, in a sense, &quot;pantonal,&quot; since resolutions that work in one key will work in all other keys.<br /> | Like blackwood, it shares a number of interesting properties which derive from the relatively small circle of fifths common to both: from any major or minor triad in the scale, one can always move away by ~3/2 or ~4/3 to reach another triad of the same type. This contrasts with the diatonic scale, in which one will eventually &quot;hit a wall&quot; if one moves by perfect fifth for long enough; the chain of fifths will eventually &quot;stop&quot; and make the next fifth a diminished fifth. This means that this scale is, in a sense, &quot;pantonal,&quot; since resolutions that work in one key will work in all other keys.<br /> | ||
<br /> | <br /> | ||
Another interesting property is that it becomes possible to construct &quot;super linked&quot; 5-limit chords. In | Another interesting property is that it becomes possible to construct &quot;super linked&quot; 5-limit chords. In Whitewood[14] (or Blackwood[10]), if one stacks alternating major and minor thirds on top of one another, one will eventually come back to the root without ever hitting a wall, and hence the pattern can continue forever. Since all of the diatonic modes can be thought of as a stacked chain of 7 alternating thirds, placed in inversion, this means that Whitewood[14] and Blackwood[10] also make for excellent &quot;panmodal&quot; scales, in which you can construct &quot;modal&quot; sounding sonorities in one key that will work in all keys.<br /> | ||
<br /> | <br /> | ||
Lastly, while blackwood fifths are sharp and thus necessitates the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning.<br /> | Lastly, while blackwood fifths are sharp and thus necessitates the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning.<br /> | ||
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Wedgie: &lt;&lt;7 -7 11 -11 -36||<br /> | Wedgie: &lt;&lt;7 -7 11 -11 -36||<br /> | ||
EDOs: 7, 14, 21, 28, 49<br /> | EDOs: 7, 14, 21, 28, 49<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x7-limit-Other Whitewood"></a><!-- ws:end:WikiTextHeadingRule:8 -->Other Whitewood</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x7-limit-Other Whitewood"></a><!-- ws:end:WikiTextHeadingRule:8 -->Other Whitewood</h2> | ||
Commas: 525/512, | Commas: 525/512, 729/700<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 378.512<br /> | ||
<br /> | <br /> | ||
Map: | Map: [&lt;7 11 0 52|, &lt;0 0 1 -2|]<br /> | ||
Wedgie: | Wedgie: &lt;&lt;0 7 -14 11 -22 -52||<br /> | ||
EDOs: 7, 35, 42<br /> | EDOs: 7, 35, 42<br /> | ||
<br /> | <br /> | ||