Whitewood family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:guest|guest]] and made on <tt>2011-02-01 00:04:25 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2011-02-01 00:06:24 UTC</tt>.

: The original revision id was <tt>~~197666844~~</tt>.

: The original revision id was <tt>197667110</tt>.

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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.

The 14-note MOS of whitewood, like the 10-note MOS of blackwood, 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 in the scale, at least keys that share the same chord quality.

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.

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 necessitate 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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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.

~~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.

The 14-note MOS of whitewood, like the 10-note MOS of blackwood, 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 in the scale, at least keys that share the same chord quality.

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.

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.

Lastly, while blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:guest|guest]] and made on <tt>2011-02-01 00:04:25 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-02-01 00:06:24 UTC</tt>.<br>
-: The original revision id was <tt>197666844</tt>.<br>
+: The original revision id was <tt>197667110</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>
@@ Line 10: / Line 10: @@
 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.
+The 14-note MOS of whitewood, like the 10-note MOS of blackwood, 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 in the scale, at least keys that share the same chord quality.
-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.
+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 necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning.
@@ Line 57: / Line 57: @@
 The 5-limit version of this temperament is called &amp;quot;whitewood&amp;quot; temperament, to serve in contrast with the &amp;quot;blackwood&amp;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.&lt;br /&gt;
 &lt;br /&gt;
-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 &amp;quot;hit a wall&amp;quot; if one moves by perfect fifth for long enough; the chain of fifths will eventually &amp;quot;stop&amp;quot; and make the next fifth a diminished fifth. This means that this scale is, in a sense, &amp;quot;pantonal,&amp;quot; since resolutions that work in one key will work in all other keys.&lt;br /&gt;
+The 14-note MOS of whitewood, like the 10-note MOS of blackwood, 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 &amp;quot;hit a wall&amp;quot; if one moves by perfect fifth for long enough; the chain of fifths will eventually &amp;quot;stop&amp;quot; and make the next fifth a diminished fifth. This means that this scale is, in a sense, &amp;quot;pantonal,&amp;quot; since resolutions that work in one key will work in all other keys in the scale, at least keys that share the same chord quality.&lt;br /&gt;
 &lt;br /&gt;
-Another interesting property is that it becomes possible to construct &amp;quot;super linked&amp;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 &amp;quot;panmodal&amp;quot; scales, in which you can construct &amp;quot;modal&amp;quot; sounding sonorities in one key that will work in all keys.&lt;br /&gt;
+Another interesting property is that it becomes possible to construct &amp;quot;super-linked&amp;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 &amp;quot;panmodal&amp;quot; scales, in which you can construct &amp;quot;modal&amp;quot; sounding sonorities in one key that will work in all keys.&lt;br /&gt;
 &lt;br /&gt;
 Lastly, while blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning.&lt;br /&gt;