16edo: 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>2010-05-03 12:18:54 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2010-05-03 12:56:43 UTC</tt>.

: The original revision id was <tt>~~139038675~~</tt>.

: The original revision id was <tt>139051703</tt>.

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In 16-tone, because of the 25 cent difference in the steps from 100 in 12-tone, a western "twelve tone ear" hears dissonance with more complexity and less familiarity than even 24-tone, yet within a more manageable number of tones and a strange familiarity - the diminished. Hence, why 16-tone is a truly Xenharmonic system.

In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales like the "Anti-Diatonic" Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable.

In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales an alternative temperament families like the "Anti-Diatonic" Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable.

Like the conventional 12-tet diatonic and pentatonic (meantone) scales, these arise from tempering out a unison vector from Fokker periodicity blocks. Only in 16-EDO, that unison vector is 135:128, instead of 81:80. Based on seeing a diagram by Erv Wilson showing the mapping of prime 5 as 3 steps in a chain of fifths- which is the mapping and generator required to produce octave-repeating scales where 135:128 vanishes.

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In 16-tone, because of the 25 cent difference in the steps from 100 in 12-tone, a western &quot;twelve tone ear&quot; hears dissonance with more complexity and less familiarity than even 24-tone, yet within a more manageable number of tones and a strange familiarity - the diminished. Hence, why 16-tone is a truly Xenharmonic system.

In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales like the &quot;Anti-Diatonic&quot; Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable.

In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales an alternative temperament families like the &quot;Anti-Diatonic&quot; Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable.

Like the conventional 12-tet diatonic and pentatonic (meantone) scales, these arise from tempering out a unison vector from Fokker periodicity blocks. Only in 16-EDO, that unison vector is 135:128, instead of 81:80. Based on seeing a diagram by Erv Wilson showing the mapping of prime 5 as 3 steps in a chain of fifths- which is the mapping and generator required to produce octave-repeating scales where 135:128 vanishes.

@@ 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>2010-05-03 12:18:54 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-05-03 12:56:43 UTC</tt>.<br>
-: The original revision id was <tt>139038675</tt>.<br>
+: The original revision id was <tt>139051703</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 19: / Line 19: @@
 In 16-tone, because of the 25 cent difference in the steps from 100 in 12-tone, a western "twelve tone ear" hears dissonance with more complexity and less familiarity than even 24-tone, yet within a more manageable number of tones and a strange familiarity - the diminished. Hence, why 16-tone is a truly Xenharmonic system.
-In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales like the "Anti-Diatonic" Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable.
+In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales an alternative temperament families like the "Anti-Diatonic" Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable.
 Like the conventional 12-tet diatonic and pentatonic (meantone) scales, these arise from tempering out a unison vector from Fokker periodicity blocks. Only in 16-EDO, that unison vector is 135:&lt;span class="text_exposed_show"&gt;128, instead of 81:80. Based on seeing a diagram by Erv Wilson showing the mapping of prime 5 as 3 steps in a chain of fifths- which is the mapping and generator required to produce octave-repeating scales where 135:128 vanishes&lt;/span&gt;.
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 &lt;br /&gt;
 In 16-tone, because of the 25 cent difference in the steps from 100 in 12-tone, a western &amp;quot;twelve tone ear&amp;quot; hears dissonance with more complexity and less familiarity than even 24-tone, yet within a more manageable number of tones and a strange familiarity - the diminished. Hence, why 16-tone is a truly Xenharmonic system.&lt;br /&gt;
-In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales like the &amp;quot;Anti-Diatonic&amp;quot; Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable.&lt;br /&gt;
+In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales an alternative temperament families like the &amp;quot;Anti-Diatonic&amp;quot; Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable.&lt;br /&gt;
 &lt;br /&gt;
 Like the conventional 12-tet diatonic and pentatonic (meantone) scales, these arise from tempering out a unison vector from Fokker periodicity blocks. Only in 16-EDO, that unison vector is 135:&lt;span class="text_exposed_show"&gt;128, instead of 81:80. Based on seeing a diagram by Erv Wilson showing the mapping of prime 5 as 3 steps in a chain of fifths- which is the mapping and generator required to produce octave-repeating scales where 135:128 vanishes&lt;/span&gt;.&lt;br /&gt;