16edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:guest|guest]] and made on <tt>2010-04-~~22 02~~:28:16 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2010-05-03 12:18:54 UTC</tt>.

: The original revision id was <tt>~~136264933~~</tt>.

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

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 9:

==Theory==

16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a Slendro temperament with a supermajor second generator ([233cents]~~250cents~~), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The ~~tuning~~ could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.

16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a rough Slendro temperament with a supermajor second generator (250cents [ideally 233cents]), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The temperament could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.

The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.

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, 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 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.

0. 1/1 C

Line 73:

Line 77:

<h2 id="toc1"><a name="x16 tone equal temperament-Theory"></a>Theory</h2>

16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a Slendro temperament with a supermajor second generator ([233cents]~~250cents~~), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The ~~tuning~~ could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.

16-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a rough Slendro temperament with a supermajor second generator (250cents [ideally 233cents]), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The temperament could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.

The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.

Line 83:

Line 87:

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, 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 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.

0. 1/1 C

@@ 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>2010-04-22 02:28:16 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-05-03 12:18:54 UTC</tt>.<br>
-: The original revision id was <tt>136264933</tt>.<br>
+: The original revision id was <tt>139038675</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 9: / Line 9: @@
 ==Theory==
--tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a Slendro temperament with a supermajor second generator ([233cents]250cents), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The tuning could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.
+-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a rough Slendro temperament with a supermajor second generator (250cents [ideally 233cents]), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The temperament could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.
 The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.
@@ 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, 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 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;.
 . 1/1 C
@@ Line 73: / Line 77: @@
   &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x16 tone equal temperament-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory&lt;/h2&gt;
--tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a Slendro temperament with a supermajor second generator ([233cents]250cents), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The tuning could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.&lt;br /&gt;
+-tone equal temperament is the division of the octave into sixteen narrow chromatic semitones. It can be thought of as a Diminished Temperament for it's 1/4 octave period. Also as a rough Slendro temperament with a supermajor second generator (250cents [ideally 233cents]), or as a Pelog or Mavila temperament generated by (fifths greater than 600 and less than 686 cents). The temperament could be popular for it's easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones.&lt;br /&gt;
 The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 83: / Line 87: @@
 &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, 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 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;
+&lt;br /&gt;
+&lt;br /&gt;
 &lt;br /&gt;
 . 1/1 C&lt;br /&gt;