21edo: Difference between revisions

Wikispaces>igliashon
**Imported revision 515172790 - Original comment: **
Wikispaces>igliashon
**Imported revision 515173490 - 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:igliashon|igliashon]] and made on <tt>2014-06-28 15:08:52 UTC</tt>.<br>
: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2014-06-28 15:30:09 UTC</tt>.<br>
: The original revision id was <tt>515172790</tt>.<br>
: The original revision id was <tt>515173490</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 22: Line 22:
**Notation** ||= **D.-R. Interval**
**Notation** ||= **D.-R. Interval**
**Types** ||= **Approximate**
**Types** ||= **Approximate**
**Ratios*** ||= &lt;span style="text-align: center;"&gt;**Approximate**&lt;/span&gt;
**Ratios*** ||= &lt;span style="display: block; text-align: center;"&gt;**Approximate**&lt;/span&gt;
&lt;span style="text-align: center;"&gt;**Ratios****&lt;/span&gt; ||= &lt;span style="text-align: center;"&gt;**Approximate**&lt;/span&gt;
&lt;span style="display: block; text-align: center;"&gt;**Ratios**&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;Approximate&lt;/span&gt;
&lt;span style="text-align: center;"&gt;**Ratios*****&lt;/span&gt; ||
Ratios* ||
|| 0 || 0 || C || C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||
|| 0 || 0 || C || C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||
|| 1 || 57.143 || C^/Dvv || C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||
|| 1 || 57.143 || C^/Dvv || C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||
Line 30: Line 30:
|| 3 || 171.429 || D || D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||
|| 3 || 171.429 || D || D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||
|| 4 || 228.571 || D^/Evv || D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||
|| 4 || 228.571 || D^/Evv || D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||
|| 5 || 285.714 || D^^/Ev || Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5 ||
|| 5 || 285.714 || D^^/Ev || Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||
|| 6 || 342.857 || E || E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||
|| 6 || 342.857 || E || E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||
|| 7 || 400 || E^/Fvv || E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 11/9, 32/25 ||
|| 7 || 400 || E^/Fvv || E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||
|| 8 || 457.143 || E^^/Fv || F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||
|| 8 || 457.143 || E^^/Fv || F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||
|| 9 || 514.286 || F || F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||
|| 9 || 514.286 || F || F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||
Line 39: Line 39:
|| 12 || 685.714 || G || G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||
|| 12 || 685.714 || G || G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||
|| 13 || 742.857 || G^/Avv || Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||
|| 13 || 742.857 || G^/Avv || Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||
|| 14 || 800 || G^^/Av || H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 18/11, 25/16 ||
|| 14 || 800 || G^^/Av || H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||
|| 15 || 857.143 || A || H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||
|| 15 || 857.143 || A || H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||
|| 16 || 914.286 || A^/Bvv || A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3 ||
|| 16 || 914.286 || A^/Bvv || A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||
|| 17 || 971.429 || A^^/Bv || A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||
|| 17 || 971.429 || A^^/Bv || A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||
|| 18 || 1028.571 || B || Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||
|| 18 || 1028.571 || B || Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||
Line 49: Line 49:


*based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament
*based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament
**based on treating 21-EDO as a 2.9/5.11/5.13/5.17/5.35/5 subgroup temperament
**based on treating 21-EDO as a 2.9/5.11/5.13/5.17/5.35/5 subgroup temperament**
***based on treating 21-EDO as 13-limit laconic temperament
*based on treating 21-EDO as 13-limit laconic temperament


**21-tone scales:**
**21-tone scales:**
Line 146: Line 146:
&lt;strong&gt;Ratios&lt;/strong&gt;*&lt;br /&gt;
&lt;strong&gt;Ratios&lt;/strong&gt;*&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;span style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style="text-align: center;"&gt;&lt;strong&gt;Ratios&lt;/strong&gt;&lt;strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Ratios&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;span style="text-align: center;"&gt;&lt;/strong&gt;Approximate&lt;strong&gt;&lt;/span&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Approximate&lt;/span&gt;&lt;br /&gt;
&lt;span style="text-align: center;"&gt;&lt;/strong&gt;Ratios*&lt;/span&gt;&lt;br /&gt;
Ratios*&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 258: Line 258:
         &lt;td style="text-align: center;"&gt;13/11, 20/17&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;13/11, 20/17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;6/5, 7/6&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 294: Line 294:
         &lt;td style="text-align: center;"&gt;44/35&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;44/35&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;5/4, 11/9, 32/25&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;5/4, 9/7, 11/9, 14/11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 420: Line 420:
         &lt;td style="text-align: center;"&gt;35/22&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;35/22&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;8/5, 18/11, 25/16&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;8/5, 11/7, 14/9, 18/11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 456: Line 456:
         &lt;td style="text-align: center;"&gt;17/10, 22/13&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;17/10, 22/13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;5/3, 12/7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 553: Line 553:
&lt;br /&gt;
&lt;br /&gt;
*based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament&lt;br /&gt;
*based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament&lt;br /&gt;
&lt;strong&gt;based on treating 21-EDO as a 2.9/5.11/5.13/5.17/5.35/5 subgroup temperament&lt;br /&gt;
&lt;strong&gt;based on treating 21-EDO as a 2.9/5.11/5.13/5.17/5.35/5 subgroup temperament&lt;/strong&gt;&lt;br /&gt;
&lt;/strong&gt;*based on treating 21-EDO as 13-limit laconic temperament&lt;br /&gt;
*based on treating 21-EDO as 13-limit laconic temperament&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;21-tone scales:&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;21-tone scales:&lt;/strong&gt;&lt;br /&gt;