21edo: Difference between revisions
Wikispaces>igliashon **Imported revision 515172790 - Original comment: ** |
Wikispaces>igliashon **Imported revision 515173490 - 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:igliashon|igliashon]] and made on <tt>2014-06-28 15: | : 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> | : 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> | ||
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**Notation** ||= **D.-R. Interval** | **Notation** ||= **D.-R. Interval** | ||
**Types** ||= **Approximate** | **Types** ||= **Approximate** | ||
**Ratios*** ||= <span style="text-align: center;">**Approximate**</span> | **Ratios*** ||= <span style="display: block; text-align: center;">**Approximate**</span> | ||
<span style="text-align: center;">**Ratios | <span style="display: block; text-align: center;">**Ratios**</span> ||= <span style="display: block; text-align: center;">Approximate</span> | ||
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 || | ||
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|| 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, | || 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 || | ||
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|| 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 | || 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 || | ||
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*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:** | ||
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<strong>Ratios</strong>*<br /> | <strong>Ratios</strong>*<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><span style="text-align: center;"><strong>Approximate</strong></span><br /> | <td style="text-align: center;"><span style="display: block; text-align: center;"><strong>Approximate</strong></span><br /> | ||
<span style="text-align: center;"><strong>Ratios</ | <span style="display: block; text-align: center;"><strong>Ratios</strong></span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><span style="text-align: center;" | <td style="text-align: center;"><span style="display: block; text-align: center;">Approximate</span><br /> | ||
Ratios*<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">13/11, 20/17<br /> | <td style="text-align: center;">13/11, 20/17<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">6/5<br /> | <td style="text-align: center;">6/5, 7/6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">44/35<br /> | <td style="text-align: center;">44/35<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">5/4, 11/9, | <td style="text-align: center;">5/4, 9/7, 11/9, 14/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">35/22<br /> | <td style="text-align: center;">35/22<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">8/5, 18/11 | <td style="text-align: center;">8/5, 11/7, 14/9, 18/11<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">17/10, 22/13<br /> | <td style="text-align: center;">17/10, 22/13<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">5/3<br /> | <td style="text-align: center;">5/3, 12/7<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<br /> | <br /> | ||
*based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament<br /> | *based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament<br /> | ||
<strong>based on treating 21-EDO as a 2.9/5.11/5.13/5.17/5.35/5 subgroup temperament< | <strong>based on treating 21-EDO as a 2.9/5.11/5.13/5.17/5.35/5 subgroup temperament</strong><br /> | ||
</ | *based on treating 21-EDO as 13-limit laconic temperament<br /> | ||
<br /> | <br /> | ||
<strong>21-tone scales:</strong><br /> | <strong>21-tone scales:</strong><br /> | ||