Meantone intervals: Difference between revisions
Wikispaces>keenanpepper **Imported revision 271804920 - Original comment: ** |
Wikispaces>phylingual **Imported revision 342644634 - 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: | : This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-04 21:35:37 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>342644634</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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In [[19edo]], in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes. | In [[19edo]], in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes. | ||
More complex meantone edos such as [[31edo]] distinguish all intervals listed on this table. | |||
See also [[http://en.wikipedia.org/wiki/List_of_meantone_intervals|Wikipedia's list of meantone intervals]] | See also [[http://en.wikipedia.org/wiki/List_of_meantone_intervals|Wikipedia's list of meantone intervals]] | ||
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|| Augmented unison (A1) || 75.5 || 28/27~25/24~21/20 || | || Augmented unison (A1) || 75.5 || 28/27~25/24~21/20 || | ||
||||||~ Seconds || | ||||||~ Seconds || | ||
|| Diminished second (d2) || 42.0 || 64/63~50/49~36/35 || | || Diminished second (d2) || 42.0 || 128/125~64/63~50/49~36/35 || | ||
|| Minor second (m2) || 117.5 || 16/15~15/14 || | || Minor second (m2) || 117.5 || 16/15~15/14 || | ||
|| Major second (M2) || 193.0 || 10/9~9/8 || | || Major second (M2) || 193.0 || 10/9~9/8 || | ||
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|| Augmented third (A3) || 461.5 || 21/16 || | || Augmented third (A3) || 461.5 || 21/16 || | ||
||||||~ Fourths || | ||||||~ Fourths || | ||
|| Diminished fourth (d4) || 428.0 || 9/7 || | || Diminished fourth (d4) || 428.0 || 9/7 (also a bit 14/11-ish) || | ||
|| Perfect fourth (P4) || 503.5 || 4/3 || | || Perfect fourth (P4) || 503.5 || 4/3 || | ||
|| Augmented fourth (A4) || 579.0 || 7/6 || | || Augmented fourth (A4) || 579.0 || 7/6 || | ||
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|| Diminished fifth (d5) || 621.0 || 10/7 || | || Diminished fifth (d5) || 621.0 || 10/7 || | ||
|| Perfect fifth (P5) || 696.5 || 3/2 || | || Perfect fifth (P5) || 696.5 || 3/2 || | ||
|| Augmented fifth (A5) || 772.0 || 14/9 || | || Augmented fifth (A5) || 772.0 || 14/9 (a bit 11/7-ish) || | ||
||||||~ Sixths || | ||||||~ Sixths || | ||
|| Diminished sixth (d6) || 738.5 || 32/21 || | || Diminished sixth (d6) || 738.5 || 32/21 || | ||
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|| Augmented seventh (A7) || 1158.0 || 35/18~49/25~63/32 || | || Augmented seventh (A7) || 1158.0 || 35/18~49/25~63/32 || | ||
||||||~ Octaves || | ||||||~ Octaves || | ||
|| Diminished octave (d8) || 1124.5 || 27/14 || | || Diminished octave (d8) || 1124.5 || 27/14~40/21 || | ||
|| Perfect octave (P8) || 1200 || 2/1 || | || Perfect octave (P8) || 1200 || 2/1 || | ||
|| Augmented octave (A8) || 1275.5 || 25/12~21/ | || Augmented octave (A8) || 1275.5 || 25/12~21/10 || | ||
``*`` In POTE septimal meantone</pre></div> | ``*`` In POTE septimal meantone</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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<br /> | <br /> | ||
In <a class="wiki_link" href="/19edo">19edo</a>, in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.<br /> | In <a class="wiki_link" href="/19edo">19edo</a>, in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.<br /> | ||
<br /> | |||
More complex meantone edos such as <a class="wiki_link" href="/31edo">31edo</a> distinguish all intervals listed on this table.<br /> | |||
<br /> | <br /> | ||
See also <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_meantone_intervals" rel="nofollow">Wikipedia's list of meantone intervals</a><br /> | See also <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_meantone_intervals" rel="nofollow">Wikipedia's list of meantone intervals</a><br /> | ||
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<td>42.0<br /> | <td>42.0<br /> | ||
</td> | </td> | ||
<td>64/63~50/49~36/35<br /> | <td>128/125~64/63~50/49~36/35<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>428.0<br /> | <td>428.0<br /> | ||
</td> | </td> | ||
<td>9/7<br /> | <td>9/7 (also a bit 14/11-ish)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>772.0<br /> | <td>772.0<br /> | ||
</td> | </td> | ||
<td>14/9<br /> | <td>14/9 (a bit 11/7-ish)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>1124.5<br /> | <td>1124.5<br /> | ||
</td> | </td> | ||
<td>27/14<br /> | <td>27/14~40/21<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>1275.5<br /> | <td>1275.5<br /> | ||
</td> | </td> | ||
<td>25/12~21/ | <td>25/12~21/10<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||