23edo: Difference between revisions
Wikispaces>guest **Imported revision 239937109 - Original comment: ** |
Wikispaces>guest **Imported revision 239938199 - 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:guest|guest]] and made on <tt>2011-07-04 13: | : This revision was by author [[User:guest|guest]] and made on <tt>2011-07-04 13:56:21 UTC</tt>.<br> | ||
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However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the "anti-pentatonic") and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a "4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale. | However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the "anti-pentatonic") and 4 1 4 1 4 4 1 4 (the "quarter-tone" version of the Blackwood/[[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Rapoport]]/Wilson 13-EDO "subminor" scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a "4/3", we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale. | ||
I would argue that the most significant modes of 23 edo are those of the 2 2 2 3 2 2 3 2 2 3 scale; | |||
This is derived from extending the ~1/3 comma tempered 13th harmonic, two of which add up to the h21 | |||
and three add up to the h17 almost perfectly (I discovered the temperament before I even realised 23 tone fits) | |||
The chord 8:13:21:34 is a fragment of the fibonacci sequence, and 16:21:26 is harmonically symmetrical | |||
(The chord 26:29:32 is also symmetric, but only 20 and 43 edo approximate the h29 as well) | |||
13:17:21 is symmetrical, and 17:21:26:32 has an interesting linear widening pattern, but more importantly, | |||
the h13 and h17 are both dual primes like 3&5 and 7&11 | |||
Thus I have named these 10 modes according to the Sephiroth as follows: | |||
2 2 2 3 2 2 3 2 2 3 - Mode Keter | |||
2 2 3 2 2 3 2 2 3 2 - Chesed | |||
2 3 2 2 3 2 2 3 2 2 - Netzach | |||
3 2 2 3 2 2 3 2 2 2 - Malkuth | |||
2 2 3 2 2 3 2 2 2 3 - Binah | |||
2 3 2 2 3 2 2 2 3 2 - Tiferet | |||
3 2 2 3 2 2 2 3 2 2 - Yesod | |||
2 2 3 2 2 2 3 2 2 3 - Chokmah | |||
2 3 2 2 2 3 2 2 3 2 - Gevurah | |||
3 2 2 2 3 2 2 3 2 2 - Keter | |||
-- Kosmorsky | |||
=Music= | =Music= | ||
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**2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** | **2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** | ||
2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 | 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 | ||
=Books= | =Books= | ||
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<br /> | <br /> | ||
However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the &quot;anti-pentatonic&quot;) and 4 1 4 1 4 4 1 4 (the &quot;quarter-tone&quot; version of the Blackwood/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Rapoport</a>/Wilson 13-EDO &quot;subminor&quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a &quot;4/3&quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.<br /> | However, one can also map 3/2 to 14 degrees of 23-EDO without significantly increasing the error, taking us to a 7-limit temperament where two 3/2's equals 7/3, meaning 28/27 is tempered out, and six 4/3's octave-reduced equals 5/4, meaning 4096/3645 is tempered out. Both of these are very large commas, so this is not at all an accurate temperament, but it is related to 13-EDO and 18-EDO and produces MOS scales of 5 and 8 notes: 5 5 4 5 4 (the &quot;anti-pentatonic&quot;) and 4 1 4 1 4 4 1 4 (the &quot;quarter-tone&quot; version of the Blackwood/<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Rapoport</a>/Wilson 13-EDO &quot;subminor&quot; scale). Alternatively we can treat this temperament as a 2.9.21 subgroup, and instead of calling 9 degrees of 23-EDO a &quot;4/3&quot;, we can call it 21/16. Here three 21/16's gets us to 9/4, meaning 1029/1024 is tempered out. This allows us to treat a triad of 0-4-9 degrees of 23-EDO as an approximation to 16:18:21, and 0-5-9 as 1/(16:18:21); both of these triads are abundant in the 8-note MOS scale.<br /> | ||
<br /> | |||
I would argue that the most significant modes of 23 edo are those of the 2 2 2 3 2 2 3 2 2 3 scale;<br /> | |||
This is derived from extending the ~1/3 comma tempered 13th harmonic, two of which add up to the h21<br /> | |||
and three add up to the h17 almost perfectly (I discovered the temperament before I even realised 23 tone fits)<br /> | |||
The chord 8:13:21:34 is a fragment of the fibonacci sequence, and 16:21:26 is harmonically symmetrical<br /> | |||
(The chord 26:29:32 is also symmetric, but only 20 and 43 edo approximate the h29 as well)<br /> | |||
13:17:21 is symmetrical, and 17:21:26:32 has an interesting linear widening pattern, but more importantly,<br /> | |||
the h13 and h17 are both dual primes like 3&amp;5 and 7&amp;11<br /> | |||
<br /> | |||
Thus I have named these 10 modes according to the Sephiroth as follows:<br /> | |||
2 2 2 3 2 2 3 2 2 3 - Mode Keter<br /> | |||
2 2 3 2 2 3 2 2 3 2 - Chesed<br /> | |||
2 3 2 2 3 2 2 3 2 2 - Netzach<br /> | |||
3 2 2 3 2 2 3 2 2 2 - Malkuth<br /> | |||
2 2 3 2 2 3 2 2 2 3 - Binah<br /> | |||
2 3 2 2 3 2 2 2 3 2 - Tiferet<br /> | |||
3 2 2 3 2 2 2 3 2 2 - Yesod<br /> | |||
2 2 3 2 2 2 3 2 2 3 - Chokmah<br /> | |||
2 3 2 2 2 3 2 2 3 2 - Gevurah<br /> | |||
3 2 2 2 3 2 2 3 2 2 - Keter<br /> | |||
<br /> | |||
-- Kosmorsky<br /> | |||
<br /> | <br /> | ||
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<strong>2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1</strong><br /> | <strong>2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1</strong><br /> | ||
2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1<br /> | 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1<br /> | ||
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