19edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 244989275 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 245874061 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-08-14 12:27:59 UTC</tt>.<br> | ||
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However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7_6|7/6]]), and a septimal whole tone ([[8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and 13 for sensi. | However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7_6|7/6]]), and a septimal whole tone ([[8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and 13 for sensi. | ||
==Intervals== | ==Intervals and linear temperaments== | ||
Since 19 is prime, all linear temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate. | |||
|| | ||~ Degrees of 19edo ||~ Cents value ||~ Generator for || | ||
|| 0 ||= 0 || || | || 0 ||= 0 || || | ||
|| 1 || 63.1579 || || | || 1 || 63.1579 || || | ||
|| 2 || 126.326 || Negri || | || 2 || 126.326 || [[Negri]] || | ||
|| 3 || 189.474 || Deutone || | || 3 || 189.474 || Deutone (index-2 subtemperament of meantone) || | ||
|| 4 || 252.632 || Godzilla || | || 4 || 252.632 || [[Godzilla]] || | ||
|| 5 || 315.789 || Kleismic || | || 5 || 315.789 || [[Kleismic]] ([[hanson]],[[keemun]],[[catakleismic]]) || | ||
|| 6 || 378.947 || Magic || | || 6 || 378.947 || [[Magic]] || | ||
|| 7 || 442.105 || Sensi || | || 7 || 442.105 || [[Sensi]] || | ||
|| 8 || 505.263 || Meantone || | || 8 || 505.263 || [[Meantone]] || | ||
|| 9 || 568.421 || Triton || | || 9 || 568.421 || [[Liese]]/[[Triton]] || | ||
|| 10 || 631.579 || Triton || | || 10 || 631.579 || Liese/Triton || | ||
|| 11 || 694.737 || Meantone || | || 11 || 694.737 || Meantone || | ||
|| 12 || 757.895 || Sensi || | || 12 || 757.895 || Sensi || | ||
|| 13 || 821.053 || Magic || | || 13 || 821.053 || Magic || | ||
|| 14 || 884.211 || Kleismic || | || 14 || 884.211 || Kleismic (hanson,keemun,catakleismic) || | ||
|| 15 || 947.368 || Godzilla || | || 15 || 947.368 || Godzilla || | ||
|| 16 || 1010.53 || Deutone || | || 16 || 1010.53 || Deutone || | ||
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However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a>. It is less successful with <a class="wiki_link" href="/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="/8_7">8/7</a>). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The <a class="wiki_link" href="/Graham%20complexity">Graham complexity</a> of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and 13 for sensi.<br /> | However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta integral edo</a>. It is less successful with <a class="wiki_link" href="/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="/8_7">8/7</a>). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The <a class="wiki_link" href="/Graham%20complexity">Graham complexity</a> of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone/flattone, 11 for triton, 12 for magic/muggles and 13 for sensi.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="Theory-Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 -->Intervals</h2> | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="Theory-Intervals and linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:5 -->Intervals and linear temperaments</h2> | ||
<br /> | Since 19 is prime, all linear temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate.<br /> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Degrees of 19edo<br /> | ||
</ | </th> | ||
< | <th>Cents value<br /> | ||
</ | </th> | ||
< | <th>Generator for<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 168: | Line 168: | ||
<td>126.326<br /> | <td>126.326<br /> | ||
</td> | </td> | ||
<td>Negri<br /> | <td><a class="wiki_link" href="/Negri">Negri</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 176: | Line 176: | ||
<td>189.474<br /> | <td>189.474<br /> | ||
</td> | </td> | ||
<td>Deutone<br /> | <td>Deutone (index-2 subtemperament of meantone)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 184: | Line 184: | ||
<td>252.632<br /> | <td>252.632<br /> | ||
</td> | </td> | ||
<td>Godzilla<br /> | <td><a class="wiki_link" href="/Godzilla">Godzilla</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 192: | Line 192: | ||
<td>315.789<br /> | <td>315.789<br /> | ||
</td> | </td> | ||
<td>Kleismic<br /> | <td><a class="wiki_link" href="/Kleismic">Kleismic</a> (<a class="wiki_link" href="/hanson">hanson</a>,<a class="wiki_link" href="/keemun">keemun</a>,<a class="wiki_link" href="/catakleismic">catakleismic</a>)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 200: | Line 200: | ||
<td>378.947<br /> | <td>378.947<br /> | ||
</td> | </td> | ||
<td>Magic<br /> | <td><a class="wiki_link" href="/Magic">Magic</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 208: | Line 208: | ||
<td>442.105<br /> | <td>442.105<br /> | ||
</td> | </td> | ||
<td>Sensi<br /> | <td><a class="wiki_link" href="/Sensi">Sensi</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 216: | Line 216: | ||
<td>505.263<br /> | <td>505.263<br /> | ||
</td> | </td> | ||
<td>Meantone<br /> | <td><a class="wiki_link" href="/Meantone">Meantone</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 224: | Line 224: | ||
<td>568.421<br /> | <td>568.421<br /> | ||
</td> | </td> | ||
<td>Triton<br /> | <td><a class="wiki_link" href="/Liese">Liese</a>/<a class="wiki_link" href="/Triton">Triton</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 232: | Line 232: | ||
<td>631.579<br /> | <td>631.579<br /> | ||
</td> | </td> | ||
<td>Triton<br /> | <td>Liese/Triton<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 264: | Line 264: | ||
<td>884.211<br /> | <td>884.211<br /> | ||
</td> | </td> | ||
<td>Kleismic<br /> | <td>Kleismic (hanson,keemun,catakleismic)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||