26edo: Difference between revisions

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//26edo// divides the octave into 26 equal parts of 46.154 cents each. It tempers out 81/80 in the 5-limit, making it a meantone tuning with a very flat fifth. In the 7-limit, it tempers out 50/49, 525/512 and 875/864, and supports [[Meantone family|injera]] and [[Meantone family|flattone]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the 13 odd limit consistently. 

=**Structure**= 

The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments.
1. In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which yields interesting but to some unsatisfying results (due mainly to the dissonance of its thirds, and its major seconds of either approximately [[10_9|10/9]] or [[8_7|8/7]], but NOT [[9_8|9/8]]).
2. As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to, for instance, 38edo) it can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of 14edo.
3. 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas 65536/65219 and 117649/117128. The 65536/65219 comma, the orgonisma, leads to [[Orgonia|orgone temperament]] with an approximate 77/64 generator of 7\26, with MOS scales of size 7, 11 and 15. The 117649/117128 comma leads to a half-octave period and an approximate 49/44 generator of 4\26, leading to MOS of size 8 and 14.

=Commas= 
26et tempers out the following commas. (Note: This assumes the val < 26 41 60 73 90 96 |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 81/80 ||< | -4 4 -1 > ||> 21.51 ||= Syntonic Comma ||= Didymos Comma ||= Meantone Comma ||
||= 5696703/5695946 ||< | -17 62 -35 > ||> 0.23 ||= Senior ||=   ||=   ||
||= 525/512 ||< | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||=   ||
||= 50/49 ||< | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma ||=   ||
||= 875/864 ||< | -5 -3 3 1 > ||> 21.90 ||= Keema ||=   ||=   ||
||= 4000/3969 ||< | 5 -4 3 -2 > ||> 13.47 ||= Octagar ||=   ||=   ||
||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma ||=   ||
||= 1029/1024 ||< | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||=   ||=   ||
||= 321489/320000 ||< | -9 8 -4 2 > ||> 8.04 ||= Varunisma ||=   ||=   ||
||= 1065875/1063543 ||< | -26 -1 1 9 > ||> 3.79 ||= Wadisma ||=   ||=   ||
||= 4375/4374 ||< | -1 -7 4 1 > ||> 0.40 ||= Ragisma ||=   ||=   ||
||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||=   ||=   ||
||= 100/99 ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||=   ||=   ||
||= 65536/65219 ||< | 16 0 0 -2 -3 > ||> 8.39 ||= Orgonisma ||=   ||=   ||
||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||=   ||=   ||
||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||=   ||=   ||
||= 3025/3024 ||< | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||=   ||=   ||
||= 9801/9800 ||< | -3 4 -2 -2 2 > ||> 0.18 ||= Kalisma ||= Gauss' Comma ||=   ||
=[[Orgonia|Orgone Temperament]]= 

[[Andrew Heathwaite]] first proposed orgone temperament to take advantage of 26edo's excellent 11 and 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:

The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. [[MOSScales|MOS]] of type [[4L 3s|4L 3s (mish)]].
The 7-tone scale in cents: 0 231 323 554 646 877 969 1200.

The 11-tone scale in degrees-in-between: 2 3 2 2 3 2 3 2 2 3 2. [[MOSScales|MOS]] of type [[4L 7s]].
The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108, 1200.

The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16_11|16:11]] and 3g approximates [[7_4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.

[[37edo]] is another orgone tuning, and [[89edo]] is better even than 26. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus:

|| 3\11 ||   ||   ||   ||   ||
||   ||   ||   ||   || 19\70 ||
||   ||   ||   || 16\59 ||   ||
||   ||   ||   ||   || 29\107 ||
||   ||   || 13\48 ||   ||   ||
||   ||   ||   ||   || 36\133 ||
||   ||   ||   || 23\85 ||   ||
||   ||   ||   ||   || 33\122 ||
||   || 10\37 ||   ||   ||   ||
||   ||   ||   ||   || 37\137 ||
||   ||   ||   || 27\100 ||   ||
||   ||   ||   ||   || 44\163 ||
||   ||   || 17\63 ||   ||   ||
||   ||   ||   ||   || 41\152 ||
||   ||   ||   || 24\89 ||   ||
||   ||   ||   ||   || 31\115 ||
|| 7\26 ||   ||   ||   ||   ||

Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.

[[image:orgone_heptatonic.jpg]]

=Intervals= 

|| degree || cents ||
|| 0 || 0 ||
|| 1 || 46.15 ||
|| 2 || 92.31 ||
|| 3 || 138.46 ||
|| 4 || 184.62 ||
|| 5 || 230.77 ||
|| 6 || 276.92 ||
|| 7 || 323.08 ||
|| 8 || 369.23 ||
|| 9 || 415.38 ||
|| 10 || 461.54 ||
|| 11 || 507.69 ||
|| 12 || 553.85 ||
|| 13 || 600.00 ||
|| 14 || 646.15 ||
|| 15 || 692.31 ||
|| 16 || 738.46 ||
|| 17 || 784.62 ||
|| 18 || 830.77 ||
|| 19 || 876.92 ||
|| 20 || 923.08 ||
|| 21 || 969.23 ||
|| 22 || 1015.38 ||
|| 23 || 1061.54 ||
|| 24 || 1107.69 ||
|| 25 || 1153.85 ||

=Additional Scalar Bases Available in 26-EDO:= 
Since the perfect 5th in 26-EDO spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12). The former approach produces MOS at 1L+4s, 5L+1s, and 5L+6s (5 5 5 5 6, 5 5 5 5 5 1, and 4 1 4 1 4 1 4 1 4 1 1 respectively), and is excellent for 4:6:7 triads. The latter produces MOS at 1L+7s and 8L+1s (3 3 3 3 3 3 3 5 and 3 3 3 3 3 3 3 3 2 respectively), and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (thought further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).

-Igs

=Literature= 

[[http://www.ronsword.com|Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]]

=Compositions= 

[[http://soundclick.com/share?songid=5683791|A Time-Yellowed Photo of the Cliffs Hangs on the Wall ]] by [[IgliashonJones|Igliashon Jones]]
[[http://www.io.com/%7Ehmiller/midi/26tet.mid|Etude in 26-tone equal tuning]] by [[Herman Miller]]
[[http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html|A New Recording of Organ Study #1]] by [[Daniel Thompson]]

Original HTML content:

<html><head><title>26edo</title></head><body><em>26edo</em> divides the octave into 26 equal parts of 46.154 cents each. It tempers out 81/80 in the 5-limit, making it a meantone tuning with a very flat fifth. In the 7-limit, it tempers out 50/49, 525/512 and 875/864, and supports <a class="wiki_link" href="/Meantone%20family">injera</a> and <a class="wiki_link" href="/Meantone%20family">flattone</a> temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the 13 odd limit consistently. <br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Structure"></a><!-- ws:end:WikiTextHeadingRule:0 --><strong>Structure</strong></h1>
 <br />
The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments.<br />
1. In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which yields interesting but to some unsatisfying results (due mainly to the dissonance of its thirds, and its major seconds of either approximately <a class="wiki_link" href="/10_9">10/9</a> or <a class="wiki_link" href="/8_7">8/7</a>, but NOT <a class="wiki_link" href="/9_8">9/8</a>).<br />
2. As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to, for instance, 38edo) it can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&amp;26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of 14edo.<br />
3. 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas 65536/65219 and 117649/117128. The 65536/65219 comma, the orgonisma, leads to <a class="wiki_link" href="/Orgonia">orgone temperament</a> with an approximate 77/64 generator of 7\26, with MOS scales of size 7, 11 and 15. The 117649/117128 comma leads to a half-octave period and an approximate 49/44 generator of 4\26, leading to MOS of size 8 and 14.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas</h1>
 26et tempers out the following commas. (Note: This assumes the val &lt; 26 41 60 73 90 96 |.)<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Monzo<br />
</th>
        <th>Value (Cents)<br />
</th>
        <th>Name 1<br />
</th>
        <th>Name 2<br />
</th>
        <th>Name 3<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: left;">| -4 4 -1 &gt;<br />
</td>
        <td style="text-align: right;">21.51<br />
</td>
        <td style="text-align: center;">Syntonic Comma<br />
</td>
        <td style="text-align: center;">Didymos Comma<br />
</td>
        <td style="text-align: center;">Meantone Comma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5696703/5695946<br />
</td>
        <td style="text-align: left;">| -17 62 -35 &gt;<br />
</td>
        <td style="text-align: right;">0.23<br />
</td>
        <td style="text-align: center;">Senior<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">525/512<br />
</td>
        <td style="text-align: left;">| -9 1 2 1 &gt;<br />
</td>
        <td style="text-align: right;">43.41<br />
</td>
        <td style="text-align: center;">Avicennma<br />
</td>
        <td style="text-align: center;">Avicenna's Enharmonic Diesis<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50/49<br />
</td>
        <td style="text-align: left;">| 1 0 2 -2 &gt;<br />
</td>
        <td style="text-align: right;">34.98<br />
</td>
        <td style="text-align: center;">Tritonic Diesis<br />
</td>
        <td style="text-align: center;">Jubilisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">875/864<br />
</td>
        <td style="text-align: left;">| -5 -3 3 1 &gt;<br />
</td>
        <td style="text-align: right;">21.90<br />
</td>
        <td style="text-align: center;">Keema<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4000/3969<br />
</td>
        <td style="text-align: left;">| 5 -4 3 -2 &gt;<br />
</td>
        <td style="text-align: right;">13.47<br />
</td>
        <td style="text-align: center;">Octagar<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1728/1715<br />
</td>
        <td style="text-align: left;">| 6 3 -1 -3 &gt;<br />
</td>
        <td style="text-align: right;">13.07<br />
</td>
        <td style="text-align: center;">Orwellisma<br />
</td>
        <td style="text-align: center;">Orwell Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1029/1024<br />
</td>
        <td style="text-align: left;">| -10 1 0 3 &gt;<br />
</td>
        <td style="text-align: right;">8.43<br />
</td>
        <td style="text-align: center;">Gamelisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">321489/320000<br />
</td>
        <td style="text-align: left;">| -9 8 -4 2 &gt;<br />
</td>
        <td style="text-align: right;">8.04<br />
</td>
        <td style="text-align: center;">Varunisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1065875/1063543<br />
</td>
        <td style="text-align: left;">| -26 -1 1 9 &gt;<br />
</td>
        <td style="text-align: right;">3.79<br />
</td>
        <td style="text-align: center;">Wadisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4375/4374<br />
</td>
        <td style="text-align: left;">| -1 -7 4 1 &gt;<br />
</td>
        <td style="text-align: right;">0.40<br />
</td>
        <td style="text-align: center;">Ragisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">99/98<br />
</td>
        <td style="text-align: left;">| -1 2 0 -2 1 &gt;<br />
</td>
        <td style="text-align: right;">17.58<br />
</td>
        <td style="text-align: center;">Mothwellsma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">100/99<br />
</td>
        <td style="text-align: left;">| 2 -2 2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">17.40<br />
</td>
        <td style="text-align: center;">Ptolemisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">65536/65219<br />
</td>
        <td style="text-align: left;">| 16 0 0 -2 -3 &gt;<br />
</td>
        <td style="text-align: right;">8.39<br />
</td>
        <td style="text-align: center;">Orgonisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td style="text-align: left;">| -7 -1 1 1 1 &gt;<br />
</td>
        <td style="text-align: right;">4.50<br />
</td>
        <td style="text-align: center;">Keenanisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">441/440<br />
</td>
        <td style="text-align: left;">| -3 2 -1 2 -1 &gt;<br />
</td>
        <td style="text-align: right;">3.93<br />
</td>
        <td style="text-align: center;">Werckisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3025/3024<br />
</td>
        <td style="text-align: left;">| -4 -3 2 -1 2 &gt;<br />
</td>
        <td style="text-align: right;">0.57<br />
</td>
        <td style="text-align: center;">Lehmerisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9801/9800<br />
</td>
        <td style="text-align: left;">| -3 4 -2 -2 2 &gt;<br />
</td>
        <td style="text-align: right;">0.18<br />
</td>
        <td style="text-align: center;">Kalisma<br />
</td>
        <td style="text-align: center;">Gauss' Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Orgone Temperament"></a><!-- ws:end:WikiTextHeadingRule:4 --><a class="wiki_link" href="/Orgonia">Orgone Temperament</a></h1>
 <br />
<a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> first proposed orgone temperament to take advantage of 26edo's excellent 11 and 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:<br />
<br />
The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%203s">4L 3s (mish)</a>.<br />
The 7-tone scale in cents: 0 231 323 554 646 877 969 1200.<br />
<br />
The 11-tone scale in degrees-in-between: 2 3 2 2 3 2 3 2 2 3 2. <a class="wiki_link" href="/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%207s">4L 7s</a>.<br />
The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108, 1200.<br />
<br />
The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates <a class="wiki_link" href="/16_11">16:11</a> and 3g approximates <a class="wiki_link" href="/7_4">7:4</a> (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.<br />
<br />
<a class="wiki_link" href="/37edo">37edo</a> is another orgone tuning, and <a class="wiki_link" href="/89edo">89edo</a> is better even than 26. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus:<br />
<br />


<table class="wiki_table">
    <tr>
        <td>3\11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>19\70<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>16\59<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>29\107<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\48<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>36\133<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>23\85<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>33\122<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>10\37<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>37\137<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>27\100<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>44\163<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>17\63<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>41\152<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>24\89<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>31\115<br />
</td>
    </tr>
    <tr>
        <td>7\26<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:652:&lt;img src=&quot;/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="orgone_heptatonic.jpg" title="orgone_heptatonic.jpg" /><!-- ws:end:WikiTextLocalImageRule:652 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1>
 <br />


<table class="wiki_table">
    <tr>
        <td>degree<br />
</td>
        <td>cents<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>46.15<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>92.31<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>138.46<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>184.62<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>230.77<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>276.92<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>323.08<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>369.23<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>415.38<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>461.54<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>507.69<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>553.85<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>600.00<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>646.15<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>692.31<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>738.46<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>784.62<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>830.77<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>876.92<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>923.08<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>969.23<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>1015.38<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>1061.54<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>1107.69<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>1153.85<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Additional Scalar Bases Available in 26-EDO:"></a><!-- ws:end:WikiTextHeadingRule:8 -->Additional Scalar Bases Available in 26-EDO:</h1>
 Since the perfect 5th in 26-EDO spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12). The former approach produces MOS at 1L+4s, 5L+1s, and 5L+6s (5 5 5 5 6, 5 5 5 5 5 1, and 4 1 4 1 4 1 4 1 4 1 1 respectively), and is excellent for 4:6:7 triads. The latter produces MOS at 1L+7s and 8L+1s (3 3 3 3 3 3 3 5 and 3 3 3 3 3 3 3 3 2 respectively), and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (thought further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).<br />
<br />
-Igs<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Literature"></a><!-- ws:end:WikiTextHeadingRule:10 -->Literature</h1>
 <br />
<a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow">Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:12 -->Compositions</h1>
 <br />
<a class="wiki_link_ext" href="http://soundclick.com/share?songid=5683791" rel="nofollow">A Time-Yellowed Photo of the Cliffs Hangs on the Wall </a> by <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a><br />
<a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/26tet.mid" rel="nofollow">Etude in 26-tone equal tuning</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br />
<a class="wiki_link_ext" href="http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html" rel="nofollow">A New Recording of Organ Study #1</a> by <a class="wiki_link" href="/Daniel%20Thompson">Daniel Thompson</a></body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 22:21:46 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-05 14:24:54 UTC</tt>.<br>
-: The original revision id was <tt>233348796</tt>.<br>
+: The original revision id was <tt>234380890</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>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=**Structure**=
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//26edo// divides the octave into 26 equal parts of 46.154 cents each. It tempers out 81/80 in the 5-limit, making it a meantone tuning with a very flat fifth. In the 7-limit, it tempers out 50/49, 525/512 and 875/864, and supports [[Meantone family|injera]] and [[Meantone family|flattone]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the 13 odd limit consistently.
-The structure of 26-EDO is an interesting beast, and I find three particular manners of understanding the chords and chordal relationships in it;
+=**Structure**=
-. In terms of traditional chord types, that is, as a variant of meantone stretched too far, which yields interesting but perhaps unsatisfying results (due mainly to the dissonance of its thirds, and its major seconds of either approximately [[10_9|10/9]] or [[8_7|8/7]], but NOT [[9_8|9/8]]). This is not meant to say that this approach is without merit.
-. As two parallel 13-EDO scales (And as I've considered, if these two chains be shifted together or apart slightly but appropriately, interesting variants may be constructed) which is suitable for more atonal melodies. In this way its internal dynamics quite resemble those of 14-EDO.
-. 26-EDO nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. The resulting scale is jagged, and it perverts common musical rules and conventions, but this particular organisation has its charm -perhaps because of this- and leads to some intriguing music.
-- K.
+The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments.
+. In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which yields interesting but to some unsatisfying results (due mainly to the dissonance of its thirds, and its major seconds of either approximately [[10_9|10/9]] or [[8_7|8/7]], but NOT [[9_8|9/8]]).
+. As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to, for instance, 38edo) it can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&amp;26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of 14edo.
+. 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas 65536/65219 and 117649/117128. The 65536/65219 comma, the orgonisma, leads to [[Orgonia|orgone temperament]] with an approximate 77/64 generator of 7\26, with MOS scales of size 7, 11 and 15. The 117649/117128 comma leads to a half-octave period and an approximate 49/44 generator of 4\26, leading to MOS of size 8 and 14.
 =Commas=
-EDO tempers out the following commas. (Note: This assumes the val &lt; 26 41 60 73 90 96 |.)
+et tempers out the following commas. (Note: This assumes the val &lt; 26 41 60 73 90 96 |.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
 ||= 81/80 ||&lt; | -4 4 -1 &gt; ||&gt; 21.51 ||= Syntonic Comma ||= Didymos Comma ||= Meantone Comma ||
@@ Line 36: / Line 36: @@
 ||= 3025/3024 ||&lt; | -4 -3 2 -1 2 &gt; ||&gt; 0.57 ||= Lehmerisma ||=   ||=   ||
 ||= 9801/9800 ||&lt; | -3 4 -2 -2 2 &gt; ||&gt; 0.18 ||= Kalisma ||= Gauss' Comma ||=   ||
-=Orgone Temperament=
+=[[Orgonia|Orgone Temperament]]=
-[[Andrew Heathwaite]] proposes a temperament family which takes advantage of 26edo's excellent 11 &amp; 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:
+[[Andrew Heathwaite]] first proposed orgone temperament to take advantage of 26edo's excellent 11 and 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:
 The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. [[MOSScales|MOS]] of type [[4L 3s|4L 3s (mish)]].
@@ Line 46: / Line 46: @@
 The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108, 1200.
-The primary triad for Orgone Temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16_11|16:11]] and 3g approximates [[7_4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.
+The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16_11|16:11]] and 3g approximates [[7_4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.
-[[37edo]] is another excellent Orgone tuning. [[11edo]] is passable, but barely. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus:
+[[37edo]] is another orgone tuning, and [[89edo]] is better even than 26. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus:
 || 3\11 ||   ||   ||   ||   ||
@@ Line 68: / Line 68: @@
 || 7\26 ||   ||   ||   ||   ||
-Orgone tempers out 65536/65219 = |16 0 0 -2 -3&gt;, and has a minimax tuning which sharpens both 7 and 11 by 1/5 of this comma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgone comma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.
+Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.
-If a name already exists for this temperament, I'd be interested to know about it. As far as I know, temperaments which ignore lower primes (in this case 3 and 5) in favor of higher ones (in this case 7 and 11) are still largely uncharted, but I am interested in finding out if someone has walked this path before.
 [[image:orgone_heptatonic.jpg]]
@@ Line 119: / Line 117: @@
 [[http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html|A New Recording of Organ Study #1]] by [[Daniel Thompson]]</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;26edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Structure"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;strong&gt;Structure&lt;/strong&gt;&lt;/h1&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;26edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;26edo&lt;/em&gt; divides the octave into 26 equal parts of 46.154 cents each. It tempers out 81/80 in the 5-limit, making it a meantone tuning with a very flat fifth. In the 7-limit, it tempers out 50/49, 525/512 and 875/864, and supports &lt;a class="wiki_link" href="/Meantone%20family"&gt;injera&lt;/a&gt; and &lt;a class="wiki_link" href="/Meantone%20family"&gt;flattone&lt;/a&gt; temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the 13 odd limit consistently. &lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Structure"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;strong&gt;Structure&lt;/strong&gt;&lt;/h1&gt;
   &lt;br /&gt;
-The structure of 26-EDO is an interesting beast, and I find three particular manners of understanding the chords and chordal relationships in it;&lt;br /&gt;
+The structure of 26edo is an interesting beast, with various approaches relating it to various rank two temperaments.&lt;br /&gt;
-. In terms of traditional chord types, that is, as a variant of meantone stretched too far, which yields interesting but perhaps unsatisfying results (due mainly to the dissonance of its thirds, and its major seconds of either approximately &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; or &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, but NOT &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;). This is not meant to say that this approach is without merit.&lt;br /&gt;
+. In terms of more traditional chord types we have flattone, a variant of meantone with flat fifths, which yields interesting but to some unsatisfying results (due mainly to the dissonance of its thirds, and its major seconds of either approximately &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; or &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, but NOT &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;).&lt;br /&gt;
-. As two parallel 13-EDO scales (And as I've considered, if these two chains be shifted together or apart slightly but appropriately, interesting variants may be constructed) which is suitable for more atonal melodies. In this way its internal dynamics quite resemble those of 14-EDO.&lt;br /&gt;
+. As two chains of meantone fifths half an octave apart, it supports injera temperament. The generator for this is an interval which can be called either 21/20 or 15/14, and which represents two steps of 26, and hence one step of 13. Hence in 26edo (as opposed to, for instance, 38edo) it can be viewed as two parallel 13edo scales, and from that point of view we can consider it as supporting the 13b&amp;amp;26 temperament, allowing the two chains be shifted slightly and which can be used for more atonal melodies. In this way its internal dynamics resemble those of 14edo.&lt;br /&gt;
-. 26-EDO nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. The resulting scale is jagged, and it perverts common musical rules and conventions, but this particular organisation has its charm -perhaps because of this- and leads to some intriguing music.&lt;br /&gt;
+. 26edo nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. In terms of subgroups, this is the 2.7.11 subgroup, and on this 26 tempers out the pair of commas 65536/65219 and 117649/117128. The 65536/65219 comma, the orgonisma, leads to &lt;a class="wiki_link" href="/Orgonia"&gt;orgone temperament&lt;/a&gt; with an approximate 77/64 generator of 7\26, with MOS scales of size 7, 11 and 15. The 117649/117128 comma leads to a half-octave period and an approximate 49/44 generator of 4\26, leading to MOS of size 8 and 14.&lt;br /&gt;
-&lt;br /&gt;
-- K.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Commas&lt;/h1&gt;
-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 26 41 60 73 90 96 |.)&lt;br /&gt;
+et tempers out the following commas. (Note: This assumes the val &amp;lt; 26 41 60 73 90 96 |.)&lt;br /&gt;
@@ Line 401: / Line 399: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Orgone Temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Orgone Temperament&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Orgone Temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;a class="wiki_link" href="/Orgonia"&gt;Orgone Temperament&lt;/a&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt; proposes a temperament family which takes advantage of 26edo's excellent 11 &amp;amp; 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:&lt;br /&gt;
+&lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt; first proposed orgone temperament to take advantage of 26edo's excellent 11 and 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:&lt;br /&gt;
 &lt;br /&gt;
 The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="/4L%203s"&gt;4L 3s (mish)&lt;/a&gt;.&lt;br /&gt;
@@ Line 411: / Line 409: @@
 The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108, 1200.&lt;br /&gt;
 &lt;br /&gt;
-The primary triad for Orgone Temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates &lt;a class="wiki_link" href="/16_11"&gt;16:11&lt;/a&gt; and 3g approximates &lt;a class="wiki_link" href="/7_4"&gt;7:4&lt;/a&gt; (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.&lt;br /&gt;
+The primary triad for orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates &lt;a class="wiki_link" href="/16_11"&gt;16:11&lt;/a&gt; and 3g approximates &lt;a class="wiki_link" href="/7_4"&gt;7:4&lt;/a&gt; (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.&lt;br /&gt;
 &lt;br /&gt;
-&lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt; is another excellent Orgone tuning. &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt; is passable, but barely. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus:&lt;br /&gt;
+&lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt; is another orgone tuning, and &lt;a class="wiki_link" href="/89edo"&gt;89edo&lt;/a&gt; is better even than 26. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus:&lt;br /&gt;
 &lt;br /&gt;
@@ Line 625: / Line 623: @@
 &lt;br /&gt;
-Orgone tempers out 65536/65219 = |16 0 0 -2 -3&amp;gt;, and has a minimax tuning which sharpens both 7 and 11 by 1/5 of this comma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgone comma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.&lt;br /&gt;
+Orgone has a minimax tuning which sharpens both 7 and 11 by 1/5 of an orgonisma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgonisma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.&lt;br /&gt;
-&lt;br /&gt;
-If a name already exists for this temperament, I'd be interested to know about it. As far as I know, temperaments which ignore lower primes (in this case 3 and 5) in favor of higher ones (in this case 7 and 11) are still largely uncharted, but I am interested in finding out if someone has walked this path before.&lt;br /&gt;
 &lt;br /&gt;
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