26edo
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[[toc]] //26edo// divides the [[octave]] into 26 equal parts of 46.154 [[cent]]s 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]], [[Meantone family|flattone]], [[Jubilismic clan#Lemba|lemba]] and [[Jubilismic clan#Doublewide|doublewide]] temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-limit|13 odd limit]] [[consistent|consistently]]. 26edo has a very good approximation of the harmonic seventh ([[7_4|7/4]]). =**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. 4. We can also treat 26-EDO as a full 13-limit temperament, since it is consistent on the 13-limit (unlike all lower EDOs). =<span style="font-size: 1.4em;">Intervals</span>= || degree || [[cent]]s DMS ||= Approximate Ratios* || Solfege || || 0 || 0 ||= 1/1 || do || || 1 || 46.154 13°50'46" ||= [[33_32|33/32]], [[49_48|49/48]], [[36_35|36/35]], [[25_24|25/24]] || di || || 2 || 92.308 27º41'32" ||= [[21_20|21/20]], [[22_21|22/21]], [[26_25|26/25]] || rih || || 3 || 138.46 41°32'18" ||= [[12_11|12/11]], [[13_12|13/12]], [[14_13|14/13]], [[16_15|16/15]] || ru || || 4 || 184.62 55°23'5" ||= [[9_8|9/8]], [[10_9|10/9]], [[11_10|11/10]] || re || || 5 || 230.77 69°13'51" ||= [[8_7|8/7]], 15/13 || ri || || 6 || 276.92 83°4'37" ||= [[7_6|7/6]], [[13_11|13/11]], [[33_28|33/28]] || ma || || 7 || 323.08 96°55'23" ||= [[6_5|6/5]] || me || || 8 || 369.23 110°46'9" ||= [[5_4|5/4]], [[11_9|11/9]], [[16_13|16/13]] || muh/mi || || 9 || 415.38 124°37'55" ||= [[9_7|9/7]], [[14_11|14/11]], [[33_26|33/26]] || maa || || 10 || 461.54 138°27'42" ||= [[21_16|21/16]], [[13_10|13/10]] || fe || || 11 || 507.69 152°18'28" ||= [[4_3|4/3]] || fa || || 12 || 553.85 166°9'14" ||= [[11_8|11/8]], [[18_13|18/13]] || fu || || 13 || 600.00 180° ||= [[7_5|7/5]], [[10_7|10/7]] || fi/se || || 14 || 646.15 193°50'46" ||= [[16_11|16/11]], [[13_9|13/9]] || su || || 15 || 692.31 207°41'32" ||= [[3_2|3/2]] || sol || || 16 || 738.46 221°32'18" ||= [[32_21|32/21]], [[20_13|20/13]] || si || || 17 || 784.62 235°23'5" ||= [[11_7|11/7]], [[14_9|14/9]] || leh || || 18 || 830.77 249°13'51" ||= [[13_8|13/8]], [[8_5|8/5]] || le/lu || || 19 || 876.92 263°4'37" ||= [[5_3|5/3]] || la || || 20 || 923.08 276°55'23" ||= [[12_7|12/7]], [[22_13|22/13]] || li || || 21 || 969.23 290°46'9" ||= [[7_4|7/4]] || ta || || 22 || 1015.4 304°37'55" ||= [[9_5|9/5]], [[16_9|16/9]], [[20_11|20/11]] || te || || 23 || 1061.5 318°46'9" ||= [[11_6|11/6]], [[13_7|13/7]], [[15_8|15/8]], [[24_13|24/13]] || tu/ti || || 24 || 1107.7 332°18'28" ||= [[21_11|21/11]], [[25_13|25/13]], [[40_21|40/21]] || to || || 25 || 1153.8 346°9'14" ||= [[64_33|64/33]], [[96_49|96/49]], [[35_18|35/18]], [[48_25|48/25]] || da || || 26 || 1200 360° ||= 2/1 || do || *based on treating 26-EDO as a 13-limit temperament; other approaches are possible. ==Selected just intervals by error== The following table contains some just intervals (and its octave-complement) intervals ordered by ascending absolute error. || Interval, complement || Error (absolute, in [[cent|cents]] || || 13/12, 24/13 || 0.111 || || 7/4, 8/7 || 0.405 || || 11/7, 14/11 || 2.123 || || 9/5, 10/9 || 2.212 || || 11/8, 16/11 || 2.528 || || 13/10, 20/13 || 7.325 || || 5/3, 6/5 || 7.436 || || 13/9, 18/13 || 9.536 || || 3/2, 4/3 || 9.647 || || 13/8, 16/13 || 9.758 || || 7/6, 12/7 || 10.052 || || 13/7, 14/13 || 10.163 || || 11/6, 12/11 || 12.176 || || 13/11, 22/13 || 12.287 || || 15/11, 22/15 || 16.895 || || 15/13, 26/15 || 16.972 || || 5/4, 8/5 || 17.083 || || 7/5, 10/7 || 17.488 || || 15/14, 28/15 || 19.019 || || 9/8, 16/9 || 19.295 || || 16/15, 15/8 || 19.424 || || 11/10, 20/11 || 19.611 || || 9/7, 14/9 || 19.699 || || 11/9, 18/11 || 21.823 || =Rank two temperaments= [[List of 26et rank two temperaments by badness]] [[List of edo-distinct 26et rank two temperaments]] ||~ Periods per octave ||~ Generator ||~ Temperaments || || 1 || 1\26 || [[Quartonic]]/Quarto || || 1 || 3\26 || [[Jerome]]/[[Chromatic pairs|Bleu]]/Secund || || 1 || 5\26 || [[Cynder]]/[[Mothra]] || || 1 || 7\26 || [[Superkleismic]]/[[Orgone]]/[[Shibboleth]] || || 1 || 9\26 || [[Roman]]/Wesley || || 1 || 11\26 || [[Meantone]]/[[Flattone]] || || 2 || 1\26 || Elvis || || 2 || 2\26 || [[Injera]] || || 2 || 3\26 || [[Fifive]]/Crepuscular || || 2 || 4\26 || [[Unidec]]/[[Gamelismic clan#Unidec-Hendec|Hendec]]/Dubbla || || 2 || 5\26 || [[Lemba]] || || 2 || 6\26 || [[Doublewide]]/Cavalier || || 13 || 1\26 || Triskaidekic || ==Hendec in 26et== [[Gamelismic clan#Unidec-Hendec|Hendec]], the 13-limit 26&46 temperament with generator ~10/9, concentrates the intervals of greatest accuracy in 26et into the lower ranges of complexity. It has a period of half an octave, with 13/12 reachable by four generators, 8/7 by two, 14/11 by one, 10/9 by one, and 11/8 by three. All of these are tuned to within 2.5 cents of accuracy. =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 ||= ||= || ||= 105/104 ||< | -3 1 1 1 0 -1 > ||> 16.567 ||= Animist ||= ||= || ||= 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]] =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= <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20A%20Time-Yellowed%20Photograph%20of%20Cliffs%20Hangs%20in%20the%20Hall.mp3|A Time-Yellowed Photo of the Cliffs Hangs on the Wall ]]</span> by [[IgliashonJones|Igliashon Jones]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3|Two Pairs of Socks]]</span> by [[IgliashonJones|Igliashon Jones]] [[http://www.io.com/%7Ehmiller/midi/26tet.mid|Etude in 26-tone equal temperament]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/26tet.mp3|play]]</span> by [[Herman Miller]] [[http://archive.org/details/UnderTheHeatdome|under the heatDome]] [[http://archive.org/download/UnderTheHeatdome/under_the_heatDome.mp3|play]] by [[Jon Lyle Smith]] [[http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html|A New Recording of Organ Study #1]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.microtonalmusic.net/audio/organstudyremix26edo.mp3|play]]</span> by [[Daniel Thompson]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/LittleFugueIn26_CBobro.mp3|Little Fugue in 26]]</span> by [[Cameron Bobro]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/26-tone-fugue.mp3|26 tone fugue (unfinished)]]</span> by Peter Kosmorsky (based on the melody he was singing in the shower, in orgone, to the presumed confusion of those in earshot) <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.96edo.com/music/micro900607.mp3|Microtonal music in 26-EDO]]</span> by [[Shaahin Mohajeri]] [[media type="custom" key="11317210"]]<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Chiapas%20Palenque.mp3|Chiapas Palenque]]</span> by [[Zach Curley]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3|Injera Jam]]</span> by [[Zach Curley]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Guitar%20Serenade%20in%20Q%20Major.mp3|Guitar Serenade in Q Major]] by [[Zach Curley]] [[http://midiguru.wordpress.com/2013/01/06/public-rituals/|Public Rituals « Jim Aikin's Oblong Blob]] “The Triumphal Procession of Nebuchadnezzar“
Original HTML content:
<html><head><title>26edo</title></head><body><!-- ws:start:WikiTextTocRule:21:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><div style="margin-left: 1em;"><a href="#Structure">Structure</a></div>
<!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div>
<!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 2em;"><a href="#Intervals-Selected just intervals by error">Selected just intervals by error</a></div>
<!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 1em;"><a href="#Rank two temperaments">Rank two temperaments</a></div>
<!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 2em;"><a href="#Rank two temperaments-Hendec in 26et">Hendec in 26et</a></div>
<!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 1em;"><a href="#Commas">Commas</a></div>
<!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 1em;"><a href="#Orgone Temperament">Orgone Temperament</a></div>
<!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 1em;"><a href="#Additional Scalar Bases Available in 26-EDO:">Additional Scalar Bases Available in 26-EDO:</a></div>
<!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 1em;"><a href="#Literature">Literature</a></div>
<!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 1em;"><a href="#Compositions">Compositions</a></div>
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --></div>
<!-- ws:end:WikiTextTocRule:32 --><em>26edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 26 equal parts of 46.154 <a class="wiki_link" href="/cent">cent</a>s each. It tempers out 81/80 in the <a class="wiki_link" href="/5-limit">5-limit</a>, making it a meantone tuning with a very flat fifth. In the <a class="wiki_link" href="/7-limit">7-limit</a>, it tempers out 50/49, 525/512 and 875/864, and supports <a class="wiki_link" href="/Meantone%20family">injera</a>, <a class="wiki_link" href="/Meantone%20family">flattone</a>, <a class="wiki_link" href="/Jubilismic%20clan#Lemba">lemba</a> and <a class="wiki_link" href="/Jubilismic%20clan#Doublewide">doublewide</a> temperaments. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the <a class="wiki_link" href="/13-limit">13 odd limit</a> <a class="wiki_link" href="/consistent">consistently</a>. 26edo has a very good approximation of the harmonic seventh (<a class="wiki_link" href="/7_4">7/4</a>).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:1:<h1> --><h1 id="toc0"><a name="Structure"></a><!-- ws:end:WikiTextHeadingRule:1 --><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&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 />
4. We can also treat 26-EDO as a full 13-limit temperament, since it is consistent on the 13-limit (unlike all lower EDOs).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:3:<h1> --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:3 --><span style="font-size: 1.4em;">Intervals</span></h1>
<table class="wiki_table">
<tr>
<td>degree<br />
</td>
<td><a class="wiki_link" href="/cent">cent</a>s<br />
DMS<br />
</td>
<td style="text-align: center;">Approximate<br />
Ratios*<br />
</td>
<td>Solfege<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td style="text-align: center;">1/1<br />
</td>
<td>do<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>46.154<br />
13°50'46"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/33_32">33/32</a>, <a class="wiki_link" href="/49_48">49/48</a>, <a class="wiki_link" href="/36_35">36/35</a>, <a class="wiki_link" href="/25_24">25/24</a><br />
</td>
<td>di<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>92.308<br />
27º41'32"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/21_20">21/20</a>, <a class="wiki_link" href="/22_21">22/21</a>, <a class="wiki_link" href="/26_25">26/25</a><br />
</td>
<td>rih<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>138.46<br />
41°32'18"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/12_11">12/11</a>, <a class="wiki_link" href="/13_12">13/12</a>, <a class="wiki_link" href="/14_13">14/13</a>, <a class="wiki_link" href="/16_15">16/15</a><br />
</td>
<td>ru<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>184.62<br />
55°23'5"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, <a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/11_10">11/10</a><br />
</td>
<td>re<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>230.77<br />
69°13'51"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/8_7">8/7</a>, 15/13<br />
</td>
<td>ri<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>276.92<br />
83°4'37"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/13_11">13/11</a>, <a class="wiki_link" href="/33_28">33/28</a><br />
</td>
<td>ma<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>323.08<br />
96°55'23"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/6_5">6/5</a><br />
</td>
<td>me<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>369.23<br />
110°46'9"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/11_9">11/9</a>, <a class="wiki_link" href="/16_13">16/13</a><br />
</td>
<td>muh/mi<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>415.38<br />
124°37'55"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/33_26">33/26</a><br />
</td>
<td>maa<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>461.54<br />
138°27'42"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/21_16">21/16</a>, <a class="wiki_link" href="/13_10">13/10</a><br />
</td>
<td>fe<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>507.69<br />
152°18'28"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a><br />
</td>
<td>fa<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>553.85<br />
166°9'14"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, <a class="wiki_link" href="/18_13">18/13</a><br />
</td>
<td>fu<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>600.00<br />
180°<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/7_5">7/5</a>, <a class="wiki_link" href="/10_7">10/7</a><br />
</td>
<td>fi/se<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>646.15<br />
193°50'46"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/16_11">16/11</a>, <a class="wiki_link" href="/13_9">13/9</a><br />
</td>
<td>su<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>692.31<br />
207°41'32"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/3_2">3/2</a><br />
</td>
<td>sol<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>738.46<br />
221°32'18"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/32_21">32/21</a>, <a class="wiki_link" href="/20_13">20/13</a><br />
</td>
<td>si<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>784.62<br />
235°23'5"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/11_7">11/7</a>, <a class="wiki_link" href="/14_9">14/9</a><br />
</td>
<td>leh<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>830.77<br />
249°13'51"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/13_8">13/8</a>, <a class="wiki_link" href="/8_5">8/5</a><br />
</td>
<td>le/lu<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>876.92<br />
263°4'37"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/5_3">5/3</a><br />
</td>
<td>la<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>923.08<br />
276°55'23"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/12_7">12/7</a>, <a class="wiki_link" href="/22_13">22/13</a><br />
</td>
<td>li<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>969.23<br />
290°46'9"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/7_4">7/4</a><br />
</td>
<td>ta<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>1015.4<br />
304°37'55"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/9_5">9/5</a>, <a class="wiki_link" href="/16_9">16/9</a>, <a class="wiki_link" href="/20_11">20/11</a><br />
</td>
<td>te<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>1061.5<br />
318°46'9"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/11_6">11/6</a>, <a class="wiki_link" href="/13_7">13/7</a>, <a class="wiki_link" href="/15_8">15/8</a>, <a class="wiki_link" href="/24_13">24/13</a><br />
</td>
<td>tu/ti<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>1107.7<br />
332°18'28"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/21_11">21/11</a>, <a class="wiki_link" href="/25_13">25/13</a>, <a class="wiki_link" href="/40_21">40/21</a><br />
</td>
<td>to<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>1153.8<br />
346°9'14"<br />
</td>
<td style="text-align: center;"><a class="wiki_link" href="/64_33">64/33</a>, <a class="wiki_link" href="/96_49">96/49</a>, <a class="wiki_link" href="/35_18">35/18</a>, <a class="wiki_link" href="/48_25">48/25</a><br />
</td>
<td>da<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1200<br />
360°<br />
</td>
<td style="text-align: center;">2/1<br />
</td>
<td>do<br />
</td>
</tr>
</table>
*based on treating 26-EDO as a 13-limit temperament; other approaches are possible.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:5:<h2> --><h2 id="toc2"><a name="Intervals-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:5 -->Selected just intervals by error</h2>
The following table contains some just intervals (and its octave-complement) intervals ordered by ascending absolute error.<br />
<table class="wiki_table">
<tr>
<td>Interval, complement<br />
</td>
<td>Error (absolute, in <a class="wiki_link" href="/cent">cents</a><br />
</td>
</tr>
<tr>
<td>13/12, 24/13<br />
</td>
<td>0.111<br />
</td>
</tr>
<tr>
<td>7/4, 8/7<br />
</td>
<td>0.405<br />
</td>
</tr>
<tr>
<td>11/7, 14/11<br />
</td>
<td>2.123<br />
</td>
</tr>
<tr>
<td>9/5, 10/9<br />
</td>
<td>2.212<br />
</td>
</tr>
<tr>
<td>11/8, 16/11<br />
</td>
<td>2.528<br />
</td>
</tr>
<tr>
<td>13/10, 20/13<br />
</td>
<td>7.325<br />
</td>
</tr>
<tr>
<td>5/3, 6/5<br />
</td>
<td>7.436<br />
</td>
</tr>
<tr>
<td>13/9, 18/13<br />
</td>
<td>9.536<br />
</td>
</tr>
<tr>
<td>3/2, 4/3<br />
</td>
<td>9.647<br />
</td>
</tr>
<tr>
<td>13/8, 16/13<br />
</td>
<td>9.758<br />
</td>
</tr>
<tr>
<td>7/6, 12/7<br />
</td>
<td>10.052<br />
</td>
</tr>
<tr>
<td>13/7, 14/13<br />
</td>
<td>10.163<br />
</td>
</tr>
<tr>
<td>11/6, 12/11<br />
</td>
<td>12.176<br />
</td>
</tr>
<tr>
<td>13/11, 22/13<br />
</td>
<td>12.287<br />
</td>
</tr>
<tr>
<td>15/11, 22/15<br />
</td>
<td>16.895<br />
</td>
</tr>
<tr>
<td>15/13, 26/15<br />
</td>
<td>16.972<br />
</td>
</tr>
<tr>
<td>5/4, 8/5<br />
</td>
<td>17.083<br />
</td>
</tr>
<tr>
<td>7/5, 10/7<br />
</td>
<td>17.488<br />
</td>
</tr>
<tr>
<td>15/14, 28/15<br />
</td>
<td>19.019<br />
</td>
</tr>
<tr>
<td>9/8, 16/9<br />
</td>
<td>19.295<br />
</td>
</tr>
<tr>
<td>16/15, 15/8<br />
</td>
<td>19.424<br />
</td>
</tr>
<tr>
<td>11/10, 20/11<br />
</td>
<td>19.611<br />
</td>
</tr>
<tr>
<td>9/7, 14/9<br />
</td>
<td>19.699<br />
</td>
</tr>
<tr>
<td>11/9, 18/11<br />
</td>
<td>21.823<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:7:<h1> --><h1 id="toc3"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:7 -->Rank two temperaments</h1>
<a class="wiki_link" href="/List%20of%2026et%20rank%20two%20temperaments%20by%20badness">List of 26et rank two temperaments by badness</a><br />
<a class="wiki_link" href="/List%20of%20edo-distinct%2026et%20rank%20two%20temperaments">List of edo-distinct 26et rank two temperaments</a><br />
<table class="wiki_table">
<tr>
<th>Periods<br />
per octave<br />
</th>
<th>Generator<br />
</th>
<th>Temperaments<br />
</th>
</tr>
<tr>
<td>1<br />
</td>
<td>1\26<br />
</td>
<td><a class="wiki_link" href="/Quartonic">Quartonic</a>/Quarto<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>3\26<br />
</td>
<td><a class="wiki_link" href="/Jerome">Jerome</a>/<a class="wiki_link" href="/Chromatic%20pairs">Bleu</a>/Secund<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>5\26<br />
</td>
<td><a class="wiki_link" href="/Cynder">Cynder</a>/<a class="wiki_link" href="/Mothra">Mothra</a><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>7\26<br />
</td>
<td><a class="wiki_link" href="/Superkleismic">Superkleismic</a>/<a class="wiki_link" href="/Orgone">Orgone</a>/<a class="wiki_link" href="/Shibboleth">Shibboleth</a><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>9\26<br />
</td>
<td><a class="wiki_link" href="/Roman">Roman</a>/Wesley<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>11\26<br />
</td>
<td><a class="wiki_link" href="/Meantone">Meantone</a>/<a class="wiki_link" href="/Flattone">Flattone</a><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>1\26<br />
</td>
<td>Elvis<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>2\26<br />
</td>
<td><a class="wiki_link" href="/Injera">Injera</a><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>3\26<br />
</td>
<td><a class="wiki_link" href="/Fifive">Fifive</a>/Crepuscular<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>4\26<br />
</td>
<td><a class="wiki_link" href="/Unidec">Unidec</a>/<a class="wiki_link" href="/Gamelismic%20clan#Unidec-Hendec">Hendec</a>/Dubbla<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>5\26<br />
</td>
<td><a class="wiki_link" href="/Lemba">Lemba</a><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>6\26<br />
</td>
<td><a class="wiki_link" href="/Doublewide">Doublewide</a>/Cavalier<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>1\26<br />
</td>
<td>Triskaidekic<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:9:<h2> --><h2 id="toc4"><a name="Rank two temperaments-Hendec in 26et"></a><!-- ws:end:WikiTextHeadingRule:9 -->Hendec in 26et</h2>
<a class="wiki_link" href="/Gamelismic%20clan#Unidec-Hendec">Hendec</a>, the 13-limit 26&46 temperament with generator ~10/9, concentrates the intervals of greatest accuracy in 26et into the lower ranges of complexity. It has a period of half an octave, with 13/12 reachable by four generators, 8/7 by two, 14/11 by one, 10/9 by one, and 11/8 by three. All of these are tuned to within 2.5 cents of accuracy.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:11:<h1> --><h1 id="toc5"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1>
26et tempers out the following commas. (Note: This assumes the val < 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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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;">105/104<br />
</td>
<td style="text-align: left;">| -3 1 1 1 0 -1 ><br />
</td>
<td style="text-align: right;">16.567<br />
</td>
<td style="text-align: center;">Animist<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 ><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 ><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 ><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 ><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 ><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:13:<h1> --><h1 id="toc6"><a name="Orgone Temperament"></a><!-- ws:end:WikiTextHeadingRule:13 --><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:1069:<img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="" title="" /> --><img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="orgone_heptatonic.jpg" title="orgone_heptatonic.jpg" /><!-- ws:end:WikiTextLocalImageRule:1069 --><br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:15:<h1> --><h1 id="toc7"><a name="Additional Scalar Bases Available in 26-EDO:"></a><!-- ws:end:WikiTextHeadingRule:15 -->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:17:<h1> --><h1 id="toc8"><a name="Literature"></a><!-- ws:end:WikiTextHeadingRule:17 -->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:19:<h1> --><h1 id="toc9"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:19 -->Compositions</h1>
<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20A%20Time-Yellowed%20Photograph%20of%20Cliffs%20Hangs%20in%20the%20Hall.mp3" rel="nofollow">A Time-Yellowed Photo of the Cliffs Hangs on the Wall </a></span> by <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3" rel="nofollow">Two Pairs of Socks</a></span> 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 temperament</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/26tet.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br />
<a class="wiki_link_ext" href="http://archive.org/details/UnderTheHeatdome" rel="nofollow">under the heatDome</a> <a class="wiki_link_ext" href="http://archive.org/download/UnderTheHeatdome/under_the_heatDome.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Jon%20Lyle%20Smith">Jon Lyle Smith</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> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/organstudyremix26edo.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Daniel%20Thompson">Daniel Thompson</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/LittleFugueIn26_CBobro.mp3" rel="nofollow">Little Fugue in 26</a></span> by <a class="wiki_link" href="/Cameron%20Bobro">Cameron Bobro</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/26-tone-fugue.mp3" rel="nofollow">26 tone fugue (unfinished)</a></span> by Peter Kosmorsky (based on the melody he was singing in the shower, in orgone, to the presumed confusion of those in earshot)<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.96edo.com/music/micro900607.mp3" rel="nofollow">Microtonal music in 26-EDO</a></span> by <a class="wiki_link" href="/Shaahin%20Mohajeri">Shaahin Mohajeri</a><br />
<!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/custom/11317210?h=0&w=0" class="WikiMedia WikiMediaCustom" id="wikitext@@media@@type=&quot;custom&quot; key=&quot;11317210&quot;" title="Custom Media"/> --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js">
</script><!-- ws:end:WikiTextMediaRule:0 --><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Chiapas%20Palenque.mp3" rel="nofollow">Chiapas Palenque</a></span> by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3" rel="nofollow">Injera Jam</a></span> by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Guitar%20Serenade%20in%20Q%20Major.mp3" rel="nofollow">Guitar Serenade in Q Major</a> by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br />
<a class="wiki_link_ext" href="http://midiguru.wordpress.com/2013/01/06/public-rituals/" rel="nofollow">Public Rituals « Jim Aikin's Oblong Blob</a> “The Triumphal Procession of Nebuchadnezzar“</body></html>