39edo: Difference between revisions

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=<span style="color: #9900ab; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span>= 

**39-EDO, 39-ED2** or **39-tET** divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of [[xenharmonic/7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, suited in [[xenharmonic/16edo|16-ED2]], and allied systems: [[xenharmonic/25edo|25-ED2]] [1/3-tone 3;2]; [[xenharmonic/41edo|41-ED2]] [1/5-tone 5;3]; and [[xenharmonic/57edo|57]] ED2 [1/7-tone 7;4]. **Hornbostel Temperaments** is included too with: [[xenharmonic/23edo|23-ED2]] [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] & [[xenharmonic/62edo|62-ED2]] [1/8-tone 8;3]. [[223edo|223-ED2]], the best accuracy for Hornbostel temperament fits very good with Armodue like 1/29-tone 29;10 version. Note that [[101edo|101]], [[131edo|131]], [[177edo|177]] & [[200edo|200]] ED2s are tempered systems that [[http://www.h-pi.com/eop-ogolevets.html|Alexei Ogolevets]] (Ukraine, 1891 - 1967) was proposing in his List of Temperaments, in which the Armodue system fits very well in all these.
However, its 23\39 fifth, 5.737 Cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 Cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, [[tel:1600000/1594323|1600000/1594323]]. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO, in some few ways, allied to 12-ET in supporting augene temperament, and is in fact, an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is <[[tel:39 62 91 110|39 62 91 110]] 135|.
A particular anecdote with this 39 divisions per 2/1 was made in the Teliochordon, in 1788 by Charles Clagget (Ireland, 1740? - 1820), a little extract [[http://ml.oxfordjournals.org/content/76/2/291.extract.jpg|here]].

As a superpyth system, 39edo is intermediate between 17edo and 22edo (39 being 17+22). While 17edo is superb for melody (as documented by George Secor), it doesn't approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the "diatonic semitone" is quarter-tone-sized, which results in a very strange-sounding diatonic scale. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents (the ideal diatonic semitone for melody being somewhere in between 60 and 80 cents, by Secor's estimates).

39edo offers not one, but many, possible ways of extending tonality beyond the diatonic scale, even if it doesn't do as good of a job at approximating JI as some other systems do. Because it can also approximate mavila as well as "anti-mavila" (oneirotonic), the latter of which it inherits from [[13edo]], this makes 39edo an extremely versatile temperament usable in a wide range of situations (both harmonic and inharmonic).


==__**39-EDO Intervals**__== 
|| **ARMODUE NOMENCLATURE 5;2 RELATION** ||
|| * **‡** = Semisharp (1/5-tone up)
* **b** = Flat (3/5-tone down)
* **#** = Sharp (3/5-tone up)
* **v** = Semiflat (1/5-tone down) ||

||~ **Degrees** ||~ **Armodue note** ||~ **Cents size** ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming
<[[tel:39 62 91 110|39 62 91 110]] 135| [[Val]] ||
|| 0 || 1 || 0 || 1/1 || 0 || None || 1/1 ||
|| 1 || 1‡ (9#) || 30.7692 || 57/56 || 30.6421 || +0.1271 ||   ||
|| 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 ||   ||
|| 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 ||   ||
|| 4 || 2v || [[tel:123.0769|123.0769]] || 44/41 || [[tel:122.2555|122.2555]] || +0.8214 ||   ||
|| 5 || 2 || [[tel:153.8462|153.8462]] || 35/32 || [[tel:155.1396|155.1396]] || -1.2934 || 12/11, 11/10 ||
|| 6 || 2‡ || [[tel:184.6154|184.6154]] || 10/9 || [[tel:182.4037|182.4037]] || +2.2117 || 10/9 ||
|| 7**·** || 3b || [[tel:215.3846|215.3846]] || 17/15 || [[tel:216.6867|216.6867]] || -1.3021 || 8/7, 9/8 ||
|| 8 || 2# || [[tel:246.1538|246.1538]] || 15/13 || [[tel:247.7411|247.7411]] || -1.5873 ||   ||
|| 9 || 3v || [[tel:276.9231|276.9231]] || 27/23 || [[tel:277.5907|277.5907]] || -0.6676 || 7/6 ||
|| 10 || 3 || [[tel:307.6923|307.6923]] || 43/36 || [[tel:307.6077|307.6077]] || +0.0846 || 6/5 ||
|| 11 || 3‡ || [[tel:338.4615|338.4615]] || 17/14 || [[tel:336.1295|336.1295]] || +2.332 || 11/9 ||
|| 12**·** || 4b || [[tel:369.2308|369.2308]] || 26/21 || [[tel:369.7468|369.7468]] || -0.516 ||   ||
|| 13 || 3# || 400 || 34/27 || [[tel:399.0904|399.0904]] || +0.9096 || 5/4 ||
|| 14 || 4v (5b) || [[tel:430.7692|430.7692]] || 41/32 || [[tel:429.0624|429.0624]] || +1.7068 || 9/7, 14/11 ||
|| 15 || 4 || [[tel:461.5385|461.5385]] || 30/23 || [[tel:459.9944|459.9944]] || +1.5441 ||   ||
|| 16 || 4‡ (5v) || [[tel:492.3077|492.3077]] || 85/64 || [[tel:491.2691|491.2691]] || +1.0386 || 4/3 ||
|| 17**·** || 5 || [[tel:523.0769|523.0769]] || 23/17 || [[tel:523.3189|523.3189]] || -0.242 ||   ||
|| 18 || 5‡ (4#) || [[tel:553.8462|553.8462]] || 11/8 || [[tel:551.3179|551.3179]] || +2.5283 || 11/8 ||
|| 19 || 6b || [[tel:584.6154|584.6154]] || 7/5 || [[tel:582.5122|582.5122]] || +2.1032 || 7/5 ||
|| 20 || 5# || [[tel:615.3846|615.3846]] || 10/7 || [[tel:617.4878|617.4878]] || -2.1032 || 10/7 ||
|| 21 || 6v || [[tel:646.1538|646.1538]] || 16/11 || [[tel:648.6821|648.6821]] || -2.5283 || 16/11 ||
|| 22**·** || 6 || [[tel:676.9231|676.9231]] || 34/23 || [[tel:676.6811|676.6811]] || +0.242 ||   ||
|| 23 || 6‡ || [[tel:707.6923|707.6923]] || 128/85 || [[tel:708.7309|708.7309]] || -1.0386 || 3/2 ||
|| 24 || 7b || [[tel:738.4615|738.4615]] || 23/15 || [[tel:740.0056|740.0056]] || -1.5441 ||   ||
|| 25 || 6# || [[tel:769.2308|769.2308]] || 64/41 || [[tel:770.9376|770.9376]] || -1.7068 || 14/9, 11/7 ||
|| 26 || 7v || 800 || 27/17 || [[tel:800.9096|800.9096]] || -0.9096 || 8/5 ||
|| 27**·** || 7 || [[tel:830.7692|830.7692]] || 21/13 || [[tel:830.2532|830.2532]] || +0.516 ||   ||
|| 28 || 7‡ || [[tel:861.5385|861.5385]] || 28/17 || [[tel:863.8705|863.8705]] || -2.332 || 18/11 ||
|| 29 || 8b || [[tel:892.3077|892.3077]] || 72/43 || [[tel:892.3923|892.3923]] || -0.0846 || 5/3 ||
|| 30 || 7# || [[tel:923.0769|923.0769]] || 46/27 || [[tel:922.4093|922.4093]] || +0.6676 || 12/7 ||
|| 31 || 8v || [[tel:953.8462|953.8462]] || 26/15 || [[tel:952.2589|952.2589]] || +1.5873 ||   ||
|| 32**·** || 8 || [[tel:984.6154|984.6154]] || 30/17 || [[tel:983.3133|983.3133]] || +1.3021 || 7/4, 16/9 ||
|| 33 || 8‡ || 1015.3846 || 9/5 || 1017.5963 || -2.2117 || 9/5 ||
|| 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||
|| 35 || 8# || 1076.9231 || 41/22 || 1077.7445 || -0.8214 ||   ||
|| 36 || 9v (1b) || 1107.6923 || 74/39 || 1108.8614 || -1.1691 ||   ||
|| 37 || 9 || 1138.4615 || 56/29 || 1139.2487 || -0.7872 ||   ||
|| 38 || 9‡ (1v) || 1169.2308 || 112/57 || 1169.3579 || -0.1271 ||   ||
|| 39**··**(or 0) || 1 || 1200 || 2/1 || 1200 || None ||   ||

==__Instruments (prototypes):__== 

[[image:TECLADO 39-EDD.PNG width="800" height="467"]]
//An illustrative image of a 39-ED2 keyboard//
[[image:xenharmonic/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png width="826" height="203" caption="39-EDD fretboard visualization"]]


==**__39 tone equal [[xenharmonic/modes|modes]]__:**== 

14 14 11 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/2L 1s|2L 1s]]
[[tel:11 11 11 6|11 11 11 6]] - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/3L 1s|3L 1s]]
[[tel:10 10 10 9|10 10 10 9]] - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/3L 1s|3L 1s]]
[[tel:11 3 11 11 3|11 3 11 11 3]] - [[xenharmonic/MOSScales|MOS]] of type [[3L 2s|3L 2s (Father pentatonic)]]
5 12 5 5 12 - [[xenharmonic/MOSScales|MOS]] of type 2L 3s (Mavila pentatonic)
7 7 9 7 9 - [[xenharmonic/MOSScales|MOS]] of type 2L 3s (Superpythagorean pentatonic)
8 8 8 8 7 - [[xenharmonic/MOSScales|MOS]] of type [[4L 1s|4L 1s (Bug pentatonic)]]
[[tel:10 3 10 3 10 3|10 3 10 3 10 3]] - [[xenharmonic/MOSScales|MOS]] of type [[3L 3s|3L 3s (Augmented hexatonic)]]
9 4 9 4 9 4 - [[xenharmonic/MOSScales|MOS]] of type [[3L 3s|3L 3s (Augmented hexatonic)]]
8 5 8 5 8 5 - [[xenharmonic/MOSScales|MOS]] of type [[3L 3s|3L 3s (Augmented hexatonic)]]
7 7 7 7 7 4 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/5L 1s|5L 1s (Grumpy hexatonic)]]
5 5 7 5 5 5 7 - [[xenharmonic/MOSScales|MOS]] of type [[2L 5s|2L 5s (heptatonic Mavila Anti-Diatonic)]]
7 7 7 2 7 7 2 - [[xenharmonic/MOSScales|MOS]] of type 5L 2s (heptatonic Superpythagorean diatonic)
5 5 5 5 5 5 5 4 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/7L 1s|7L 1s (Grumpy octatonic)]]
**5 5 5 2 5 5 5 5 2** - [[xenharmonic/MOSScales|MOS]] of type [[7L 2s|7L 2s (nonatonic Mavila Superdiatonic)]]
5 5 3 5 5 3 5 5 3 - [[xenharmonic/MOSScales|MOS]] of type [[6L 3s|6L 3s (unfair Augmented nonatonic)]]
5 4 4 5 4 4 5 4 4 - [[xenharmonic/MOSScales|MOS]] of type [[3L 6s|3L 6s (fair Augmented nonatonic)]]
4 4 4 4 4 4 4 4 4 3 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/9L 1s|9L 1s (Grumpy decatonic)]]
**3 3 5 3 3 3 5 3 3 3 5** - [[xenharmonic/MOSScales|MOS]] of type [[3L 8s|3L 8s (Anti-Sensi hendecatonic)]]
2 5 2 2 5 2 5 2 5 2 2 5 - [[xenharmonic/MOSScales|MOS]] of type 5L 7s
**3 3 3 4 3 3 3 4 3 3 3 4 -** [[xenharmonic/MOSScales|MOS]] of type 3L 9s
**3 3 3 2 3 3 3 3 2 3 3 3 3 2** - [[xenharmonic/MOSScales|MOS]] of type [[11L 3s|11L 3s (Ketradektriatoh tetradecatonic)]]
3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/9L 6s|9L 6s]]
3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/7L 9s|7L 9s]]
**2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3** - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/5L 12s|5L 12s]]
2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/3L 15s|3L 15s]]
**3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3** - <span style="cursor: pointer;">[[xenharmonic/MOSScales|MOS]]</span> of type [[xenharmonic/10L 9s|10L 9s]]
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/19L 1s|19L 1s]]
2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/17L 5s|17L 5s]]
**2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1** - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/16L 7s|16L 7s]]
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/13L 13s|13L 13s]]
**2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/10L 19s|10L 19s]]
2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/8L 23s|8L 23s]]

==**__39edo and world music:__**== 

39edo is a good candidate for a "universal tuning" in that it offers reasonable approximations of many different world music traditions; it is one of the simplest edos that can make this claim. Because of this, composers wishing to combine multiple world music traditions (for example, gamelan with maqam singing) within one unified framework would find 39edo an interesting possibility.

===Western:=== 

39edo offers not one, but several different ways to realize the traditional Western diatonic scale. One way is to simply take a chain of fifths (the diatonic MOS: **7 7 2 7 7 7 2**). Because 39edo is a superpyth rather than a meantone system, this means that the harmonic quality of its diatonic scale will differ somewhat, since "minor" and "major" triads now approximate 6:7:9 and 14:18:21 respectively, rather than 10:12:15 and 4:5:6 as in meantone diatonic systems. Diatonic compositions translated onto this scale thus acquire a wildly different harmonic character, albeit still very pleasing.

Another option is to use a MODMOS, such as **7 6 3 7 6 7 3**; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, the wolf fifth can be avoided by introducing accidental notes when necessary. There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in //many// different ways, acquiring a distinctly different but still harmonious character each time.

The MOS and the MODMOS's all have smaller-than-usual semitones, which makes them more effective for melody than their counterparts in 12edo or meantone systems.

Because 39edo and 12edo both have an overall sharp character and share the same major third, they have a relatively similar sound. Thus, 39edo (unlike, say, 22edo or 19edo, which are both "acquired tastes") does not sound all that xenharmonic to people used to 12edo. Check out [[https://www.prismnet.com/~hmiller/midi/canon39.mid|Pachelbel's Canon in 39edo]] (using the **7 6 3 7 6 7 3** MODMOS), for example.

===**Indian:**=== 

A similar situation arises with Indian music since the sruti system, like the Western system, also has multiple possible mappings in 39edo. Many of these are modified versions of the 17L 5s MOS (where the generator is a perfect fifth).

===**[[Arabic, Turkish, Persian]]:**=== 

While middle-eastern music is commonly approximated using 24edo, 39edo offers a potentially better alternative. 17edo and 24edo both satisfy the "Level 1" requirements for maqam tuning sytems. 39edo is a Level 2 system because:

* It has two types of "neutral" seconds (154 and 185 cents)
* It has two minor seconds (92 and 123 cents), which when added together give a whole tone (215 cents)

whereas neither 17edo nor 24edo satisfy these properties.

39edo will likely be more suited to some middle-eastern scales than others. Specifically, Turkish music (in which the Rast makam has a "major-like" wide neutral third and a wide "neutral" second approaching 10/9), will likely be especially well suited to 39edo.

===**Blues / Jazz / African-American:**=== 

The harmonic seventh ("barbershop seventh") tetrad is reasonably well approximated in 39edo, and some temperaments (augene in particular) give scales that are liberally supplied with them. John Coltrane [[https://en.wikipedia.org/wiki/Coltrane_changes|would have loved augene]].

Tritone substitution, which is a major part of jazz and blues harmony, is more complicated in 39edo because there are two types of tritones. Therefore the tritone substitution of one seventh chord will need to be a different type of seventh chord. However, this also opens new possibilities; if the substituted chord is of a more consonant type than the original, then the tritone substitution may function as a //resolution// rather than a suspension.

Blue notes, rather than being considered inflections, can be notated as accidentals instead; for example, a "blue major third" can be identified as either of the two neutral thirds. There are two possible mappings for 7:4 which are about equal in closeness. The sharp mapping is the normal one because it works better with the 5:4 and 3:2, but using the flat one instead (as an accidental) allows for another type of blue note.

===Other:=== 

39edo offers a good approximation of pelog / mavila using the flat fifth as a generator.

It also offers //many// possible pentatonic scales, including the 2L+3S MOS (which is **9 7 7 9 7**). Slendro can be approximated using this scale or using something like the quasi-equal **8 8 8 8 7**. A more expressive pentatonic scale is the oneirotonic subset **9 6 9 9 6**. Many Asian and African musical styles can thus be accomodated.

Original HTML content:

<html><head><title>39edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x39 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #9900ab; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span></h1>
 <br />
<strong>39-EDO, 39-ED2</strong> or <strong>39-tET</strong> divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%202s">Superdiatonic</a> LLLsLLLLs like a basical scale for notation and theory, suited in <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16edo">16-ED2</a>, and allied systems: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/25edo">25-ED2</a> [1/3-tone 3;2]; <a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo">41-ED2</a> [1/5-tone 5;3]; and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/57edo">57</a> ED2 [1/7-tone 7;4]. <strong>Hornbostel Temperaments</strong> is included too with: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/23edo">23-ED2</a> [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] &amp; <a class="wiki_link" href="http://xenharmonic.wikispaces.com/62edo">62-ED2</a> [1/8-tone 8;3]. <a class="wiki_link" href="/223edo">223-ED2</a>, the best accuracy for Hornbostel temperament fits very good with Armodue like 1/29-tone 29;10 version. Note that <a class="wiki_link" href="/101edo">101</a>, <a class="wiki_link" href="/131edo">131</a>, <a class="wiki_link" href="/177edo">177</a> &amp; <a class="wiki_link" href="/200edo">200</a> ED2s are tempered systems that <a class="wiki_link_ext" href="http://www.h-pi.com/eop-ogolevets.html" rel="nofollow">Alexei Ogolevets</a> (Ukraine, 1891 - 1967) was proposing in his List of Temperaments, in which the Armodue system fits very well in all these.<br />
However, its 23\39 fifth, 5.737 Cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 Cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, [[tel:1600000/1594323|1600000/1594323]]. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO, in some few ways, allied to 12-ET in supporting augene temperament, and is in fact, an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;<a class="wiki_link" href="http://tel.wikispaces.com/39%2062%2091%20110">39 62 91 110</a> 135|.<br />
A particular anecdote with this 39 divisions per 2/1 was made in the Teliochordon, in 1788 by Charles Clagget (Ireland, 1740? - 1820), a little extract <a class="wiki_link_ext" href="http://ml.oxfordjournals.org/content/76/2/291.extract.jpg" rel="nofollow">here</a>.<br />
<br />
As a superpyth system, 39edo is intermediate between 17edo and 22edo (39 being 17+22). While 17edo is superb for melody (as documented by George Secor), it doesn't approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the &quot;diatonic semitone&quot; is quarter-tone-sized, which results in a very strange-sounding diatonic scale. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents (the ideal diatonic semitone for melody being somewhere in between 60 and 80 cents, by Secor's estimates).<br />
<br />
39edo offers not one, but many, possible ways of extending tonality beyond the diatonic scale, even if it doesn't do as good of a job at approximating JI as some other systems do. Because it can also approximate mavila as well as &quot;anti-mavila&quot; (oneirotonic), the latter of which it inherits from <a class="wiki_link" href="/13edo">13edo</a>, this makes 39edo an extremely versatile temperament usable in a wide range of situations (both harmonic and inharmonic).<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x39 tone equal temperament-39-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><u><strong>39-EDO Intervals</strong></u></h2>
 

<table class="wiki_table">
    <tr>
        <td><strong>ARMODUE NOMENCLATURE 5;2 RELATION</strong><br />
</td>
    </tr>
    <tr>
        <td><ul><li><strong>‡</strong> = Semisharp (1/5-tone up)</li><li><strong>b</strong> = Flat (3/5-tone down)</li><li><strong>#</strong> = Sharp (3/5-tone up)</li><li><strong>v</strong> = Semiflat (1/5-tone down)</li></ul></td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <th><strong>Degrees</strong><br />
</th>
        <th><strong>Armodue note</strong><br />
</th>
        <th><strong>Cents size</strong><br />
</th>
        <th><strong><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Nearest%20just%20interval">Nearest Just I</a>nterval</strong><br />
</th>
        <th><strong>Cents value</strong><br />
</th>
        <th><strong>Error</strong><br />
</th>
        <th>11-limit Ratio Assuming<br />
&lt;<a class="wiki_link" href="http://tel.wikispaces.com/39%2062%2091%20110">39 62 91 110</a> 135| <a class="wiki_link" href="/Val">Val</a><br />
</th>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>1<br />
</td>
        <td>0<br />
</td>
        <td>1/1<br />
</td>
        <td>0<br />
</td>
        <td>None<br />
</td>
        <td>1/1<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1‡ (9#)<br />
</td>
        <td>30.7692<br />
</td>
        <td>57/56<br />
</td>
        <td>30.6421<br />
</td>
        <td>+0.1271<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>2b<br />
</td>
        <td>61.5385<br />
</td>
        <td>29/28<br />
</td>
        <td>60.7513<br />
</td>
        <td>+0.7872<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>1#<br />
</td>
        <td>92.3077<br />
</td>
        <td>39/37<br />
</td>
        <td>91.1386<br />
</td>
        <td>+1.1691<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>2v<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/123.0769">123.0769</a><br />
</td>
        <td>44/41<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/122.2555">122.2555</a><br />
</td>
        <td>+0.8214<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>2<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/153.8462">153.8462</a><br />
</td>
        <td>35/32<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/155.1396">155.1396</a><br />
</td>
        <td>-1.2934<br />
</td>
        <td>12/11, 11/10<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>2‡<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/184.6154">184.6154</a><br />
</td>
        <td>10/9<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/182.4037">182.4037</a><br />
</td>
        <td>+2.2117<br />
</td>
        <td>10/9<br />
</td>
    </tr>
    <tr>
        <td>7<strong>·</strong><br />
</td>
        <td>3b<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/215.3846">215.3846</a><br />
</td>
        <td>17/15<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/216.6867">216.6867</a><br />
</td>
        <td>-1.3021<br />
</td>
        <td>8/7, 9/8<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>2#<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/246.1538">246.1538</a><br />
</td>
        <td>15/13<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/247.7411">247.7411</a><br />
</td>
        <td>-1.5873<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>3v<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/276.9231">276.9231</a><br />
</td>
        <td>27/23<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/277.5907">277.5907</a><br />
</td>
        <td>-0.6676<br />
</td>
        <td>7/6<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>3<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/307.6923">307.6923</a><br />
</td>
        <td>43/36<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/307.6077">307.6077</a><br />
</td>
        <td>+0.0846<br />
</td>
        <td>6/5<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>3‡<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/338.4615">338.4615</a><br />
</td>
        <td>17/14<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/336.1295">336.1295</a><br />
</td>
        <td>+2.332<br />
</td>
        <td>11/9<br />
</td>
    </tr>
    <tr>
        <td>12<strong>·</strong><br />
</td>
        <td>4b<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/369.2308">369.2308</a><br />
</td>
        <td>26/21<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/369.7468">369.7468</a><br />
</td>
        <td>-0.516<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>3#<br />
</td>
        <td>400<br />
</td>
        <td>34/27<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/399.0904">399.0904</a><br />
</td>
        <td>+0.9096<br />
</td>
        <td>5/4<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>4v (5b)<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/430.7692">430.7692</a><br />
</td>
        <td>41/32<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/429.0624">429.0624</a><br />
</td>
        <td>+1.7068<br />
</td>
        <td>9/7, 14/11<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>4<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/461.5385">461.5385</a><br />
</td>
        <td>30/23<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/459.9944">459.9944</a><br />
</td>
        <td>+1.5441<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>4‡ (5v)<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/492.3077">492.3077</a><br />
</td>
        <td>85/64<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/491.2691">491.2691</a><br />
</td>
        <td>+1.0386<br />
</td>
        <td>4/3<br />
</td>
    </tr>
    <tr>
        <td>17<strong>·</strong><br />
</td>
        <td>5<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/523.0769">523.0769</a><br />
</td>
        <td>23/17<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/523.3189">523.3189</a><br />
</td>
        <td>-0.242<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>5‡ (4#)<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/553.8462">553.8462</a><br />
</td>
        <td>11/8<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/551.3179">551.3179</a><br />
</td>
        <td>+2.5283<br />
</td>
        <td>11/8<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>6b<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/584.6154">584.6154</a><br />
</td>
        <td>7/5<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/582.5122">582.5122</a><br />
</td>
        <td>+2.1032<br />
</td>
        <td>7/5<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>5#<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/615.3846">615.3846</a><br />
</td>
        <td>10/7<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/617.4878">617.4878</a><br />
</td>
        <td>-2.1032<br />
</td>
        <td>10/7<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>6v<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/646.1538">646.1538</a><br />
</td>
        <td>16/11<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/648.6821">648.6821</a><br />
</td>
        <td>-2.5283<br />
</td>
        <td>16/11<br />
</td>
    </tr>
    <tr>
        <td>22<strong>·</strong><br />
</td>
        <td>6<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/676.9231">676.9231</a><br />
</td>
        <td>34/23<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/676.6811">676.6811</a><br />
</td>
        <td>+0.242<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>6‡<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/707.6923">707.6923</a><br />
</td>
        <td>128/85<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/708.7309">708.7309</a><br />
</td>
        <td>-1.0386<br />
</td>
        <td>3/2<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>7b<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/738.4615">738.4615</a><br />
</td>
        <td>23/15<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/740.0056">740.0056</a><br />
</td>
        <td>-1.5441<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>6#<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/769.2308">769.2308</a><br />
</td>
        <td>64/41<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/770.9376">770.9376</a><br />
</td>
        <td>-1.7068<br />
</td>
        <td>14/9, 11/7<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>7v<br />
</td>
        <td>800<br />
</td>
        <td>27/17<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/800.9096">800.9096</a><br />
</td>
        <td>-0.9096<br />
</td>
        <td>8/5<br />
</td>
    </tr>
    <tr>
        <td>27<strong>·</strong><br />
</td>
        <td>7<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/830.7692">830.7692</a><br />
</td>
        <td>21/13<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/830.2532">830.2532</a><br />
</td>
        <td>+0.516<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>7‡<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/861.5385">861.5385</a><br />
</td>
        <td>28/17<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/863.8705">863.8705</a><br />
</td>
        <td>-2.332<br />
</td>
        <td>18/11<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>8b<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/892.3077">892.3077</a><br />
</td>
        <td>72/43<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/892.3923">892.3923</a><br />
</td>
        <td>-0.0846<br />
</td>
        <td>5/3<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>7#<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/923.0769">923.0769</a><br />
</td>
        <td>46/27<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/922.4093">922.4093</a><br />
</td>
        <td>+0.6676<br />
</td>
        <td>12/7<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>8v<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/953.8462">953.8462</a><br />
</td>
        <td>26/15<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/952.2589">952.2589</a><br />
</td>
        <td>+1.5873<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32<strong>·</strong><br />
</td>
        <td>8<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/984.6154">984.6154</a><br />
</td>
        <td>30/17<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/983.3133">983.3133</a><br />
</td>
        <td>+1.3021<br />
</td>
        <td>7/4, 16/9<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>8‡<br />
</td>
        <td>1015.3846<br />
</td>
        <td>9/5<br />
</td>
        <td>1017.5963<br />
</td>
        <td>-2.2117<br />
</td>
        <td>9/5<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>9b<br />
</td>
        <td>1046.1538<br />
</td>
        <td>64/35<br />
</td>
        <td>1044.8604<br />
</td>
        <td>+1.2934<br />
</td>
        <td>11/6, 20/11<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>8#<br />
</td>
        <td>1076.9231<br />
</td>
        <td>41/22<br />
</td>
        <td>1077.7445<br />
</td>
        <td>-0.8214<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>9v (1b)<br />
</td>
        <td>1107.6923<br />
</td>
        <td>74/39<br />
</td>
        <td>1108.8614<br />
</td>
        <td>-1.1691<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>9<br />
</td>
        <td>1138.4615<br />
</td>
        <td>56/29<br />
</td>
        <td>1139.2487<br />
</td>
        <td>-0.7872<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>9‡ (1v)<br />
</td>
        <td>1169.2308<br />
</td>
        <td>112/57<br />
</td>
        <td>1169.3579<br />
</td>
        <td>-0.1271<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>39<strong>··</strong>(or 0)<br />
</td>
        <td>1<br />
</td>
        <td>1200<br />
</td>
        <td>2/1<br />
</td>
        <td>1200<br />
</td>
        <td>None<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x39 tone equal temperament-Instruments (prototypes):"></a><!-- ws:end:WikiTextHeadingRule:4 --><u>Instruments (prototypes):</u></h2>
 <br />
<!-- ws:start:WikiTextLocalImageRule:704:&lt;img src=&quot;/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 467px; width: 800px;&quot; /&gt; --><img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /><!-- ws:end:WikiTextLocalImageRule:704 --><br />
<em>An illustrative image of a 39-ED2 keyboard</em><br />
<!-- ws:start:WikiTextLocalImageRule:705:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&quot; alt=&quot;39-EDD fretboard visualization&quot; title=&quot;39-EDD fretboard visualization&quot; style=&quot;height: 203px; width: 826px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /></td></tr><tr><td class="imageCaption">39-EDD fretboard visualization</td></tr></table><!-- ws:end:WikiTextLocalImageRule:705 --><br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x39 tone equal temperament-39 tone equal modes:"></a><!-- ws:end:WikiTextHeadingRule:6 --><strong><u>39 tone equal <a class="wiki_link" href="http://xenharmonic.wikispaces.com/modes">modes</a></u>:</strong></h2>
 <br />
14 14 11 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%201s">2L 1s</a><br />
<a class="wiki_link" href="http://tel.wikispaces.com/11%2011%2011%206">11 11 11 6</a> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%201s">3L 1s</a><br />
<a class="wiki_link" href="http://tel.wikispaces.com/10%2010%2010%209">10 10 10 9</a> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%201s">3L 1s</a><br />
<a class="wiki_link" href="http://tel.wikispaces.com/11%203%2011%2011%203">11 3 11 11 3</a> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%202s">3L 2s (Father pentatonic)</a><br />
5 12 5 5 12 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type 2L 3s (Mavila pentatonic)<br />
7 7 9 7 9 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type 2L 3s (Superpythagorean pentatonic)<br />
8 8 8 8 7 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/4L%201s">4L 1s (Bug pentatonic)</a><br />
<a class="wiki_link" href="http://tel.wikispaces.com/10%203%2010%203%2010%203">10 3 10 3 10 3</a> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s (Augmented hexatonic)</a><br />
9 4 9 4 9 4 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s (Augmented hexatonic)</a><br />
8 5 8 5 8 5 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%203s">3L 3s (Augmented hexatonic)</a><br />
7 7 7 7 7 4 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%201s">5L 1s (Grumpy hexatonic)</a><br />
5 5 7 5 5 5 7 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/2L%205s">2L 5s (heptatonic Mavila Anti-Diatonic)</a><br />
7 7 7 2 7 7 2 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type 5L 2s (heptatonic Superpythagorean diatonic)<br />
5 5 5 5 5 5 5 4 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%201s">7L 1s (Grumpy octatonic)</a><br />
<strong>5 5 5 2 5 5 5 5 2</strong> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/7L%202s">7L 2s (nonatonic Mavila Superdiatonic)</a><br />
5 5 3 5 5 3 5 5 3 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/6L%203s">6L 3s (unfair Augmented nonatonic)</a><br />
5 4 4 5 4 4 5 4 4 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%206s">3L 6s (fair Augmented nonatonic)</a><br />
4 4 4 4 4 4 4 4 4 3 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%201s">9L 1s (Grumpy decatonic)</a><br />
<strong>3 3 5 3 3 3 5 3 3 3 5</strong> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/3L%208s">3L 8s (Anti-Sensi hendecatonic)</a><br />
2 5 2 2 5 2 5 2 5 2 2 5 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type 5L 7s<br />
<strong>3 3 3 4 3 3 3 4 3 3 3 4 -</strong> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type 3L 9s<br />
<strong>3 3 3 2 3 3 3 3 2 3 3 3 3 2</strong> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="/11L%203s">11L 3s (Ketradektriatoh tetradecatonic)</a><br />
3 2 3 3 2 3 2 3 3 2 3 2 3 3 2 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%206s">9L 6s</a><br />
3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 2 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%209s">7L 9s</a><br />
<strong>2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3</strong> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%2012s">5L 12s</a><br />
2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2015s">3L 15s</a><br />
<strong>3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3</strong> - <span style="cursor: pointer;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a></span> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/10L%209s">10L 9s</a><br />
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/19L%201s">19L 1s</a><br />
2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17L%205s">17L 5s</a><br />
<strong>2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1</strong> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16L%207s">16L 7s</a><br />
2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/13L%2013s">13L 13s</a><br />
<strong>2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1</strong> - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/10L%2019s">10L 19s</a><br />
2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%2023s">8L 23s</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x39 tone equal temperament-39edo and world music:"></a><!-- ws:end:WikiTextHeadingRule:8 --><strong><u>39edo and world music:</u></strong></h2>
 <br />
39edo is a good candidate for a &quot;universal tuning&quot; in that it offers reasonable approximations of many different world music traditions; it is one of the simplest edos that can make this claim. Because of this, composers wishing to combine multiple world music traditions (for example, gamelan with maqam singing) within one unified framework would find 39edo an interesting possibility.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x39 tone equal temperament-39edo and world music:-Western:"></a><!-- ws:end:WikiTextHeadingRule:10 -->Western:</h3>
 <br />
39edo offers not one, but several different ways to realize the traditional Western diatonic scale. One way is to simply take a chain of fifths (the diatonic MOS: <strong>7 7 2 7 7 7 2</strong>). Because 39edo is a superpyth rather than a meantone system, this means that the harmonic quality of its diatonic scale will differ somewhat, since &quot;minor&quot; and &quot;major&quot; triads now approximate 6:7:9 and 14:18:21 respectively, rather than 10:12:15 and 4:5:6 as in meantone diatonic systems. Diatonic compositions translated onto this scale thus acquire a wildly different harmonic character, albeit still very pleasing.<br />
<br />
Another option is to use a MODMOS, such as <strong>7 6 3 7 6 7 3</strong>; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, the wolf fifth can be avoided by introducing accidental notes when necessary. There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in <em>many</em> different ways, acquiring a distinctly different but still harmonious character each time.<br />
<br />
The MOS and the MODMOS's all have smaller-than-usual semitones, which makes them more effective for melody than their counterparts in 12edo or meantone systems.<br />
<br />
Because 39edo and 12edo both have an overall sharp character and share the same major third, they have a relatively similar sound. Thus, 39edo (unlike, say, 22edo or 19edo, which are both &quot;acquired tastes&quot;) does not sound all that xenharmonic to people used to 12edo. Check out <a class="wiki_link_ext" href="https://www.prismnet.com/~hmiller/midi/canon39.mid" rel="nofollow">Pachelbel's Canon in 39edo</a> (using the <strong>7 6 3 7 6 7 3</strong> MODMOS), for example.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x39 tone equal temperament-39edo and world music:-Indian:"></a><!-- ws:end:WikiTextHeadingRule:12 --><strong>Indian:</strong></h3>
 <br />
A similar situation arises with Indian music since the sruti system, like the Western system, also has multiple possible mappings in 39edo. Many of these are modified versions of the 17L 5s MOS (where the generator is a perfect fifth).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="x39 tone equal temperament-39edo and world music:-Arabic, Turkish, Persian:"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong><a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic, Turkish, Persian</a>:</strong></h3>
 <br />
While middle-eastern music is commonly approximated using 24edo, 39edo offers a potentially better alternative. 17edo and 24edo both satisfy the &quot;Level 1&quot; requirements for maqam tuning sytems. 39edo is a Level 2 system because:<br />
<br />
<ul><li>It has two types of &quot;neutral&quot; seconds (154 and 185 cents)</li><li>It has two minor seconds (92 and 123 cents), which when added together give a whole tone (215 cents)</li></ul><br />
whereas neither 17edo nor 24edo satisfy these properties.<br />
<br />
39edo will likely be more suited to some middle-eastern scales than others. Specifically, Turkish music (in which the Rast makam has a &quot;major-like&quot; wide neutral third and a wide &quot;neutral&quot; second approaching 10/9), will likely be especially well suited to 39edo.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="x39 tone equal temperament-39edo and world music:-Blues / Jazz / African-American:"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>Blues / Jazz / African-American:</strong></h3>
 <br />
The harmonic seventh (&quot;barbershop seventh&quot;) tetrad is reasonably well approximated in 39edo, and some temperaments (augene in particular) give scales that are liberally supplied with them. John Coltrane <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Coltrane_changes" rel="nofollow">would have loved augene</a>.<br />
<br />
Tritone substitution, which is a major part of jazz and blues harmony, is more complicated in 39edo because there are two types of tritones. Therefore the tritone substitution of one seventh chord will need to be a different type of seventh chord. However, this also opens new possibilities; if the substituted chord is of a more consonant type than the original, then the tritone substitution may function as a <em>resolution</em> rather than a suspension.<br />
<br />
Blue notes, rather than being considered inflections, can be notated as accidentals instead; for example, a &quot;blue major third&quot; can be identified as either of the two neutral thirds. There are two possible mappings for 7:4 which are about equal in closeness. The sharp mapping is the normal one because it works better with the 5:4 and 3:2, but using the flat one instead (as an accidental) allows for another type of blue note.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x39 tone equal temperament-39edo and world music:-Other:"></a><!-- ws:end:WikiTextHeadingRule:18 -->Other:</h3>
 <br />
39edo offers a good approximation of pelog / mavila using the flat fifth as a generator.<br />
<br />
It also offers <em>many</em> possible pentatonic scales, including the 2L+3S MOS (which is <strong>9 7 7 9 7</strong>). Slendro can be approximated using this scale or using something like the quasi-equal <strong>8 8 8 8 7</strong>. A more expressive pentatonic scale is the oneirotonic subset <strong>9 6 9 9 6</strong>. Many Asian and African musical styles can thus be accomodated.</body></html>

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 <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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-27 23:55:01 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-28 10:47:39 UTC</tt>.<br>
-: The original revision id was <tt>597357774</tt>.<br>
+: The original revision id was <tt>597388098</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>
@@ Line 9: / Line 9: @@
 **39-EDO, 39-ED2** or **39-tET** divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of [[xenharmonic/7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, suited in [[xenharmonic/16edo|16-ED2]], and allied systems: [[xenharmonic/25edo|25-ED2]] [1/3-tone 3;2]; [[xenharmonic/41edo|41-ED2]] [1/5-tone 5;3]; and [[xenharmonic/57edo|57]] ED2 [1/7-tone 7;4]. **Hornbostel Temperaments** is included too with: [[xenharmonic/23edo|23-ED2]] [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] &amp; [[xenharmonic/62edo|62-ED2]] [1/8-tone 8;3]. [[223edo|223-ED2]], the best accuracy for Hornbostel temperament fits very good with Armodue like 1/29-tone 29;10 version. Note that [[101edo|101]], [[131edo|131]], [[177edo|177]] &amp; [[200edo|200]] ED2s are tempered systems that [[http://www.h-pi.com/eop-ogolevets.html|Alexei Ogolevets]] (Ukraine, 1891 - 1967) was proposing in his List of Temperaments, in which the Armodue system fits very well in all these.
-However, its 23\39 fifth, 5.737 Cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 Cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO, in some few ways, allied to 12-ET in supporting augene temperament, and is in fact, an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.
+However, its 23\39 fifth, 5.737 Cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 Cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, [[tel:1600000/1594323|1600000/1594323]]. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO, in some few ways, allied to 12-ET in supporting augene temperament, and is in fact, an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;[[tel:39 62 91 110|39 62 91 110]] 135|.
 A particular anecdote with this 39 divisions per 2/1 was made in the Teliochordon, in 1788 by Charles Clagget (Ireland, 1740? - 1820), a little extract [[http://ml.oxfordjournals.org/content/76/2/291.extract.jpg|here]].
@@ Line 25: / Line 25: @@
 ||~ **Degrees** ||~ **Armodue note** ||~ **Cents size** ||~ **[[xenharmonic/Nearest just interval|Nearest Just I]]nterval** ||~ **Cents value** ||~ **Error** ||~ 11-limit Ratio Assuming
-&lt;39 62 91 110 135| [[Val]] ||
+&lt;[[tel:39 62 91 110|39 62 91 110]] 135| [[Val]] ||
 || 0 || 1 || 0 || 1/1 || 0 || None || 1/1 ||
 || 1 || 1‡ (9#) || 30.7692 || 57/56 || 30.6421 || +0.1271 ||   ||
 || 2 || 2b || 61.5385 || 29/28 || 60.7513 || +0.7872 ||   ||
 || 3 || 1# || 92.3077 || 39/37 || 91.1386 || +1.1691 ||   ||
-|| 4 || 2v || 123.0769 || 44/41 || 122.2555 || +0.8214 ||   ||
+|| 4 || 2v || [[tel:123.0769|123.0769]] || 44/41 || [[tel:122.2555|122.2555]] || +0.8214 ||   ||
-|| 5 || 2 || 153.8462 || 35/32 || 155.1396 || -1.2934 || 12/11, 11/10 ||
+|| 5 || 2 || [[tel:153.8462|153.8462]] || 35/32 || [[tel:155.1396|155.1396]] || -1.2934 || 12/11, 11/10 ||
-|| 6 || 2‡ || 184.6154 || 10/9 || 182.4037 || +2.2117 || 10/9 ||
+|| 6 || 2‡ || [[tel:184.6154|184.6154]] || 10/9 || [[tel:182.4037|182.4037]] || +2.2117 || 10/9 ||
-|| 7**·** || 3b || 215.3846 || 17/15 || 216.6867 || -1.3021 || 8/7, 9/8 ||
+|| 7**·** || 3b || [[tel:215.3846|215.3846]] || 17/15 || [[tel:216.6867|216.6867]] || -1.3021 || 8/7, 9/8 ||
-|| 8 || 2# || 246.1538 || 15/13 || 247.7411 || -1.5873 ||   ||
+|| 8 || 2# || [[tel:246.1538|246.1538]] || 15/13 || [[tel:247.7411|247.7411]] || -1.5873 ||   ||
-|| 9 || 3v || 276.9231 || 27/23 || 277.5907 || -0.6676 || 7/6 ||
+|| 9 || 3v || [[tel:276.9231|276.9231]] || 27/23 || [[tel:277.5907|277.5907]] || -0.6676 || 7/6 ||
-|| 10 || 3 || 307.6923 || 43/36 || 307.6077 || +0.0846 || 6/5 ||
+|| 10 || 3 || [[tel:307.6923|307.6923]] || 43/36 || [[tel:307.6077|307.6077]] || +0.0846 || 6/5 ||
-|| 11 || 3‡ || 338.4615 || 17/14 || 336.1295 || +2.332 || 11/9 ||
+|| 11 || 3‡ || [[tel:338.4615|338.4615]] || 17/14 || [[tel:336.1295|336.1295]] || +2.332 || 11/9 ||
-|| 12**·** || 4b || 369.2308 || 26/21 || 369.7468 || -0.516 ||   ||
+|| 12**·** || 4b || [[tel:369.2308|369.2308]] || 26/21 || [[tel:369.7468|369.7468]] || -0.516 ||   ||
-|| 13 || 3# || 400 || 34/27 || 399.0904 || +0.9096 || 5/4 ||
+|| 13 || 3# || 400 || 34/27 || [[tel:399.0904|399.0904]] || +0.9096 || 5/4 ||
-|| 14 || 4v (5b) || 430.7692 || 41/32 || 429.0624 || +1.7068 || 9/7, 14/11 ||
+|| 14 || 4v (5b) || [[tel:430.7692|430.7692]] || 41/32 || [[tel:429.0624|429.0624]] || +1.7068 || 9/7, 14/11 ||
-|| 15 || 4 || 461.5385 || 30/23 || 459.9944 || +1.5441 ||   ||
+|| 15 || 4 || [[tel:461.5385|461.5385]] || 30/23 || [[tel:459.9944|459.9944]] || +1.5441 ||   ||
-|| 16 || 4‡ (5v) || 492.3077 || 85/64 || 491.2691 || +1.0386 || 4/3 ||
+|| 16 || 4‡ (5v) || [[tel:492.3077|492.3077]] || 85/64 || [[tel:491.2691|491.2691]] || +1.0386 || 4/3 ||
-|| 17**·** || 5 || 523.0769 || 23/17 || 523.3189 || -0.242 ||   ||
+|| 17**·** || 5 || [[tel:523.0769|523.0769]] || 23/17 || [[tel:523.3189|523.3189]] || -0.242 ||   ||
-|| 18 || 5‡ (4#) || 553.8462 || 11/8 || 551.3179 || +2.5283 || 11/8 ||
+|| 18 || 5‡ (4#) || [[tel:553.8462|553.8462]] || 11/8 || [[tel:551.3179|551.3179]] || +2.5283 || 11/8 ||
-|| 19 || 6b || 584.6154 || 7/5 || 582.5122 || +2.1032 || 7/5 ||
+|| 19 || 6b || [[tel:584.6154|584.6154]] || 7/5 || [[tel:582.5122|582.5122]] || +2.1032 || 7/5 ||
-|| 20 || 5# || 615.3846 || 10/7 || 617.4878 || -2.1032 || 10/7 ||
+|| 20 || 5# || [[tel:615.3846|615.3846]] || 10/7 || [[tel:617.4878|617.4878]] || -2.1032 || 10/7 ||
-|| 21 || 6v || 646.1538 || 16/11 || 648.6821 || -2.5283 || 16/11 ||
+|| 21 || 6v || [[tel:646.1538|646.1538]] || 16/11 || [[tel:648.6821|648.6821]] || -2.5283 || 16/11 ||
-|| 22**·** || 6 || 676.9231 || 34/23 || 676.6811 || +0.242 ||   ||
+|| 22**·** || 6 || [[tel:676.9231|676.9231]] || 34/23 || [[tel:676.6811|676.6811]] || +0.242 ||   ||
-|| 23 || 6‡ || 707.6923 || 128/85 || 708.7309 || -1.0386 || 3/2 ||
+|| 23 || 6‡ || [[tel:707.6923|707.6923]] || 128/85 || [[tel:708.7309|708.7309]] || -1.0386 || 3/2 ||
-|| 24 || 7b || 738.4615 || 23/15 || 740.0056 || -1.5441 ||   ||
+|| 24 || 7b || [[tel:738.4615|738.4615]] || 23/15 || [[tel:740.0056|740.0056]] || -1.5441 ||   ||
-|| 25 || 6# || 769.2308 || 64/41 || 770.9376 || -1.7068 || 14/9, 11/7 ||
+|| 25 || 6# || [[tel:769.2308|769.2308]] || 64/41 || [[tel:770.9376|770.9376]] || -1.7068 || 14/9, 11/7 ||
-|| 26 || 7v || 800 || 27/17 || 800.9096 || -0.9096 || 8/5 ||
+|| 26 || 7v || 800 || 27/17 || [[tel:800.9096|800.9096]] || -0.9096 || 8/5 ||
-|| 27**·** || 7 || 830.7692 || 21/13 || 830.2532 || +0.516 ||   ||
+|| 27**·** || 7 || [[tel:830.7692|830.7692]] || 21/13 || [[tel:830.2532|830.2532]] || +0.516 ||   ||
-|| 28 || 7‡ || 861.5385 || 28/17 || 863.8705 || -2.332 || 18/11 ||
+|| 28 || 7‡ || [[tel:861.5385|861.5385]] || 28/17 || [[tel:863.8705|863.8705]] || -2.332 || 18/11 ||
-|| 29 || 8b || 892.3077 || 72/43 || 892.3923 || -0.0846 || 5/3 ||
+|| 29 || 8b || [[tel:892.3077|892.3077]] || 72/43 || [[tel:892.3923|892.3923]] || -0.0846 || 5/3 ||
-|| 30 || 7# || 923.0769 || 46/27 || 922.4093 || +0.6676 || 12/7 ||
+|| 30 || 7# || [[tel:923.0769|923.0769]] || 46/27 || [[tel:922.4093|922.4093]] || +0.6676 || 12/7 ||
-|| 31 || 8v || 953.8462 || 26/15 || 952.2589 || +1.5873 ||   ||
+|| 31 || 8v || [[tel:953.8462|953.8462]] || 26/15 || [[tel:952.2589|952.2589]] || +1.5873 ||   ||
-|| 32**·** || 8 || 984.6154 || 30/17 || 983.3133 || +1.3021 || 7/4, 16/9 ||
+|| 32**·** || 8 || [[tel:984.6154|984.6154]] || 30/17 || [[tel:983.3133|983.3133]] || +1.3021 || 7/4, 16/9 ||
 || 33 || 8‡ || 1015.3846 || 9/5 || 1017.5963 || -2.2117 || 9/5 ||
 || 34 || 9b || 1046.1538 || 64/35 || 1044.8604 || +1.2934 || 11/6, 20/11 ||
@@ Line 76: / Line 76: @@
 ==**__39 tone equal [[xenharmonic/modes|modes]]__:**==
-15 9 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/2L 1s|2L 1s]]
 14 11 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/2L 1s|2L 1s]]
-11 11 6 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/3L 1s|3L 1s]]
+[[tel:11 11 11 6|11 11 11 6]] - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/3L 1s|3L 1s]]
-10 10 9 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/3L 1s|3L 1s]]
+[[tel:10 10 10 9|10 10 10 9]] - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/3L 1s|3L 1s]]
-3 11 11 3 - [[xenharmonic/MOSScales|MOS]] of type [[3L 2s|3L 2s (Father pentatonic)]]
+[[tel:11 3 11 11 3|11 3 11 11 3]] - [[xenharmonic/MOSScales|MOS]] of type [[3L 2s|3L 2s (Father pentatonic)]]
+12 5 5 12 - [[xenharmonic/MOSScales|MOS]] of type 2L 3s (Mavila pentatonic)
+7 9 7 9 - [[xenharmonic/MOSScales|MOS]] of type 2L 3s (Superpythagorean pentatonic)
 8 8 8 7 - [[xenharmonic/MOSScales|MOS]] of type [[4L 1s|4L 1s (Bug pentatonic)]]
-3 10 3 10 3 - [[xenharmonic/MOSScales|MOS]] of type [[3L 3s|3L 3s (Augmented hexatonic)]]
+[[tel:10 3 10 3 10 3|10 3 10 3 10 3]] - [[xenharmonic/MOSScales|MOS]] of type [[3L 3s|3L 3s (Augmented hexatonic)]]
 4 9 4 9 4 - [[xenharmonic/MOSScales|MOS]] of type [[3L 3s|3L 3s (Augmented hexatonic)]]
 5 8 5 8 5 - [[xenharmonic/MOSScales|MOS]] of type [[3L 3s|3L 3s (Augmented hexatonic)]]
@@ Line 156: / Line 156: @@
   &lt;br /&gt;
 &lt;strong&gt;39-EDO, 39-ED2&lt;/strong&gt; or &lt;strong&gt;39-tET&lt;/strong&gt; divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%202s"&gt;Superdiatonic&lt;/a&gt; LLLsLLLLs like a basical scale for notation and theory, suited in &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/16edo"&gt;16-ED2&lt;/a&gt;, and allied systems: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/25edo"&gt;25-ED2&lt;/a&gt; [1/3-tone 3;2]; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo"&gt;41-ED2&lt;/a&gt; [1/5-tone 5;3]; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/57edo"&gt;57&lt;/a&gt; ED2 [1/7-tone 7;4]. &lt;strong&gt;Hornbostel Temperaments&lt;/strong&gt; is included too with: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/23edo"&gt;23-ED2&lt;/a&gt; [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] &amp;amp; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/62edo"&gt;62-ED2&lt;/a&gt; [1/8-tone 8;3]. &lt;a class="wiki_link" href="/223edo"&gt;223-ED2&lt;/a&gt;, the best accuracy for Hornbostel temperament fits very good with Armodue like 1/29-tone 29;10 version. Note that &lt;a class="wiki_link" href="/101edo"&gt;101&lt;/a&gt;, &lt;a class="wiki_link" href="/131edo"&gt;131&lt;/a&gt;, &lt;a class="wiki_link" href="/177edo"&gt;177&lt;/a&gt; &amp;amp; &lt;a class="wiki_link" href="/200edo"&gt;200&lt;/a&gt; ED2s are tempered systems that &lt;a class="wiki_link_ext" href="http://www.h-pi.com/eop-ogolevets.html" rel="nofollow"&gt;Alexei Ogolevets&lt;/a&gt; (Ukraine, 1891 - 1967) was proposing in his List of Temperaments, in which the Armodue system fits very well in all these.&lt;br /&gt;
-However, its 23\39 fifth, 5.737 Cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 Cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO, in some few ways, allied to 12-ET in supporting augene temperament, and is in fact, an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &amp;lt;39 62 91 110 135|.&lt;br /&gt;
+However, its 23\39 fifth, 5.737 Cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 Cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, [[tel:1600000/1594323|1600000/1594323]]. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO, in some few ways, allied to 12-ET in supporting augene temperament, and is in fact, an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &amp;lt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/39%2062%2091%20110"&gt;39 62 91 110&lt;/a&gt; 135|.&lt;br /&gt;
 A particular anecdote with this 39 divisions per 2/1 was made in the Teliochordon, in 1788 by Charles Clagget (Ireland, 1740? - 1820), a little extract &lt;a class="wiki_link_ext" href="http://ml.oxfordjournals.org/content/76/2/291.extract.jpg" rel="nofollow"&gt;here&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 195: / Line 195: @@
 &lt;/th&gt;
          &lt;th&gt;11-limit Ratio Assuming&lt;br /&gt;
-&amp;lt;39 62 91 110 135| &lt;a class="wiki_link" href="/Val"&gt;Val&lt;/a&gt;&lt;br /&gt;
+&amp;lt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/39%2062%2091%20110"&gt;39 62 91 110&lt;/a&gt; 135| &lt;a class="wiki_link" href="/Val"&gt;Val&lt;/a&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 267: / Line 267: @@
          &lt;td&gt;2v&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;123.0769&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/123.0769"&gt;123.0769&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;44/41&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;122.2555&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/122.2555"&gt;122.2555&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+0.8214&lt;br /&gt;
@@ Line 283: / Line 283: @@
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;153.8462&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/153.8462"&gt;153.8462&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;35/32&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;155.1396&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/155.1396"&gt;155.1396&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;-1.2934&lt;br /&gt;
@@ Line 299: / Line 299: @@
          &lt;td&gt;2‡&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;184.6154&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/184.6154"&gt;184.6154&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;10/9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;182.4037&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/182.4037"&gt;182.4037&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+2.2117&lt;br /&gt;
@@ Line 315: / Line 315: @@
          &lt;td&gt;3b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;215.3846&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/215.3846"&gt;215.3846&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;17/15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;216.6867&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/216.6867"&gt;216.6867&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;-1.3021&lt;br /&gt;
@@ Line 331: / Line 331: @@
          &lt;td&gt;2#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;246.1538&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/246.1538"&gt;246.1538&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;247.7411&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/247.7411"&gt;247.7411&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;-1.5873&lt;br /&gt;
@@ Line 347: / Line 347: @@
          &lt;td&gt;3v&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;276.9231&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/276.9231"&gt;276.9231&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;277.5907&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/277.5907"&gt;277.5907&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;-0.6676&lt;br /&gt;
@@ Line 363: / Line 363: @@
          &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;307.6923&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/307.6923"&gt;307.6923&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;43/36&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;307.6077&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/307.6077"&gt;307.6077&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+0.0846&lt;br /&gt;
@@ Line 379: / Line 379: @@
          &lt;td&gt;3‡&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;338.4615&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/338.4615"&gt;338.4615&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;17/14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;336.1295&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/336.1295"&gt;336.1295&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+2.332&lt;br /&gt;
@@ Line 395: / Line 395: @@
          &lt;td&gt;4b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;369.2308&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/369.2308"&gt;369.2308&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;26/21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;369.7468&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/369.7468"&gt;369.7468&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;-0.516&lt;br /&gt;
@@ Line 415: / Line 415: @@
          &lt;td&gt;34/27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;399.0904&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/399.0904"&gt;399.0904&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+0.9096&lt;br /&gt;
@@ Line 427: / Line 427: @@
          &lt;td&gt;4v (5b)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;430.7692&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/430.7692"&gt;430.7692&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;41/32&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;429.0624&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/429.0624"&gt;429.0624&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+1.7068&lt;br /&gt;
@@ Line 443: / Line 443: @@
          &lt;td&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;461.5385&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/461.5385"&gt;461.5385&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;30/23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;459.9944&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/459.9944"&gt;459.9944&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+1.5441&lt;br /&gt;
@@ Line 459: / Line 459: @@
          &lt;td&gt;4‡ (5v)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;492.3077&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/492.3077"&gt;492.3077&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;85/64&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;491.2691&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/491.2691"&gt;491.2691&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+1.0386&lt;br /&gt;
@@ Line 475: / Line 475: @@
          &lt;td&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;523.0769&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/523.0769"&gt;523.0769&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;23/17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;523.3189&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/523.3189"&gt;523.3189&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;-0.242&lt;br /&gt;
@@ Line 491: / Line 491: @@
          &lt;td&gt;5‡ (4#)&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;553.8462&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/553.8462"&gt;553.8462&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;11/8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;551.3179&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/551.3179"&gt;551.3179&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+2.5283&lt;br /&gt;
@@ Line 507: / Line 507: @@
          &lt;td&gt;6b&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;584.6154&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/584.6154"&gt;584.6154&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;582.5122&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/582.5122"&gt;582.5122&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+2.1032&lt;br /&gt;
@@ Line 523: / Line 523: @@
          &lt;td&gt;5#&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;615.3846&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/615.3846"&gt;615.3846&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;10/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;617.4878&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/617.4878"&gt;617.4878&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;-2.1032&lt;br /&gt;
@@ Line 539: / Line 539: @@
          &lt;td&gt;6v&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;646.1538&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/646.1538"&gt;646.1538&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;16/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;648.6821&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/648.6821"&gt;648.6821&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;-2.5283&lt;br /&gt;
@@ Line 555: / Line 555: @@
          &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;676.9231&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/676.9231"&gt;676.9231&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;34/23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;676.6811&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/676.6811"&gt;676.6811&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;+0.242&lt;br /&gt;
@@ Line 571: / Line 571: @@
          &lt;td&gt;6‡&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;707.6923&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/707.6923"&gt;707.6923&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
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-15 9 - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%201s"&gt;2L 1s&lt;/a&gt;&lt;br /&gt;
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-&lt;br /&gt;
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+7 9 7 9 - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type 2L 3s (Superpythagorean pentatonic)&lt;br /&gt;
 8 8 8 7 - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="/4L%201s"&gt;4L 1s (Bug pentatonic)&lt;/a&gt;&lt;br /&gt;
-3 10 3 10 3 - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="/3L%203s"&gt;3L 3s (Augmented hexatonic)&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="http://tel.wikispaces.com/10%203%2010%203%2010%203"&gt;10 3 10 3 10 3&lt;/a&gt; - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="/3L%203s"&gt;3L 3s (Augmented hexatonic)&lt;/a&gt;&lt;br /&gt;
 4 9 4 9 4 - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="/3L%203s"&gt;3L 3s (Augmented hexatonic)&lt;/a&gt;&lt;br /&gt;
 5 8 5 8 5 - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="/3L%203s"&gt;3L 3s (Augmented hexatonic)&lt;/a&gt;&lt;br /&gt;

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