37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/31edo|31edo]] and coming before [[xenharmonic/41edo|41edo]].
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[xenharmonic/porcupine|porcupine]] temperament. (It is the optimal patent val for [[Porcupine family#Porcupinefish|porcupinefish]], which is about as accurate as "13-limit porcupine" will be.) Using its alternative flat fifth, it tempers out 16875/16384, making it a [[xenharmonic/negri|negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[xenharmonic/gorgo|gorgo]]/[[xenharmonic/laconic|laconic]]).
== Theory ==
37edo has very accurate approximations of harmonics [[5/1|5]], [[7/1|7]], [[11/1|11]] and [[13/1|13]], making it a good choice for a [[no-threes subgroup temperaments|no-threes]] approach. Harmonic 11 is particularly accurate, being only 0.03 cents sharp.
37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[porcupine]] temperament. It is the [[optimal patent val]] for [[Porcupine family #Porcupinefish|porcupinefish]], which is about as accurate as 13-limit porcupine extensions will be. Using its alternative flat fifth, it tempers out [[16875/16384]], making it a [[negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[gorgo]]/[[laconic]]).
37edo is also a very accurate equal tuning for [[undecimation]] temperament, which has a [[generator]] of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a [[7L 2s]] enneatonic [[mos]], which in 37edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16-note mos.
[[toc|flat]]
In the no-3 [[13-odd-limit]], 37edo maintains the smallest relative error of any edo until [[851edo]], and the smallest absolute error until [[103edo]]{{clarify}}. <!-- what is the metric being used? -->
----
=Subgroups=
=== Odd harmonics ===
37edo offers close approximations to [[xenharmonic/OverToneSeries|harmonics]] 5, 7, 11, and 13 [and a usable approximation of 9 as well].
{{Harmonics in equal|37}}
12\37 = 389.2 cents
=== Subsets and supersets ===
30\37 = 973.0 cents
37edo is the 12th [[prime edo]], following [[31edo]] and coming before [[41edo]].
17\37 = 551.4 cents
26\37 = 843.2 cents
[6\37edo = 194.6 cents]
This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111et. In fact, on the larger [[xenharmonic/k*N subgroups|3*37 subgroup]] 2.27.5.7.11.13.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas. A simpler but less accurate approach is to use the 2*37-subgroup, 2.9.7.11.13.17.19, on which it has the same tuning and commas as 74et.
[[74edo]], which doubles it, provides an alternative approximation to harmonic 3 that supports [[meantone]]. [[111edo]], which triples it, gives a very accurate approximation of harmonic 3, and manifests itself as a great higher-limit system. [[296edo]], which slices its step in eight, is a good 13-limit system.
=The Two Fifths=
=== Subgroups ===
The just [[xenharmonic/perfect fifth|perfect fifth]] of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo:
37edo offers close approximations to [[Harmonic series|harmonics]] 5, 7, 11, and 13, and a usable approximation of 9 as well.
* 12\37 = 389.2 cents
* 30\37 = 973.0 cents
* 17\37 = 551.4 cents
* 26\37 = 843.2 cents
* [6\37 = 194.6 cents]
This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as [[111edo]]. In fact, on the larger [[k*N subgroups|3*37 subgroup]] 2.27.5.7.11.13.51.57 subgroup not only shares the same tuning as 19-limit 111edo, it tempers out the same commas. A simpler but less accurate approach is to use the 2*37-subgroup, 2.9.7.11.13.17.19, on which it has the same tuning and commas as [[74edo]].
=== Dual fifths ===
The just [[perfect fifth]] of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo:
The flat fifth is 21\37 = 681.1 cents (37b val)
The flat fifth is 21\37 = 681.1 cents
The sharp fifth is 22\37 = 713.5 cents
The sharp fifth is 22\37 = 713.5 cents
21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6
21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6
If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variant of [[xenharmonic/The Biosphere|Biome]] temperament.
If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variant of [[The Biosphere|Oceanfront]] temperament.
37edo can only barely be considered as "dual-fifth", because the sharp fifth is 12 cents sharp of 3/2, has a regular diatonic scale, and can be interpreted as somewhat accurate regular temperaments like [[archy]] and the aforementioned oceanfront. In contrast, the flat fifth is 21 cents flat and the only low-limit interpretation is as the very inaccurate [[mavila]].
Interestingly, the "major thirds" of both systems are not 12\37 = 389.2¢, the closest approximation to 5/4 available in 37edo.
Since both fifths do not support [[meantone]], the "major thirds" of both systems are not 12\37 = 389.2¢, the closest approximation to 5/4 available in 37edo.
37edo has great potential as a near-just xenharmonic system, with high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions. The 9/8 approximation is usable but introduces error. One may choose to treat either of the intervals close to 3/2 as 3/2, introducing additional approximations with considerable error (see interval table below).
37edo has great potential as a near-just xenharmonic system, with high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions. The 9/8 approximation is usable but introduces error. One may choose to treat either of the intervals close to 3/2 as 3/2, introducing additional approximations with considerable error (see interval table below).
=Intervals=
=== No-3 approach ===
||~ Degrees of 37edo ||~ Cents Value ||~ Approximate Ratios
If prime 3 is ignored, 37edo represents the no-3 23-odd-limit consistently, and is distinctly consistent within the no-3 16-integer-limit.
37edo can be notated using [[ups and downs notation]]:
{| class="wikitable center-all right-2 left-3"
|-
! Degrees
! Cents
! colspan="3" | [[Ups and downs notation]]
|-
| 0
| 0.00
| Perfect 1sn
| P1
| D
|-
| 1
| 32.43
| Minor 2nd
| m2
| Eb
|-
| 2
| 64.86
| Upminor 2nd
| ^m2
| ^Eb
|-
| 3
| 97.30
| Downmid 2nd
| v~2
| ^^Eb
|-
| 4
| 129.73
| Mid 2nd
| ~2
| Ed
|-
| 5
| 162.16
| Upmid 2nd
| ^~2
| vvE
|-
| 6
| 194.59
| Downmajor 2nd
| vM2
| vE
|-
| 7
| 227.03
| Major 2nd
| M2
| E
|-
| 8
| 259.46
| Minor 3rd
| m3
| F
|-
| 9
| 291.89
| Upminor 3rd
| ^m3
| ^F
|-
| 10
| 324.32
| Downmid 3rd
| v~3
| ^^F
|-
| 11
| 356.76
| Mid 3rd
| ~3
| Ft
|-
| 12
| 389.19
| Upmid 3rd
| ^~3
| vvF#
|-
| 13
| 421.62
| Downmajor 3rd
| vM3
| vF#
|-
| 14
| 454.05
| Major 3rd
| M3
| F#
|-
| 15
| 486.49
| Perfect 4th
| P4
| G
|-
| 16
| 518.92
| Up 4th, Dim 5th
| ^4, d5
| ^G, Ab
|-
| 17
| 551.35
| Downmid 4th, Updim 5th
| v~4, ^d5
| ^^G, ^Ab
|-
| 18
| 583.78
| Mid 4th, Downmid 5th
| ~4, v~5
| Gt, ^^Ab
|-
| 19
| 616.22
| Mid 5th, Upmid 4th
| ~5, ^~4
| Ad, vvG#
|-
| 20
| 648.65
| Upmid 5th, Downaug 5th
| ^~5, vA4
| vvA, vG#
|-
| 21
| 681.08
| Down 5th, Aug 4th
| v5, A4
| vA, G#
|-
| 22
| 713.51
| Perfect 5th
| P5
| A
|-
| 23
| 745.95
| Minor 6th
| m6
| Bb
|-
| 24
| 778.38
| Upminor 6th
| ^m6
| ^Bb
|-
| 25
| 810.81
| Downmid 6th
| v~6
| ^^Bb
|-
| 26
| 843.24
| Mid 6th
| ~6
| Bd
|-
| 27
| 875.68
| Upmid 6th
| ^~6
| vvB
|-
| 28
| 908.11
| Downmajor 6th
| vM6
| vB
|-
| 29
| 940.54
| Major 6th
| M6
| B
|-
| 30
| 972.97
| Minor 7th
| m7
| C
|-
| 31
| 1005.41
| Upminor 7th
| ^m7
| ^C
|-
| 32
| 1037.84
| Downmid 7th
| v~7
| ^^C
|-
| 33
| 1070.27
| Mid 7th
| ~7
| Ct
|-
| 34
| 1102.70
| Upmid 7th
| ^~7
| vvC#
|-
| 35
| 1135.14
| Downmajor 7th
| vM7
| vC#
|-
| 36
| 1167.57
| Major 7th
| M7
| C#
|-
| 37
| 1200.00
| Perfect 8ve
| P8
| D
|}
37edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
{{Sharpness-sharp6a}}
Half-sharps and half-flats can be used to avoid triple arrows:
{{Sharpness-sharp6b}}
[[Alternative symbols for ups and downs notation#Sharp-6| Alternative ups and downs]] have sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp6}}
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt}}
=== Ivan Wyschnegradsky's notation ===
Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used:
{{Sharpness-sharp6-iw}}
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[23edo#Second-best fifth notation|23b]], [[30edo#Sagittal notation|30]], and [[44edo#Sagittal notation|44]].
==== Evo and Revo flavors ====
<imagemap>
File:37-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 599 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:37-EDO_Sagittal.svg]]
</imagemap>
==== Alternative Evo flavor ====
<imagemap>
File:37-EDO_Alternative_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 639 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
rect 300 0 623 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]]
default [[File:37-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.5
| {{monzo| 86 -37 }}
| {{mapping| 37 86 }}
| −0.619
| 0.619
| 1.91
|-
| 2.5.7
| 3136/3125, 4194304/4117715
| {{mapping| 37 86 104 }}
| −0.905
| 0.647
| 2.00
|-
| 2.5.7.11
| 176/175, 1375/1372, 65536/65219
| {{mapping| 37 86 104 128 }}
| −0.681
| 0.681
| 2.10
|-
| 2.5.7.11.13
| 176/175, 640/637, 847/845, 1375/1372
| {{mapping| 37 86 104 128 137 }}
| −0.692
| 0.610
| 1.88
|}
* 37et is most prominent in the no-3 11-, 13-, 17-, 19- and 23-limit subgroups. The next equal temperaments doing better in these subgroups are 109, 581, 103, 124 and 93, respectively.
=== Rank-2 temperaments ===
* [[List of 37et rank two temperaments by badness]]
|| 16\37 || || **Not** [[xenharmonic/mavila|mavila]] (this is "undecimation") ||
|| 17\37 || [[xenharmonic/Emka|Emka]] || ||
|| 18\37 || || ||
; [[Ray Perlner]]
* [https://www.youtube.com/watch?v=8reCr2nDGbw ''Porcupine Lullaby''] (2020) – in Porcupine, 37edo tuning
* [https://www.youtube.com/watch?v=j8C9ECvfyQM ''Fugue for Brass in 37EDO sssLsss "Dingoian"''] (2022) – in Porcupine[7], 37edo tuning
* [https://www.youtube.com/watch?v=_xfvNKUu8gY ''Fugue for Klezmer Band in 37EDO Porcupine<nowiki>[</nowiki>7<nowiki>]</nowiki> sssssLs "Lemurian"''] (2023) – in Porcupine[7], 37edo tuning
=Music in 37edo=
; [[Phanomium]]
[[http://www.akjmusic.com/audio/toccata_bianca_37edo.mp3|Toccata Bianca 37edo]] by [[http://www.akjmusic.com/|Aaron Krister Johnson]]
[[@http://andrewheathwaite.bandcamp.com/track/shorn-brown|Shorn Brown]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2002%20Shorn%20Brown.mp3|play]] and [[@http://andrewheathwaite.bandcamp.com/track/jellybear|Jellybear]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2003%20Jellybear.mp3|play]] by [[xenharmonic/Andrew Heathwaite|Andrew Heathwaite]]
* [https://www.youtube.com/watch?v=BbexOU-9700 ''cat jam 37''] (2025)
[[http://micro.soonlabel.com/gene_ward_smith/Others/Monzo/monzo_kog-sisters_2014-0405.mp3|The Kog Sisters]] by [[Joe Monzo]]
=Links=
; [[Togenom]]
[[http://tonalsoft.com/enc/number/37-edo/37edo.aspx|37edo at Tonalsoft]]</pre></div>
* "Canals of Mars" from ''Xenharmonics, Vol. 5'' (2024) – [https://open.spotify.com/track/7v2dpCjiRKUfVVBZw8aWSf Spotify] |[https://togenom.bandcamp.com/track/canals-of-mars Bandcamp] | [https://www.youtube.com/watch?v=qPcEl_bifC0 YouTube]
37edo is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th <a class="wiki_link" href="http://xenharmonic.wikispaces.com/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/31edo">31edo</a> and coming before <a class="wiki_link" href="http://xenharmonic.wikispaces.com/41edo">41edo</a>.<br />
<br />
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/porcupine">porcupine</a> temperament. (It is the optimal patent val for <a class="wiki_link" href="/Porcupine%20family#Porcupinefish">porcupinefish</a>, which is about as accurate as &quot;13-limit porcupine&quot; will be.) Using its alternative flat fifth, it tempers out 16875/16384, making it a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/negri">negri</a> tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/gorgo">gorgo</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/laconic">laconic</a>).<br />
<br />
37 edo is also a very accurate equal tuning for Undecimation Temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS.<br />
37edo offers close approximations to <a class="wiki_link" href="http://xenharmonic.wikispaces.com/OverToneSeries">harmonics</a> 5, 7, 11, and 13 [and a usable approximation of 9 as well].<br />
<br />
12\37 = 389.2 cents<br />
30\37 = 973.0 cents<br />
17\37 = 551.4 cents<br />
26\37 = 843.2 cents<br />
[6\37edo = 194.6 cents]<br />
<br />
This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111et. In fact, on the larger <a class="wiki_link" href="http://xenharmonic.wikispaces.com/k%2AN%20subgroups">3*37 subgroup</a> 2.27.5.7.11.13.51.57 subgroup not only shares the same tuning as 19-limit 111et, it tempers out the same commas. A simpler but less accurate approach is to use the 2*37-subgroup, 2.9.7.11.13.17.19, on which it has the same tuning and commas as 74et.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="The Two Fifths"></a><!-- ws:end:WikiTextHeadingRule:2 -->The Two Fifths</h1>
The just <a class="wiki_link" href="http://xenharmonic.wikispaces.com/perfect%20fifth">perfect fifth</a> of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo:<br />
<br />
The flat fifth is 21\37 = 681.1 cents<br />
The sharp fifth is 22\37 = 713.5 cents<br />
<br />
21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6<br />
If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variant of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Biosphere">Biome</a> temperament.<br />
<br />
Interestingly, the &quot;major thirds&quot; of both systems are not 12\37 = 389.2¢, the closest approximation to 5/4 available in 37edo.<br />
<br />
37edo has great potential as a near-just xenharmonic system, with high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions. The 9/8 approximation is usable but introduces error. One may choose to treat either of the intervals close to 3/2 as 3/2, introducing additional approximations with considerable error (see interval table below).<br />
<a class="wiki_link" href="/List%20of%2037et%20rank%20two%20temperaments%20by%20badness">List of 37et rank two temperaments by badness</a><br />
37 equal divisions of the octave (abbreviated 37edo or 37ed2), also called 37-tone equal temperament (37tet) or 37 equal temperament (37et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 37 equal parts of about 32.4 ¢ each. Each step represents a frequency ratio of 21/37, or the 37th root of 2.
37edo has very accurate approximations of harmonics 5, 7, 11 and 13, making it a good choice for a no-threes approach. Harmonic 11 is particularly accurate, being only 0.03 cents sharp.
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of porcupine temperament. It is the optimal patent val for porcupinefish, which is about as accurate as 13-limit porcupine extensions will be. Using its alternative flat fifth, it tempers out 16875/16384, making it a negri tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth (gorgo/laconic).
37edo is also a very accurate equal tuning for undecimation temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L 2s enneatonic mos, which in 37edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16-note mos.
74edo, which doubles it, provides an alternative approximation to harmonic 3 that supports meantone. 111edo, which triples it, gives a very accurate approximation of harmonic 3, and manifests itself as a great higher-limit system. 296edo, which slices its step in eight, is a good 13-limit system.
Subgroups
37edo offers close approximations to harmonics 5, 7, 11, and 13, and a usable approximation of 9 as well.
12\37 = 389.2 cents
30\37 = 973.0 cents
17\37 = 551.4 cents
26\37 = 843.2 cents
[6\37 = 194.6 cents]
This means 37 is quite accurate on the 2.5.7.11.13 subgroup, where it shares the same tuning as 111edo. In fact, on the larger 3*37 subgroup 2.27.5.7.11.13.51.57 subgroup not only shares the same tuning as 19-limit 111edo, it tempers out the same commas. A simpler but less accurate approach is to use the 2*37-subgroup, 2.9.7.11.13.17.19, on which it has the same tuning and commas as 74edo.
Dual fifths
The just perfect fifth of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo:
The flat fifth is 21\37 = 681.1 cents (37b val)
The sharp fifth is 22\37 = 713.5 cents
21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6
If the minor third of 259.5 cents is mapped to 7/6, this superpythagorean scale can be thought of as a variant of Oceanfront temperament.
37edo can only barely be considered as "dual-fifth", because the sharp fifth is 12 cents sharp of 3/2, has a regular diatonic scale, and can be interpreted as somewhat accurate regular temperaments like archy and the aforementioned oceanfront. In contrast, the flat fifth is 21 cents flat and the only low-limit interpretation is as the very inaccurate mavila.
Since both fifths do not support meantone, the "major thirds" of both systems are not 12\37 = 389.2¢, the closest approximation to 5/4 available in 37edo.
37edo has great potential as a near-just xenharmonic system, with high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions. The 9/8 approximation is usable but introduces error. One may choose to treat either of the intervals close to 3/2 as 3/2, introducing additional approximations with considerable error (see interval table below).
No-3 approach
If prime 3 is ignored, 37edo represents the no-3 23-odd-limit consistently, and is distinctly consistent within the no-3 16-integer-limit.
37et is most prominent in the no-3 11-, 13-, 17-, 19- and 23-limit subgroups. The next equal temperaments doing better in these subgroups are 109, 581, 103, 124 and 93, respectively.
