37edo

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Note from User:ground: hey sorry this was copied from my notes so I'm gradually making my way through the formatting

37edo is the tuning that I use the largest number of distinct scales in. Here are the ones I could think of:

• 5:2:1 trackdye 5L2m8s
  • Step tunings: (227¢) : 162¢ : 97¢ : 62¢
  • This is the quintessential Aberration scale. There are seven possible structures depending on which diatonic mode you choose to aberrate. It's basically 12edo with all the 13-limit intervals that make 37edo so strong.
• 5:3:2 blackdye 5L2m3s
  • Step tunings: (227¢) : 162¢ : 97¢ : 62¢, patent val (9/8) : 10/9 : 16/15 : 81/80
  • A subset of Ultrapyth[17], rather 15edo-like. It's close to the m=s Blackwood degenerate tuning, and the patent val 10/9 is a Porcupine neutral second. The 65¢ interval is possibly usable as an aberrisma, but too wide for me. I think it makes sense to use Blackwood cues here to apply it as a sort of alternate semitone, although I don't have much experience doing this. I usually just avoid it and insert fragments of the neogothic blackdye when I want an aberrisma.
  • Acute Minor / Grave Major modes: The standard pental scales of 37edo. The harmony is quite nice, the semitone is familiarly sized, but the whole tones are very distorted, leading to a scale that makes it trivial to achieve a xenharmonic sound. This is one of my favorite things about 37edo.
  • Grave Minor / Acute Major modes: One way to improve septal melody over the diatonic scale. I prefer the sound of the neogothic blackdye for this, but this one has the possible advantage of using the 422¢ major third in grave Aeolian and Dorian, which is more third-like than the 454¢ alternative.
• 6:2:1 blackdye 5L2m3s
  • Step tunings: (227¢) : 195¢ : 65¢ : 32¢
  • A subset of Ultrapyth[12], one of the two simple neogothic blackdye scales, the other being 32edo's 5:2:1. The melody is something expected from septal diasem, which makes it desirable to infuse that quality into 37edo music. The aberrisma is medium-small, which is very versatile.
  • Acute Minor / Grave Major modes: The standard neogothic scales of 37edo. On top of the melodic properties, I also like neogothic minor chords, so I use this one about as much as the pental blackdye.
  • Grave Minor / Acute Major modes: My preferred way to insert subminor thirds into 37edo music. Just like in the pental blackdye, no mode exists that has the inframinor sixth and diatonic fifth over the tonic, so I don't use this scale in its entirety, instead opting to mix its structures with other modes and scales.
• 7:1 diatonic 5L2s
  • Step tunings: 227¢ : 32¢
  • Ultrapyth[7], or Oceanfront temperament in other words. Just like with neogothic blackdye, the other Oceanfront tuning is 32edo's 6:1. This is about as hard as you can push a diatonic scale before it stops making sense, as the 454¢ major third is an effectively just 13/10, the interseptimal on the boundary between major thirds and subfourths. It still has a usable 7/6 however, due to the fifth being so sharp, and I often prefer 13/10 to 9/7 anyway because it's past the peak of "majorness". Diatonic context is powerful, so as long as the instrumentation allows the comma-sized semitones to be audible, chords and melodies still make sense.
• 6:3:1 pinedye R/L 5L2m1s
  • Step tunings: (227¢) : 195¢ : 97¢ : 32¢
  • Unlike softer tunings like 27edo's 4:3:1, this doesn't much resemble the pental JI tuning. Instead it's closer to 25edo's 4:2:1, a compressed 12edo diatonic that uses both the flat and sharp fifth. The compressed thirds are close to 13/11 and 5/4, an excellent combination to my preference.
• 5:4:2 diasem R/L 5L2m2s
  • Step tunings: (227¢) : 162¢ : 130¢ : 65¢
  • This is 37edo's only tuning of diasem, and a highly distorted one at that, using the flat fifth instead of the sharp diatonic one. Like pinedye, it combines ~13/11 and ~5/4, but with no alternate fifth. I don't use this much, but it's worth mentioning because of its connection to the other scales, and the fact that it's the only concrete scale on this list to have a 130¢ step. Because the s step is 2\37, it can be split in half for a related 5:4:1 diaslen 5L2m4s.
• 6:1 archaeotonic 6L1s and 5:1 6L7s
  • Step tunings: (227¢) : 195¢ : 32¢ and (195¢) : 162¢ : 32¢
  • These are the scales of the whole-tone Didacus temperament. Normally I would just use archaeotonic, but 37edo's tuning is only remarkable when extended to higher limits.
• 7:5 onyx 1L6s and 5:2 pine 7L1s
  • Step tunings: 227¢ : 162¢ and (227¢) : 162¢ : 65¢
  • I don't use much Porcupine, but when I do, this is basically the perfect tuning. A better 6/5 than 27edo, a better 3/2 than 15edo, and a better 5/4 and 11/8 than both. Porcupine structures occasionally show up when I write chord progressions, which is always cool because I like neutral seconds.
• 7:3 smitonic 4L3s
  • Step tunings: 227¢ : 97¢
  • I've long been an enjoyer of the 5|1 "Vivecan" mode of smitonic. It's one of the few scales that I prefer to tune soft rather than hard, but tunings that are basic or slightly harder allow access to the very good 2.7.11 Orgone temperament. Being used to 11edo, I prefer this to the slightly harder 26edo tuning. I've been learning to accept ~11/7 as a fifth, extended from 11edo's ~14/9.
• 5:2 slentonic 5L6s
  • Step tunings: (227¢) : 162¢ : 65¢
  • This might be the weirdest one. I normally want Slendric for this scale structure rather than Laconic, but I've been using this to test the boundaries of my perception for drastically compressed and stretched diatonic-coded intervals. 8/7 isn't a minor third, but it might possibly be usable as one in this scale, for example.
• TODO Things I missed: mosh, mosh3s, 11/8-generated low-complexity 2.11.13 temperament, oneirotonic (I find it most useful for the 8edo-like chords it generates), neutral second mod-ternary scale, dia8s (7 orders; TODO MOS-substitution naming of step orders for ambiguous step signatures), Shallowtone[16] (or [12] for a smaller ternary scale more analogous to deeptone)

37edo chord list also from Discord

My quasi-diatonic chord set in 37edo is like

• neominor [[7th]] (basic minor)
• compressed 6:7:9 (basic subminor which I don't use nearly enough)
• compressed 9:12:16:19 with stretched 9:12 (basic 47b9 ground chord)
• pental major/minor [[7th]] (basic major, alternate minor)
• pentagoth major (alternate major)
• ~10:13:15 (like major with sus quality)
• various approximations of sus4 [7th]
• ~[4]:5:6:7 (basic dominant/diminished)
• 16:19:22 (alternate diminished)
• 8:11:13 (basic superfourth/subfifth chord, tempered retroversion of 13:16:19)

Triad inversions are considered the same chord. Major and minor can be swapped (triads or tetrads retroverted), but these are situation-specific.

37edo has a nearly perfect stretched gentle triad:

1200*13/37*log2(13/11*14/11)/(22/37)

= 417.606

1200*log2(14/11)

= 417.508

1200*9/37*log2(13/11*14/11)/(22/37)

= 289.112

1200*log2(13/11)

= 289.210

I don’t know if this is audibly significant, but at least it’s a cool justification for specifically 37edo as a neogothic blackdye tuning.