User:BudjarnLambeth/My favourite hexanies using at least one odd greater than 15

Main article: Gallery of combination product sets

Top favourites

The ones from the below lists that I like the most :)

5-7-15-17 hexany

(best when rotated above 17/14) (a 17-limit scale with consonances, that doesn't sound at all like 12edo) (here's a musical example (on YouTube))

Rotated intervals:

• 21/17
• 7/5
• 3/2
• 28/17
• 30/17
• 2/1

3-7-9-19 hexany

(best when unrotated) (pretty, floaty, aquatic sound with a bendy quarter/sixth-tone; like bubbles in a coral reef)

Intervals:

• 57/56
• 9/7
• 19/14
• 3/2
• 19/12
• 2/1

1-13-19-23 hexany

(best when rotated above 19/16) (very fun to use because of the two distinct flavours of neutral thirds and the 368/247 which is a better 3/2 than 7edo)

Rotated intervals:

• 23/19
• 16/13
• 368/247
• 32/19
• 23/13
• 2/1

7-19-21-23 hexany

(best when rotated above 23/19) (sounds halfway between 6afdo and the porcupine[6] MOS scale)

Rotated intervals:

• 57/46
• 19/14
• 3/2
• 38/23
• 42/23
• 2/1

17-odd-limit

• 1-3-5-17 hexany (best when unrotated) (sounds like a cross between the augmented and whole tone scales)
• 1-7-13-17 hexany (best when rotated above 13/8) (a really pretty pentachord with a bendy quarter tone interval that sounds xenharmonic in a pleasing way)
• 3-5-9-17 hexany (best when rotated above 17/10; almost exactly approximated in 12edo, and yet it sounds quite 'xenmelodic', very non-diatonic, a little Stravinsky-esque)
• 3-9-15-17 hexany (best when rotated above 17/9) (sounds like a subset of an over-17, neji of 12edo; sounds like phrygian dominant hexatonic)
• 5-7-15-17 hexany (best when rotated above 17/14) (a 17-limit scale with consonances, that doesn't sound at all like 12edo)
• 5-13-15-17 hexany (best when rotated above 17/13) (sounds dissonant if you try to use diatonic methods but if approached on its own terms, has some really beautiful sparkly consonances)
• 7-9-11-17 hexany (best when rotated above 187/126) (sounds dissonant if you try to use diatonic methods but if approached on its own terms, has some really beautiful sparkly consonances)

19-odd-limit

• 1-3-11-19 hexany (best when rotated above 19/12) (as JI it sounds melodically but not harmonically nice, but when tempered to 15edo, 27edo, 31edo, or 34edo, it sounds gorgeous both melody- and harmony-wise)
• 1-3-17-19 hexany (best when rotated above 19/12) (sounds like a subset of an over-19, neji of 12edo; sounds like phrygian dominant hexatonic)
• 1-11-13-19 hexany (best when rotated above 13/8) (very xenharmonic scale with no fifth; has an interval that is just small enough (~8 cents) that it switches between sounding like two versions of the same note or two different notes, like an optical illusion with sound)
• 1-13-15-19 hexany (best when rotated above 19/16) (very xenharmonic scale with no fifth; the 336/247 acts as a pseudo-11/8)
• 3-5-11-19 hexany (best when unrotated) (a possible 19-limit detempering of the augmented[6] MOS)
• 3-5-15-19 hexany (best when unrotated) (another possible 19-limit detempering of the augmented[6] MOS)
• 3-7-9-19 hexany (best when unrotated) (pretty, floaty, aquatic sound with a bendy quarter/sixth-tone; like bubbles in a coral reef)
• 3-7-11-19 hexany (best when rotated above 11/6) (oceanic; very dissonant, but yet sparkly and oddly sweet)

21-odd-limit

• 1-3-19-21 hexany (best when rotated above 7/4) (sounds like a very mournful, grief-stricken version of hexatonic minor; sounds best with string instrument timbres like cello)
• 1-7-11-21 hexany (best when rotated above 11/8) (extremely dissonant, but in a potentially fun way if used with skill; sounds creepy, violent, shadowy)
• 3-5-7-21 hexany (best when rotated above 7/5; surprisingly xenharmonic in sound despite not being that far off 12edo; sounds halfway between lydian and locrian, as if they got so far away from each other that they started to come back together again: more lydian than lydian and more locrian than locrian)
• 3-5-9-21 hexany (best when unrotated) (having both a harmonic 7th (7/4) and a classic minor 7th (9/5), it is an excellent scale for training a composer or musician to feel the difference between those two main types of minor 7th, which normally get tempered away into one interval in 12edo, but actually have quite different characters)
• 3-7-9-21 hexany (best when unrotated) (the otonalpentad but with 9/7 replacing 5/4)
• 5-9-15-21 hexany (best when unrotated) (quite xenharmonic, the 21 comes through much more than one would imagine)
• 7-9-11-21 hexany (best when unrotated) (augmented but from a parallel universe where everything is inside-out and cooler; you could think of it as "antipental augmented" in the same way that antipental blues works)

23-odd-limit

• 1-3-5-23 hexany (best when rotated above 23/12) (like phrygian dominant hexatonic, but with a 23-limit fourth close to 13/10, and a close pseudo-7/4 tuned very far away from 12edo)
• 1-7-11-23 hexany (best when rotated above 253/224) (very xenharmonic, probably requiring the use of xentimbres; melodically very interesting - like a cross between antipental blues and the whole tone scale (6edo))
• 1-13-19-23 hexany (best when rotated above 19/16) (very fun to use because of the two distinct flavours of neutral thirds and the 368/247 which is a better 3/2 than 7edo)
• 3-15-19-23 hexany (best when rotated above 19/15) (like a quite xenharmonic, and very hard tuning of the augmented[6] MOS scale)
• 7-19-21-23 hexany (best when rotated above 23/19) (sounds halfway between 6afdo and the porcupine[6] MOS scale)

Higher limits

to be completed...