TemperamentOrphanage

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Welcome to the Temperament Orphanage

These temperaments need to be adopted into a family

These are some temperaments that were found floating around. It isn't clear what family they belong to, so for now they're in the temperament orphanage. Should you know how to match these temperaments back up with their temperament family, feel free to remove them from the orphanage and put them on the right page. If a temperament listed doesn't have a name, give it a name.

Please give a short description of whatever temperament you leave here so that someone can help to match this temperament back to its rightful progenitors.

Smite - 5-limit - tempers 3125/2916

7&25 temperament. It equates (6/5)^5 with 8/3. It is also called "sixix", a name by Petr Parizek which has priority. The generator is a really sharp minor third, the contraction of which is "smite."

POTE generator: ~6/5 = 338.365

Map: [<1 3 4|, <0 -5 -6|]

EDOs: 7, 25, 32

Smate - 5-limit - tempers 2048/1875

3&8b temperament. It equates (5/4)^4 with 8/3. It is so named because the generator is a sharp major third. I don't think "smate" is actually a word, but it is now.

POTE generator: ~5/4 = 420.855

Map: [<1 2 3|, <0 -4 1|]

Status: Adopted

Enipucrop - 5-limit - tempers 1125/1024

6b&7 temperament. Its name is "porcupine" spelled backwards, because that's what this temperament is - it's porcupine, with the generator sharp of 2\7 such that the major and minor thirds switch places. The fifths are very flat, meaning that this is more of a melodic temperament than a harmonic one.

POTE generator: ~16/15 = 173.101

Map: [<1 2 2|, <0 -3 2|]

Absurdity - 5-limit - tempers 10460353203/10240000000

7&84 temperament. So named because this is just an absurd temperament. If you have a better name for it then it doesn't have to be absurdity anymore. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also a part of the syntonic-chromatic equivalence continuum, in this case where (81/80)^5 = 25/24.

http://x31eq.com/cgi-bin/rt. cgi?ets=7_84&limit=5

POTE generator: ~10/9 = 185.901 cents

Map: [<7 0 -17|, <0 1 3|]

EDOs: 7, 70, 77, 84, 91, 161

Sevond - 5-limit - tempers 5000000/4782969

This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4.

POTE generator: ~3/2 = 706.288 cents

Map: [<7 0 -6|, <0 1 2|]

EDOs: 7, 42, 49, 56, 119

Adding 875/864 to the commas extends this to the 7-limit:

POTE generator: ~3/2 = 705.613 cents

Map: [<7 0 -6 53|, <0 1 2 -3|]

EDOs: 7, 56, 63, 119

http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&limit=5

Seville - 5-limit - tempers 78125/69984

This is similar to the above, but provides a less complex avenue to 5, but this time at the sake of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4.

Comma: 78125/69984

POTE generator: ~3/2 = 706.410 cents

Map: [<7 0 5|, <0 1 1|]

EDOs: 7, 56

http://x31eq.com/cgi-bin/rt.cgi?ets=7_49c&limit=5