Talk:Comma

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Calculated 5–limit commas

I was in a calculation of 5–limit commas 4294967296 integer limit below 100 cents. The calculation was blazingly fast but was in a rudimentary format.

List 1:

1600000/1594323 6.153558074133514
81/80 21.5062895967165
131072000/129140163 25.70612688291476
20000/19683 27.65984767084646
128/125 41.05885840550059
6561/6400 43.012579193433 (square of 81/80)
43046721/41943040 44.96629998136541
1638400/1594323 47.21241647963268
250/243 49.166137267562604
648/625 62.565148002217086
531441/512000 64.51886879015092 (cube of 81/80)
3486784401/3355443200 66.4725895780748
20480/19683 68.71870607634492
25/24 70.67242686427875
43046721/40960000 86.025158386866 (fourth power of 81/80)
409600000/387420489 96.37855374719493

6561 3125 84.07143759893216 3 3125 29.613568458779582 129140163 15625 15.352731522582985 59049 15625 98.33227453512521 243 15625 8.107278862061662 1 15625 82.11771681100117 4782969 78125 76.825984938408 19683 78125 13.399010734655548 387420489 390625 55.31969534169292 1594323 390625 34.905300331368494 729 390625 78.77970572634041 3 390625 11.445289946721005 129140163 1953125 56.41158992808357 59049 1953125 57.27341612962533 243 1953125 32.951579543438925 4782969 9765625 35.767126532910254 19683 9765625 54.457869140154 9 9765625 59.227136917559164 387420489 48828125 14.260836936190913 1594323 48828125 75.9641587368705 729 48828125 37.7208473208384 3 48828125 52.504148352227276 129140163 244140625 97.47044833358558 59049 244140625 16.214557724123324 243 244140625 74.01043794894235 1162261467 1220703125 84.93326380046966 4782969 1220703125 5.291731872591754 19683 1220703125 95.51672754565459 9 1220703125 18.168278512052893

List 2: 2197265625 39.674568108773656 263671875 30.997858755506513 4271484375 9.491569158785751 17578125 80.73342651427424 512578125 80.1639960230716 2109375 10.060999649994073 34171875 31.56728924670915 15625 82.11771681100117 553584375 53.073578843429914 253125 60.611427214286095 4100625 39.10513761757102 16875 51.11985805549466 66430125 17.59884802085594 273375 72.62614765220974 125 41.05885840550059 1076168025 3.907441575864823 4428675 94.1324372489305 2025 19.55256880878551 7971615 88.27127488513042 32805 1.9537207879324114 135 92.17871646099525 129140163 66.76498528842103 531441 23.46001038464749 243 90.22499567306284 1 0

List 1 repeats 3 numbers: a power of 3, a power of 5 and a cents value. The fractions have to be manually multiplied with powers of two for octave reduction.

List 2 repeats 2 numbers: a fraction part and a cents value. The fraction part must be counterparted with a power of two.

There may also be redundant squares, cubes, etc. of the fractions. Hope we can get a complete comma list from it!

And someone, please merge Comma with Unnoticeable commas back so that we can have a closer comparison, and complete blank fraction spaces up to like 25 digits.

PiotrGrochowski (talk) 11:54, 18 September 2018 (UTC)