32edt: Difference between revisions

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''32edt'' means the division of 3, the tritave, into 32 equal parts of 59.436 cents each, corresponding to 20.190 edo. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13 and 17 are all sharp. It tempers out 3125/3087 in the 7-limit, 891/875, 1331/1323 and 2475/2401 in the 11-limit, 275/273, 351/343, 729/714, 847/845 and 1575/1573 in the 13-limit, 121/119, 189/197 and 225/221 in the 17-limit. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|zeta peak tritave division]].
''32edt'' means the division of 3, the tritave, into 32 equal parts of 59.436 cents each, corresponding to 20.190 edo. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13 and 17 are all sharp. It tempers out 3125/3087 in the 7-limit, 891/875, 1331/1323 and 2475/2401 in the 11-limit, 275/273, 351/343, 729/714, 847/845 and 1575/1573 in the 13-limit, 121/119, 189/197 and 225/221 in the 17-limit. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|zeta peak tritave division]].


=<span style="font-size: 1.4em;">Intervals</span>=
=Intervals=


{| class="wikitable"
{| class="wikitable"
|-
! step
! cents
|-
|-
| | 1
| | 1
| | 59.43609¢
| | 59.436
|-
|-
| | 2
| | 2
| | 118.87219
| | 118.872
|-
|-
| | 3
| | 3
| | 178.30828
| | 178.308
|-
|-
| | 4
| | 4
| | 237.74438
| | 237.744
|-
|-
| | 5
| | 5
| | 297.18047
| | 297.180
|-
|-
| | 6
| | 6
| | 356.61656
| | 356.617
|-
|-
| | 7
| | 7
| | 416.05266
| | 416.053
|-
|-
| | 8
| | 8
| | 475.48875
| | 475.489
|-
|-
| | 9
| | 9
| | 534.92484
| | 534.925
|-
|-
| | 10
| | 10
| | 594.36094
| | 594.361
|-
|-
| | 11
| | 11
| | 653.79703
| | 653.797
|-
|-
| | 12
| | 12
| | 713.23312
| | 713.233
|-
|-
| | 13
| | 13
| | 772.66922
| | 772.669
|-
|-
| | 14
| | 14
| | 832.10531
| | 832.105
|-
|-
| | 15
| | 15
| | 891.54141
| | 891.541
|-
|-
| | 16
| | 16
| | 950.9775
| | 950.978
|-
|-
| | 17
| | 17
| | 1010.41359
| | 1010.414
|-
|-
| | 18
| | 18
| | 1069.84969
| | 1069.850
|-
|-
| | 19
| | 19
| | 1129.28578
| | 1129.286
|-
|-
| | 20
| | 20
| | 1188.72188
| | 1188.722
|-
|-
| | 21
| | 21
| | 1248.15797
| | 1248.158
|-
|-
| | 22
| | 22
| | 1307.59406
| | 1307.594
|-
|-
| | 23
| | 23
| | 1367.03016
| | 1367.030
|-
|-
| | 24
| | 24
| | 1426.46625
| | 1426.466
|-
|-
| | 25
| | 25
| | 1485.90234
| | 1485.902
|-
|-
| | 26
| | 26
| | 1545.33844
| | 1545.338
|-
|-
| | 27
| | 27
| | 1604.77453
| | 1604.775
|-
|-
| | 28
| | 28
| | 1664.21063
| | 1664.211
|-
|-
| | 29
| | 29
| | 1723.64672
| | 1723.647
|-
|-
| | 30
| | 30
| | 1783.08281
| | 1783.083
|-
|-
| | 31
| | 31
| | 1842.51891
| | 1842.519
|-
|-
| | 32
| | 32
| | 1901.955
| | 1901.955
|}
|}