32edt: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Wikispaces>FREEZE
No edit summary
Spt3125 (talk | contribs)
autopatrolled, Sysops
523 edits
m formatting, unified precision
Line 1: Line 1:
''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
|}
|}

Revision as of 17:55, 8 December 2018

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 zeta peak tritave division.

Intervals

step cents
1 59.436
2 118.872
3 178.308
4 237.744
5 297.180
6 356.617
7 416.053
8 475.489
9 534.925
10 594.361
11 653.797
12 713.233
13 772.669
14 832.105
15 891.541
16 950.978
17 1010.414
18 1069.850
19 1129.286
20 1188.722
21 1248.158
22 1307.594
23 1367.030
24 1426.466
25 1485.902
26 1545.338
27 1604.775
28 1664.211
29 1723.647
30 1783.083
31 1842.519
32 1901.955
Retrieved from "https://en.xen.wiki/index.php?title=32edt&oldid=38895"