Hemififths: Difference between revisions

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Add 13-limit ratios
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== Interval Chain ==
== Interval Chain ==
{| class="wikitable center-1 right-2 center-3"
{| class="wikitable center-all right-2"
! #
! rowspan="2" | #
! Cents*
! rowspan="2" | Cents*
! Approximate Ratios
! colspan="2" | Approximate Ratios
|-
!11-limit
!13-limit
|-
|-
|0
|0
|0.000
|0.000
|1/1
|1/1
|
|-
|-
|1
|1
|351.477
|351.477
|11/9~27/22
|11/9~27/22
|16/13~39/32
|-
|-
|2
|2
|702.955
|702.955
|3/2
|3/2
|
|-
|-
|3
|3
|1054.432
|1054.432
|11/6
|11/6
|24/13
|-
|-
|4
|4
|205.910
|205.910
|9/8
|9/8
|
|-
|-
|5
|5
|557.387
|557.387
|11/8
|11/8
|18/13
|-
|-
|6
|6
|908.865
|908.865
|27/16
|27/16
|22/13
|-
|-
|7
|7
|60.342
|60.342
|33/32~28/27
|33/32~28/27
|27/26
|-
|-
|8
|8
|411.819
|411.819
|14/11~81/64~80/63
|14/11~81/64~80/63
|33/26
|-
|-
|9
|9
|763.297
|763.297
|14/9
|14/9
|
|-
|-
|10
|10
|1114.774
|1114.774
|21/11~40/21
|21/11~40/21
|
|-
|-
|11
|11
|266.252
|266.252
|7/6
|7/6
|
|-
|-
|12
|12
|617.729
|617.729
|10/7
|10/7
|
|-
|-
|13
|13
|969.206
|969.206
|7/4
|7/4
|
|-
|-
|14
|14
|120.684
|120.684
|15/14
|15/14
|14/13
|-
|-
|15
|15
|472.161
|472.161
|21/16
|21/16
|
|-
|-
|16
|16
|823.639
|823.639
|45/28
|45/28
|21/13
|-
|-
|17
|17
|1175.116
|1175.116
|63/32~160/81
|63/32~160/81
|
|-
|-
|18
|18
|326.594
|326.594
|40/33
|40/33
|
|-
|-
|19
|19
|678.071
|678.071
|40/27
|40/27
|
|-
|-
|20
|20
|1029.549
|1029.549
|20/11
|20/11
|
|-
|-
|21
|21
|181.026
|181.026
|10/9
|10/9
|
|-
|-
|22
|22
|532.503
|532.503
|15/11
|15/11
|
|-
|-
|23
|23
|883.981
|883.981
|5/3
|5/3
|
|-
|-
|24
|24
|35.458
|35.458
|45/44~55/54
|45/44~55/54
|
|-
|-
|25
|25
|386.936
|386.936
|5/4
|5/4
|
|}
|}
<nowiki>*</nowiki>in 7-limit POTE tuning
<nowiki>*</nowiki>in 7-limit POTE tuning

Revision as of 02:14, 7 June 2020

See Breedsmic temperaments.

Gencom: [2 11/9; 144/143 196/195 243/242 364/363]

Gencom map: [<1 1 -5 -1 2 4|, <0 2 25 13 5 -1|]

Interval Chain

# Cents* Approximate Ratios
11-limit 13-limit
0 0.000 1/1
1 351.477 11/9~27/22 16/13~39/32
2 702.955 3/2
3 1054.432 11/6 24/13
4 205.910 9/8
5 557.387 11/8 18/13
6 908.865 27/16 22/13
7 60.342 33/32~28/27 27/26
8 411.819 14/11~81/64~80/63 33/26
9 763.297 14/9
10 1114.774 21/11~40/21
11 266.252 7/6
12 617.729 10/7
13 969.206 7/4
14 120.684 15/14 14/13
15 472.161 21/16
16 823.639 45/28 21/13
17 1175.116 63/32~160/81
18 326.594 40/33
19 678.071 40/27
20 1029.549 20/11
21 181.026 10/9
22 532.503 15/11
23 883.981 5/3
24 35.458 45/44~55/54
25 386.936 5/4

*in 7-limit POTE tuning

Spectrum of Hemififths Tunings by Eigenmonzos

Eigenmonzo Neutral Third
11/9 347.408
12/11 349.788
7\24 350.000
11/8 350.264
4/3 350.978
12\41 351.220
15/14 351.389
16/15 351.417
41\140 351.429
8/7 351.448 (7, 9 and 11 limit hemif minimax)
5/4 351.453 (5, 7, 9 and 11 limit minimax)
7/5 351.457
6/5 351.494
29\99 351.515
7/6 351.534
10/9 351.543
9/7 351.657
15/11 351.680
15/13 351.705 (15 limit minimax)
17\58 351.724
11/10 351.750
13/10 351.761 (13 limit minimax)
13/11 351.798 (13 and 15 limit hemif minimax)
22\75 352.000
14/13 352.021
14/11 352.188
18/13 352.676
13/12 353.809
16/13 359.472
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