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See [[Breedsmic temperaments #Hemififths]].
The '''hemififths''' temperament tempers out the breedsma, [[2401/2400]], and the hemifamity comma, [[5120/5103]], and as the name suggests, uses a neutral-third generator. '''Hemif''' is the no-5 subgroup version of hemififths.  


Gencom: [2 11/9; 144/143 196/195 243/242 364/363]
See [[Breedsmic temperaments #Hemififths]] for more technical data.


Gencom map: [<1 1 -5 -1 2 4|, <0 2 25 13 5 -1|]
== Interval chain ==
 
In the following table, prime harmonics are labeled in '''bold'''.
== Interval Chain ==
{| class="wikitable center-1 right-2"
{| class="wikitable center-all right-2"
! rowspan="2" | #
! rowspan="2" | #
! rowspan="2" | Cents*
! rowspan="2" | Cents*
! colspan="2" | Approximate Ratios
! colspan="2" | Approximate Ratios
|-
|-
!11-limit
! 7-limit
!13-limit
! 13-limit Extension
|-
|-
|0
| 0
|0.000
| 0.000
|1/1
| 1/1
|
|
|-
|-
|1
| 1
|351.477
| 351.477
|11/9~27/22
| 49/40, 60/49
|16/13~39/32
| 11/9, '''16/13''', 27/22, 39/32
|-
|-
|2
| 2
|702.955
| 702.955
|3/2
| '''3/2'''
|
|
|-
|-
|3
| 3
|1054.432
| 1054.432
|11/6
| 90/49
|24/13
| 11/6, 24/13
|-
|-
|4
| 4
|205.910
| 205.910
|9/8
| 9/8
|
|  
|-
|-
|5
| 5
|557.387
| 557.387
|11/8
| 112/81
|18/13
| '''11/8''', 18/13
|-
|-
|6
| 6
|908.865
| 908.865
|27/16
| 27/16
|22/13
| 22/13
|-
|-
|7
| 7
|60.342
| 60.342
|33/32~28/27
| 28/27
|27/26
| 33/32, 27/26
|-
|-
|8
| 8
|411.819
| 411.819
|14/11~81/64~80/63
| 81/64, 80/63
|33/26
| 14/11, 33/26
|-
|-
|9
| 9
|763.297
| 763.297
|14/9
| 14/9
|
|  
|-
|-
|10
| 10
|1114.774
| 1114.774
|21/11~40/21
| 40/21
|
| 21/11
|-
|-
|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
| 14/13
|-
|-
|15
| 15
|472.161
| 472.161
|21/16
| 21/16
|
|  
|-
|-
|16
| 16
|823.639
| 823.639
|45/28
| 45/28
|21/13
| 21/13
|-
|-
|17
| 17
|1175.116
| 1175.116
|63/32~160/81
| 63/32, 160/81
|
|
|-
|-
|18
| 18
|326.594
| 326.594
|40/33
| 98/81, 135/112
|
| 40/33
|-
|-
|19
| 19
|678.071
| 678.071
|40/27
| 40/27
|
|  
|-
|-
|20
| 20
|1029.549
| 1029.549
|20/11
| 49/27
|
| 20/11
|-
|-
|21
| 21
|181.026
| 181.026
|10/9
| 10/9
|
|  
|-
|-
|22
| 22
|532.503
| 532.503
|15/11
| 49/36
|
| 15/11
|-
|-
|23
| 23
|883.981
| 883.981
|5/3
| 5/3
|
|  
|-
|-
|24
| 24
|35.458
| 35.458
|45/44~55/54
| 49/48, 50/49
|
| 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


== Spectrum of Hemififths Tunings by Eigenmonzos ==
== Chords ==
{{Main| Chords of hemififths }}


{| class="wikitable"
== Scales ==
* [[Hemif7]]
* [[Hemif10]]
* [[Hemif17]]
 
== Tuning spectrum ==
 
Gencom: [2 11/9; 144/143 196/195 243/242 364/363]
 
Gencom map: [{{val| 1 1 -5 -1 2 4 }}, {{val| 0 2 25 13 5 -1 }}]
 
{| class="wikitable center-all left-3"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Neutral Third
! Generator
! Comments
|-
|-
| | 11/9
| 11/9
| | 347.408
| 347.408
|
|-
|-
| | 12/11
| 12/11
| | 349.788
| 349.788
|
|-
|-
| | 7\24
| (7\24)
| | 350.000
| 350.000
|
|-
|-
| | 11/8
| 11/8
| | 350.264
| 350.264
|
|-
|-
| | 4/3
| 4/3
| | 350.978
| 350.978
|
|-
|-
| | 12\41
| (12\41)
| | 351.220
| 351.220
|
|-
|-
| | 15/14
| 15/14
| | 351.389
| 351.389
|
|-
|-
| | 16/15
| 16/15
| | 351.417
| 351.417
|
|-
|-
| | 41\140
| (41\140)
| | 351.429
| 351.429
|
|-
|-
| | 8/7
| 8/7
| | 351.448 (7, 9 and 11 limit hemif minimax)
| 351.448
| 7-, 9- and 11-odd-limit hemif minimax
|-
|-
| | 5/4
| 5/4
| | 351.453 (5, 7, 9 and 11 limit minimax)
| 351.453
| 5-, 7-, 9- and 11-odd-limit minimax
|-
|-
| | 7/5
| 7/5
| | 351.457
| 351.457
|
|-
|-
| | 6/5
| 6/5
| | 351.494
| 351.494
|
|-
|-
| | 29\99
| (29\99)
| | 351.515
| 351.515
|
|-
|-
| | 7/6
| 7/6
| | 351.534
| 351.534
|
|-
|-
| | 10/9
| 10/9
| | 351.543
| 351.543
|
|-
|-
| | 9/7
| 9/7
| | 351.657
| 351.657
|
|-
|-
| | 15/11
| 15/11
| | 351.680
| 351.680
|
|-
|-
| | 15/13
| 15/13
| | 351.705 (15 limit minimax)
| 351.705
| 15-odd-limit minimax
|-
|-
| | 17\58
| (17\58)
| | 351.724
| 351.724
|
|-
|-
| | 11/10
| 11/10
| | 351.750
| 351.750
|
|-
|-
| | 13/10
| 13/10
| | 351.761 (13 limit minimax)
| 351.761
| 13-odd-limit minimax
|-
|-
| | 13/11
| 13/11
| | 351.798 (13 and 15 limit hemif minimax)
| 351.798
| 13- and 15-odd-limit hemif minimax
|-
|-
| | 22\75
| (22\75)
| | 352.000
| 352.000
|
|-
|-
| | 14/13
| 14/13
| | 352.021
| 352.021
|
|-
|-
| | 14/11
| 14/11
| | 352.188
| 352.188
|
|-
|-
| | 18/13
| 18/13
| | 352.676
| 352.676
|
|-
|-
| | 13/12
| 13/12
| | 353.809
| 353.809
|
|-
|-
| | 16/13
| 16/13
| | 359.472
| 359.472
|
|}
|}
[[Category:Hemififths]]
 
{{IoT}}
[[Category:Hemififths| ]] <!-- main article -->
[[Category:Breedsmic temperaments]]
[[Category:Hemifamity temperaments]]
[[Category:Hemimage temperaments]]
Retrieved from "https://en.xen.wiki/w/Hemififths"