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'''Septidiasemi''', in this article, is the rank-two regular temperament for the 2.3.5.7.13.17 subgroup defined by tempering out 2401/2400 and 2152828125/2147483648 in the 7-limit; 2205/2197 and 4096/4095 in the 13-limit; 833/832, 1275/1274, and 2025/2023 in the 17-limit.
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'''Septidiasemi''', in this article, is the [[Rank-2 temperament|rank-two regular temperament]] for the 2.3.5.7.13.17 [[subgroup]] defined by [[tempering out]] 2401/2400 and 2152828125/2147483648 in the 7-limit; 2205/2197 and 4096/4095 in the 13-limit; 833/832, 1275/1274, and 2025/2023 in the 17-limit.


It can be seen as implying a rank-two tuning which is [[generator|generated]] by a large semitone of about 119.3 cents which represents [[15/14]] (septimal diatonic semitone) and from this it derives its name. Equal temperaments that support septidiasemi include [[10edo|10EDO]] (generator 1\10), [[151edo|151EDO]] (generator 15\151), [[161edo|161EDO]] (generator 16\161), and [[171edo|171EDO]] (generator 17\171).
It can be seen as implying a rank-two tuning which is [[generator|generated]] by a large semitone of about 119.3 cents which represents [[15/14]] (septimal diatonic semitone) and from this it derives its name. Equal temperaments that support septidiasemi include [[10edo|10EDO]] (generator 1\10), [[151edo|151EDO]] (generator 15\151), [[161edo|161EDO]] (generator 16\161), and [[171edo|171EDO]] (generator 17\171).
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== Intervals ==
== Intervals ==
{| class="wikitable right-1"
{| class="wikitable right-all center-3"
|-
|-
! Generators
! Generator <br> steps
! Cents<sup>*</sup>
! Cents<sup>*</sup>
! Approximate ratios<sup>†</sup>
! Approximate <br> ratios<sup>†</sup>
|-
|-
| 0
| 0
Line 22: Line 23:
| 2
| 2
| 238.593
| 238.593
|  
| 39/34
|-
|-
| 3
| 3
Line 30: Line 31:
| 4
| 4
| 477.186
| 477.186
|  
| 112/85, 120/91
|-
|-
| 5
| 5
Line 38: Line 39:
| 6
| 6
| 715.779
| 715.779
|  
| 68/45
|-
|-
| 7
| 7
Line 54: Line 55:
| 10
| 10
| 1192.965
| 1192.965
|  
| 448/225, 255/128, <br>544/273, 576/289
|-
|-
| 11
| 11
Line 66: Line 67:
| 13
| 13
| 350.855
| 350.855
|  
| 60/49, 49/40
|-
|-
| 14
| 14
Line 78: Line 79:
| 16
| 16
| 708.745
| 708.745
|  
| 128/85
|-
|-
| 17
| 17
Line 90: Line 91:
| 19
| 19
| 1066.634
| 1066.634
|  
| (close to 50/27)
|-
|-
| 20
| 20
| 1185.931
| 1185.931
|  
| 119/60, 135/68
|-
|-
| 21
| 21
Line 106: Line 107:
| 23
| 23
| 343.820
| 343.820
|  
| 39/32
|-
|-
| 24
| 24
Line 134: Line 135:
| 30
| 30
| 1178.896
| 1178.896
|  
| (close to 160/81)
|-
|-
| 31
| 31
Line 158: Line 159:
| 36
| 36
| 694.676
| 694.676
|  
| 112/75
|-
|-
| 37
| 37
Line 174: Line 175:
| 40
| 40
| 1171.862
| 1171.862
| 63/32~128/65
| 63/32, 128/65
|-
|-
| 41
| 41
Line 254: Line 255:
| 60
| 60
| 1157.793
| 1157.793
|  
| 39/20
|-
|-
| 61
| 61
Line 338: Line 339:
| 81
| 81
| 63.020
| 63.020
|  
| (close to 28/27)
|-
|-
| 82
| 82
Line 366: Line 367:
| 88
| 88
| 898.096
| 898.096
|  
| 42/25
|-
|-
| 89
| 89
| 1017.392
| 1017.392
| 9/5
| 9/5
|-
| 90
| 1136.689
| 27/14
|}
|}


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== See also ==
== See also ==
* [[15/14]] - septimal diatonic semitone
* [[15/14]] - septimal diatonic semitone
* [[15/14ths equal temperament|15/14s equal temperament]]


[[Category:Temperament]]
[[Category:Septidiasemi| ]] <!-- main article -->
[[Category:Breed]]
[[Category:Rank-2 temperaments]]
[[Category:Breedsmic temperaments]]
Retrieved from "https://en.xen.wiki/w/Septidiasemi"