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Superpyth: Difference between revisions

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VisualWikitext
In that case it's prolly better to just write 22 & 27e
→Tunings: split the spectrum for 11-limit superpyth
Line 253: Line 253:
* DKW (2.3.7 archy): ~2 = 1200.000{{c}}, ~3/2 = 712.585{{c}}
* DKW (2.3.7 archy): ~2 = 1200.000{{c}}, ~3/2 = 712.585{{c}}


=== Tuning spectrum ===
=== Tuning spectra ===
{| class="wikitable center-all left-4"
==== Archy ====
{| class="wikitable center-all left-4 left-5"
|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]*
! [[Eigenmonzo|Unchanged&nbsp;interval<br>(eigenmonzo)]]*
! Generator (¢)
! Generator&nbsp;(¢)
! Extension
! Comments
! Comments
|-
|-
| '''[[7edo|4\7]]'''
|
| '''685.714'''
|
| '''Lower bound of 2.3.7-subgroup 9-odd-limit diamond monotone'''
|-
| [[12edo|7\12]]
|
| 700.000
| ↓&nbsp;Dominant
|  
|  
|-
|
| 3/2
| 3/2
| 701.955
| 701.955
|
| Pythagorean tuning
| Pythagorean tuning
|-
|-
| [[17edo|10\17]]
| [[17edo|10\17]]
|  
|
| 705.882
| 705.882
|  
| ↑&nbsp;Dominant<br>↓&nbsp;Quasisuper
|
|-
|-
|  
|
| 81/56
| 81/56
| 706.499
| 706.499
|
| 1/6 comma
| 1/6 comma
|-
|-
|  
|
| 27/14
| 27/14
| 707.408
| 707.408
|
| 1/5 comma
| 1/5 comma
|-
|-
| [[39edo|23\39]]
| [[39edo|23\39]]
|
| 707.692
|
| 39d val
|-
|
| 9/7
| 708.771
|
| 1/4 comma, 2.3.7-subgroup 9-odd-limit minimax
|-
| [[22edo|13\22]]
|
| 709.091
| ↑&nbsp;Quasisuper<br>↓&nbsp;Superpyth
|
|-
|
| 49/27
| 709.745
|
| 2/7 comma
|-
| [[49edo|29\49]]
|
| 710.204
|
|
|-
|
| 7/6
| 711.043
|
| 1/3 comma, 2.3.7-subgroup 7-odd-limit minimax
|-
| [[27edo|16\27]]
|
| 711.111
| ↑&nbsp;Superpyth<br>↓&nbsp;Quasiultra
|
|-
| [[59edo|35\59]]
|
| 711.864
|
|
|-
| [[32edo|19\32]]
|
| 712.500
| ↑&nbsp;Quasiultra<br>↓&nbsp;Ultrapyth
|
|-
|
| 49/48
| 712.861
|
| 2/5 comma, 2.3.7-subgroup CEE tuning
|-
| [[37edo|22\37]]
|
| 713.514
|
|
|-
| [[42edo|25\42]]
|
| 714.286
|
|
|-
|
| 7/4
| 715.587
|
| 1/2 comma
|-
| '''[[5edo|3\5]]'''
|
| '''720.000'''
| ↑&nbsp;Ultrapyth
| '''Upper bound of 2.3.7-subgroup 7- and 9-odd-limit diamond monotone'''
|-
|
| 21/16
| 729.219
|
| Full comma
|}
<nowiki/>* Besides the octave
==== Superpyth ====
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged&nbsp;interval<br>(eigenmonzo)]]*
! Generator&nbsp;(¢)
! Comments
|-
|
| 3/2
| 701.955
| Pythagorean tuning
|-
| [[17edo|10\17]]
|  
|  
| 707.692
| 705.882
| 39cd val
| 17e val
|-
|-
|  
|  
| 9/7
| 9/7
| 708.771
| 708.771
| 1/4 comma, {{nowrap|<nowiki>{1, 3, 7, 9}</nowiki>}} minimax
|  
|-
|-
|  
|  
| 15/8
| 15/8
| 708.807
| 708.807
|
|-
|
| 11/10
| 709.286
|  
|  
|-
|-
Line 299: Line 427:
|  
|  
| '''709.091'''
| '''709.091'''
| '''Lower bound of 7- and 9-odd-limit diamond monotone'''
| '''Lower bound of 7-, 9-, and 11-odd-limit diamond monotone'''
|-
|
| 11/8
| 709.457
|
|-
|-
|  
|  
Line 305: Line 438:
| 709.590
| 709.590
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|
| 49/27
| 709.745
| 2/7 comma
|-
|-
| [[71edo|42\71]]
| [[71edo|42\71]]
Line 319: Line 447:
| 15/14
| 15/14
| 709.954
| 709.954
|
|-
|
| 11/6
| 709.958
|  
|  
|-
|-
Line 324: Line 457:
| 25/24
| 25/24
| 710.040
| 710.040
|
|-
|
| 11/7
| 710.138
|  
|  
|-
|-
Line 329: Line 467:
|  
|  
| 710.204
| 710.204
|
|-
|
| 15/11
| 710.508
|  
|  
|-
|-
Line 334: Line 477:
|  
|  
| 710.526
| 710.526
| 76bcd val
| 76bcdee val
|-
|
| 11/9
| 710.529
|
|-
|-
|  
|  
| 5/3
| 5/3
| 710.545
| 710.545
|
|-
|
| 21/11
| 710.620
|  
|  
|-
|-
Line 349: Line 502:
| 7/6
| 7/6
| 711.043
| 711.043
| 1/3 comma, {{nowrap|<nowiki>{1, 3, 7}</nowiki>}} minimax
|  
|-
|-
| [[27edo|16\27]]
| '''[[27edo|16\27]]'''
|
| 711.111
|  
|  
| '''711.111'''
| 27e val, '''upper bound of 11-odd-limit diamond monotone'''
|-
|-
|  
|  
Line 365: Line 518:
| 711.772
| 711.772
|  
|  
|-
| [[59edo|35\59]]
|
| 711.864
| 59cc val
|-
|-
| [[32edo|19\32]]
| [[32edo|19\32]]
|  
|  
| 712.500
| 712.500
| 32c val
| 32cee val
|-
|
| 55/32
| 712.544
| Suprapyth mapping
|-
|
| 49/48
| 712.861
| 2/5 comma, 2.3.7 subgroup CEE tuning
|-
| [[37edo|22\37]]
|
| 713.514
| 37cc val
|-
| [[42edo|25\42]]
|
| 714.286
| 42cc val
|-
|-
|  
|  
| 7/4
| 7/4
| 715.587
| 715.587
| 1/2 comma
|  
|-
|-
| '''[[5edo|3\5]]'''
| '''[[5edo|3\5]]'''
|  
|  
| '''720.000'''
| '''720.000'''
| '''Upper bound of 7- and 9-odd-limit diamond monotone'''
| 5e val, '''upper bound of 7- and 9-odd-limit diamond monotone'''
|-
|-
|  
|  
| 21/16
| 21/16
| 729.219
| 729.219
| Full comma
|  
|}
|}
<nowiki/>* Besides the octave
<nowiki/>* Besides the octave
Retrieved from "https://en.xen.wiki/w/Superpyth"