Xenharmonic Wiki

Xenial: Difference between revisions

← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,012 edits
No edit summary
Tags: Mobile edit Mobile web edit
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,012 edits
No edit summary
Tags: Mobile edit Mobile web edit
 
Line 8: Line 8:
| MOS scales = [[6L 1s]], [[6L 7s]], [[13L 6s]], <br>[[19L 13s]], [[19L 32s]], [[19L 51s]]
| MOS scales = [[6L 1s]], [[6L 7s]], [[13L 6s]], <br>[[19L 13s]], [[19L 32s]], [[19L 51s]]
| Pergen = (P8, P11/9)
| Pergen = (P8, P11/9)
| Odd limit 1 = 7 | Mistuning 1 = 4.6 | Complexity 1 = 51
| Odd limit 1 = 7 | Mistuning 1 = 4.60 | Complexity 1 = 51
| Odd limit 2 = 9 | Mistuning 2 = 6.3 | Complexity 2 = 51
| Odd limit 2 = 9 | Mistuning 2 = 6.27 | Complexity 2 = 51
| Odd limit 3 = 17 | Mistuning 3 = 8.9 | Complexity 3 = 70
| Odd limit 3 = 17 | Mistuning 3 = 8.90 | Complexity 3 = 70
| Odd limit 4 = 23 | Mistuning 4 = 9.0 | Complexity 4 = 70
| Odd limit 4 = 23 | Mistuning 4 = 8.96 | Complexity 4 = 70
}}
}}
'''Xenial''' is a [[rank-2]] [[regular temperament|temperament]] that is [[generator|generated]] by a sharpened minor whole tone of [[~]][[10/9]], so that nine generators reach [[4/3]], 17 reach [[8/5]], 21 reach [[16/13]] and 33 reach [[8/7]] with octave reduction. It is also generated by dividing [[11/1|11th harmonic]] into 22 equal parts, [[17/1|17th harmonic]] into 26 equal parts, or [[19/1|19th harmonic]] into 27 equal parts.
'''Xenial''' is a [[rank-2]] [[regular temperament|temperament]] that is [[generator|generated]] by a sharpened minor whole tone of [[~]][[10/9]], so that nine generators reach [[4/3]], 17 reach [[8/5]], 21 reach [[16/13]] and 33 reach [[8/7]] with octave reduction. It is also generated by dividing [[11/1|11th harmonic]] into 22 equal parts, [[17/1|17th harmonic]] into 26 equal parts, or [[19/1|19th harmonic]] into 27 equal parts.
Line 179: Line 179:
|-
|-
! Tenney
! Tenney
| CTE: ~10/9 = 188.8535 {{c}}
| CTE: ~10/9 = 188.8535{{c}}
| CWE: ~10/9 = 188.8544 {{c}}
| CWE: ~10/9 = 188.8544{{c}}
| POTE: ~10/9 = 188.8548 {{c}}
| POTE: ~10/9 = 188.8548{{c}}
|}
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~10/9 = 188.8295{{c}}
| CWE: ~10/9 = 188.8085{{c}}
| POTE: ~10/9 = 188.8028{{c}}
|}
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~10/9 = 188.7987{{c}}
| CWE: ~10/9 = 188.7898{{c}}
| POTE: ~10/9 = 188.7875{{c}}
|}
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 17-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~10/9 = 188.7811{{c}}
| CWE: ~10/9 = 188.7677{{c}}
| POTE: ~10/9 = 188.7655{{c}}
|}
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 19-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~10/9 = 188.7828{{c}}
| CWE: ~10/9 = 188.7770{{c}}
| POTE: ~10/9 = 188.7762{{c}}
|}
|}
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 23-limit norm-based tunings
|+ style="font-size: 105%; white-space: nowrap;" | 23-limit norm-based tunings
Line 195: Line 254:
|-
|-
! Tenney
! Tenney
| CTE: ~10/9 = 188.7849 {{c}}
| CTE: ~10/9 = 188.7849{{c}}
| CWE: ~10/9 = 188.7755 {{c}}
| CWE: ~10/9 = 188.7755{{c}}
| POTE: ~10/9 = 188.7744 {{c}}
| POTE: ~10/9 = 188.7744{{c}}
|}
|}


Line 210: Line 269:
|  
|  
| 9/5
| 9/5
| 182.404
| 182.4037
|  
|  
|-
|-
|  
|  
| 13/10
| 13/10
| 186.447
| 186.4465
|  
|  
|-
|-
| 5 ⧵ 32
| 5 ⧵ 32
|  
|  
| 187.500
| 187.5000
| 32cddefgh val <br>Lower bound of 7-odd-limit diamond monotone
| 32cddefgh val <br>Lower bound of 7-odd-limit diamond monotone
|-
|-
|  
|  
| 23/12
| 23/12
| 187.720
| 187.7199
|  
|  
|-
|-
|  
|  
| 13/9
| 13/9
| 187.794
| 187.7941
|  
|  
|-
|-
|  
|  
| 23/13
| 23/13
| 188.208
| 188.2081
|  
|  
|-
|-
| 8 ⧵ 51
| 8 ⧵ 51
|  
|  
| 188.235
| 188.2353
| 51cdh val <br>Lower bound of 9-odd-limit diamond monotone
| 51cdh val <br>Lower bound of 9-odd-limit diamond monotone
|-
|-
|  
|  
| 23/18
| 23/18
| 188.291
| 188.2910
|  
|  
|-
|-
|  
|  
| 17/11
| 17/11
| 188.409
| 188.4094
|  
|  
|-
|-
|  
|  
| 13/12
| 13/12
| 188.452
| 188.4523
|  
|  
|-
|-
|  
|  
| 15/14
| 15/14
| 188.492
| 188.4918
|  
|  
|-
|-
|  
|  
| 13/8
| 13/8
| 188.546
| 188.5463
|  
|  
|-
|-
| 11 ⧵ 70
| 11 ⧵ 70
|  
|  
| 188.571
| 188.5714
| Lower bound of 11, 13, 15 and 17-odd-limit diamond monotone
| Lower bound of 11, 13, 15 and 17-odd-limit diamond monotone
|-
|-
|  
|  
| 7/5
| 7/5
| 188.593
| 188.5930
|  
|  
|-
|-
|  
|  
| 17/13
| 17/13
| 188.605
| 188.6048
|  
|  
|-
|-
|  
|  
| 21/20
| 21/20
| 188.621
| 188.6213
|  
|  
|-
|-
|  
|  
| 13/11
| 13/11
| 188.623
| 188.6230
| 13-odd-limit minimax
| 13-odd-limit minimax
|-
|-
|  
|  
| 23/14
| 23/14
| 188.648
| 188.6483
|  
|  
|-
|-
|  
|  
| 17/16
| 17/16
| 188.652
| 188.6521
|  
|  
|-
|-
|  
|  
| 23/21
| 23/21
| 188.654
| 188.6537
|  
|  
|-
|-
|  
|  
| 17/12
| 17/12
| 188.657
| 188.6572
|  
|  
|-
|-
|  
|  
| 17/9
| 17/9
| 188.660
| 188.6601
|  
|  
|-
|-
|  
|  
| 3/2
| 3/2
| 188.672
| 188.6717
| 9, 15 and 17-odd-limit minimax
| 9, 15 and 17-odd-limit minimax
|-
|-
|  
|  
| 11/9
| 11/9
| 188.685
| 188.6852
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
|  
|  
| 19/13
| 19/13
| 188.687
| 188.6872
| 19, 21 and 23-odd-limit minimax
| 19, 21 and 23-odd-limit minimax
|-
|-
|  
|  
| 11/6
| 11/6
| 188.689
| 188.6891
|  
|  
|-
|-
Line 350: Line 409:
|  
|  
| 23/20
| 23/20
| 188.711
| 188.7115
|  
|  
|-
|-
|  
|  
| 21/17
| 21/17
| 188.738
| 188.7379
|  
|  
|-
|-
|  
|  
| 19/18
| 19/18
| 188.747
| 188.7467
|  
|  
|-
|-
|  
|  
| 17/14
| 17/14
| 188.748
| 188.7480
|  
|  
|-
|-
|  
|  
| 21/11
| 21/11
| 188.758
| 188.7584
|  
|  
|-
|-
| 14 ⧵ 89
| 14 ⧵ 89
|  
|  
| 188.764
| 188.7640
| 19, 21 and 23-odd-limit diamond monotone (singleton)
| 19, 21 and 23-odd-limit diamond monotone (singleton)
|-
|-
|  
|  
| 19/12
| 19/12
| 188.766
| 188.7655
|  
|  
|-
|-
|  
|  
| 11/7
| 11/7
| 188.773
| 188.7726
|  
|  
|-
|-
|  
|  
| 17/15
| 17/15
| 188.782
| 188.7824
|  
|  
|-
|-
|  
|  
| 21/16
| 21/16
| 188.791
| 188.7909
|  
|  
|-
|-
|  
|  
| 21/19
| 21/19
| 188.793
| 188.7932
|  
|  
|-
|-
|  
|  
| 19/16
| 19/16
| 188.797
| 188.7968
|  
|  
|-
|-
|  
|  
| 17/10
| 17/10
| 188.806
| 188.8056
|  
|  
|-
|-
|  
|  
| 19/14
| 19/14
| 188.811
| 188.8115
|  
|  
|-
|-
|  
|  
| 15/11
| 15/11
| 188.814
| 188.8135
|  
|  
|-
|-
|  
|  
| 7/4
| 7/4
| 188.823
| 188.8235
|  
|  
|-
|-
|  
|  
| 11/10
| 11/10
| 188.846
| 188.8463
|  
|  
|-
|-
|  
|  
| 23/17
| 23/17
| 188.851
| 188.8511
|  
|  
|-
|-
|  
|  
| 19/15
| 19/15
| 188.854
| 188.8537
|  
|  
|-
|-
|  
|  
| 7/6
| 7/6
| 188.880
| 188.8804
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|-
|  
|  
| 19/10
| 19/10
| 188.891
| 188.8909
|  
|  
|-
|-
|  
|  
| 15/8
| 15/8
| 188.913
| 188.9127
|  
|  
|-
|-
|  
|  
| 23/22
| 23/22
| 188.922
| 188.9217
|  
|  
|-
|-
|  
|  
| 23/19
| 23/19
| 188.975
| 188.9746
|  
|  
|-
|-
|  
|  
| 9/7
| 9/7
| 189.006
| 189.0056
|  
|  
|-
|-
|  
|  
| 21/13
| 21/13
| 189.036
| 189.0356
|  
|  
|-
|-
|  
|  
| 5/4
| 5/4
| 189.040
| 189.0404
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|  
|  
| 19/11
| 19/11
| 189.239
| 189.2390
|  
|  
|-
|-
|  
|  
| 13/7
| 13/7
| 189.308
| 189.3085
|  
|  
|-
|-
|  
|  
| 5/3
| 5/3
| 189.455
| 189.4552
|  
|  
|-
|-
| 3 ⧵ 19
| 3 ⧵ 19
|  
|  
| 189.473
| 189.4737
| Upper bound of 7, 9, 11, 13, 15 and 17-odd-limit diamond monotone
| Upper bound of 7, 9, 11, 13, 15 and 17-odd-limit diamond monotone
|-
|-
|  
|  
| 15/13
| 15/13
| 190.452
| 190.4518
|  
|  
|-
|-
|  
|  
| 23/16
| 23/16
| 190.575
| 190.5752
|  
|  
|-
|-
|  
|  
| 19/17
| 19/17
| 192.558
| 192.5576
|  
|  
|}
|}
Retrieved from "https://en.xen.wiki/w/Xenial"