Xenharmonic Wiki

Lemba: Difference between revisions

← Older editNewer edit →
VisualWikitext
Yourmusic Productions (talk | contribs)
autopatrolled, emailconfirmed
1,936 edits
m Fix formatting
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
→Spectrum of lemba tunings by eigenmonzos: improve and standardize tuning spectra tables
Line 72: Line 72:
<nowiki>*</nowiki> In 13-limit POTE tuning. This tuning is very close to [[26edo]].
<nowiki>*</nowiki> In 13-limit POTE tuning. This tuning is very close to [[26edo]].


== Spectrum of lemba tunings by eigenmonzos ==
== Tuning spectrum ==


Gencom: [7/5 8/7; 45/44 50/49 65/64 78/77]
Gencom: [7/5 8/7; 45/44 50/49 65/64 78/77]
Line 78: Line 78:
Gencom map: [{{val| 2 2 5 6 5 7 }},[{{val| 0 3 -1 -1 5 1 }}]
Gencom map: [{{val| 2 2 5 6 5 7 }},[{{val| 0 3 -1 -1 5 1 }}]


{| class="wikitable center-1 right-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! ET<br>generator
! Supermajor<br>Second
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! Comments
! supermajor<br>second (¢)
! comments
|-
|-
|
| 5/4
| 5/4
| 213.686
| 213.686
|  
|  
|-
|-
|
| 15/11
| 15/11
| 221.016
| 221.016
|  
|  
|-
|-
|
| 12/11
| 12/11
| 224.681
| 224.681
|  
|  
|-
|-
| (3\16)
| 3\16
|
| 225.000
| 225.000
|  
|  
|-
|-
|
| 13/10
| 13/10
| 227.107
| 227.107
|  
|  
|-
|-
|
| 11/10
| 11/10
| 227.501
| 227.501
|  
|  
|-
|-
|
| 13/11
| 13/11
| 227.698
| 227.698
|  
|  
|-
|-
| (8\42)
| 8\42
|
| 228.571
| 228.571
|  
|  
|-
|-
|
| 6/5
| 6/5
| 228.910
| 228.910
Line 121: Line 131:
|-
|-
| (2 - Φ)\2
| (2 - Φ)\2
|
| 229.179
| 229.179
| Golden Lemba. L/s ratios are always precisely Φ, and MOS scales are always precisely 2Φ
| Golden Lemba<ref>L/s ratios are always precisely Φ, and MOS scales are always precisely 2Φ</ref>
|-
|-
|
| 21/13
| 21/13
| 230.253
| 230.253
|  
|  
|-
|-
|
| 11/8
| 11/8
| 230.264
| 230.264
|  
|  
|-
|-
|
| 14/11
| 14/11
| 230.415
| 230.415
| 15-odd-limit minimax
| 15-odd-limit minimax
|-
|-
|
| 13/12
| 13/12
| 230.714
| 230.714
|  
|  
|-
|-
| (5\26)
| 5\26
|
| 230.769
| 230.769
|  
|  
|-
|-
|
| 10/9
| 10/9
| 231.085
| 231.085
| 9-, 11- and 13-odd-limit minimax
| 9-, 11- and 13-odd-limit minimax
|-
|-
|
| 8/7
| 8/7
| 231.174
| 231.174
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|-
|
| {{monzo| 0 63 -20 -20 22 -6 }}
| {{monzo| 0 63 -20 -20 22 -6 }}
| 231.250
| 231.250
| 13-odd-limit least squares
| 13-odd-limit least squares
|-
|-
|
| {{monzo| 0 17 -6 -6 6 }}
| {{monzo| 0 17 -6 -6 6 }}
| 231.294
| 231.294
| 11-odd-limit least squares
| 11-odd-limit least squares
|-
|-
|
| 52521875/177147
| 52521875/177147
| 231.298
| 231.298
| 7-odd-limit least squares
| 7-odd-limit least squares
|-
|-
|
| {{monzo| 0 66 -17 -23 25 -7 }}
| {{monzo| 0 66 -17 -23 25 -7 }}
| 231.399
| 231.399
| 15-odd-limit least squares
| 15-odd-limit least squares
|-
|-
|
| 17/13
| 17/13
| 232.213
| 232.213
|  
|  
|-
|-
| (12\62)
| 12\62
|
| 232.258
| 232.258
|  
|  
|-
|-
|
| 129140163/1500625
| 129140163/1500625
| 232.418
| 232.418
| 9-odd-limit least squares
| 9-odd-limit least squares
|-
|-
|
| 18/13
| 18/13
| 232.676
| 232.676
|  
|  
|-
|-
|
| Φ
| Φ
| 233.090
| 233.090
|  
|  
|-
|-
|
| 7/6
| 7/6
| 233.282
| 233.282
|  
|  
|-
|-
| (7\36)
| 7\36
|
| 233.333
| 233.333
|  
|  
|-
|-
|
| 9/7
| 9/7
| 233.583
| 233.583
|  
|  
|-
|-
|
| 4/3
| 4/3
| 233.985
| 233.985
|  
|  
|-
|-
|
| 21/17
| 21/17
| 234.274
| 234.274
|  
|  
|-
|-
|
|  
|  
| 234.485
| 234.485
| 2.3.7.17 subgroup least squares {{clarify}}
| 2.3.7.17 subgroup least squares {{clarify}}
|-
|-
| (9\46)
| 9\46
|
| 234.783
| 234.783
|  
|  
|-
|-
|
| 17/16
| 17/16
| 234.985
| 234.985
|  
|  
|-
|-
|
| 21/16
| 21/16
| 235.390
| 235.390
|  
|  
|-
|-
| (11\56)
| 11\56
|
| 235.714
| 235.714
|  
|  
|-
|-
|
| 14/13
| 14/13
| 235.851
| 235.851
|  
|  
|-
|-
|
| 11/9
| 11/9
| 236.851
| 236.851
|  
|  
|-
|-
|
| 16/15
| 16/15
| 237.243
| 237.243
|  
|  
|-
|-
|
| 15/14
| 15/14
| 239.814
| 239.814
|  
|  
|-
|-
|
| 16/13
| 16/13
| 240.528
| 240.528
|  
|  
|-
|-
|
| 15/13
| 15/13
| 247.741
| 247.741
Retrieved from "https://en.xen.wiki/w/Lemba"