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Lemba: Difference between revisions

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→Tunings: + prime-optimized tunings
→Tunings: move the target tunings that don't correspond to significant eigenintervals out of the tuning spectra. Simplify the ratios. Note vals
Line 75: Line 75:


== Tunings ==
== Tunings ==
=== Prime-optimized tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
Line 121: Line 122:
| CWE: ~8/7 = 231.1617{{c}}
| CWE: ~8/7 = 231.1617{{c}}
| POTE: ~8/7 = 230.9665{{c}}
| POTE: ~8/7 = 230.9665{{c}}
|}
=== Target tunings ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Minimax tunings
|-
! Target
! Generator
! Eigenmonzo*
|-
| 5-odd-limit
| ~8/7 = 228.910{{c}}
| 5/3
|-
| 7-odd-limit
| ~8/7 = 231.174{{c}}
| 7/4
|-
| 9-odd-limit
| ~8/7 = 231.085{{c}}
| 9/5
|-
| 11-odd-limit
| ~8/7 = 231.085{{c}}
| 9/5
|-
| 13-odd-limit
| ~8/7 = 231.085{{c}}
| 9/5
|-
| 15-odd-limit
| ~8/7 = 230.415{{c}}
| 11/7
|}
{| class="wikitable center-all left-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Least squares tunings
|-
! Target
! Generator
! Eigenmonzo*
|-
| 7-odd-limit
| ~8/7 = 231.298{{c}}
| {{Monzo| 0 -11 5 5 }}
|-
| 9-odd-limit
| ~8/7 = 232.418{{c}}
| {{Monzo| 0 17 -4 -4 }}
|-
| 11-odd-limit
| ~8/7 = 231.294{{c}}
| {{Monzo| 0 17 -6 -6 6 }}
|-
| 13-odd-limit
| ~8/7 = 231.250{{c}}
| {{Monzo| 0 63 -20 -20 22 -6 }}
|-
| 15-odd-limit
| ~8/7 = 231.399{{c}}
| {{Monzo| 0 66 -17 -23 25 -7 }}
|}
|}


Line 142: Line 204:
|-
|-
|
|
| 12/11
| 11/6
| 224.681
| 224.681
|  
|  
Line 169: Line 231:
|  
|  
| 228.571
| 228.571
|  
| 42bc val
|-
|-
|
|
| 6/5
| 5/3
| 228.910
| 228.910
| 5-odd-limit minimax
| 5-odd-limit minimax
Line 192: Line 254:
|-
|-
|
|
| 14/11
| 11/7
| 230.415
| 230.415
| 15-odd-limit minimax
| 15-odd-limit minimax
Line 207: Line 269:
|-
|-
|
|
| 10/9
| 9/5
| 231.085
| 231.085
| 9-, 11- and 13-odd-limit minimax
| 9-, 11- and 13-odd-limit minimax
|-
|-
|
|
| 8/7
| 7/4
| 231.174
| 231.174
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|
| {{monzo| 0 63 -20 -20 22 -6 }}
| 231.250
| 13-odd-limit least squares
|-
|
| {{monzo| 0 17 -6 -6 6 }}
| 231.294
| 11-odd-limit least squares
|-
|
| 52521875/177147
| 231.298
| 7-odd-limit least squares
|-
|
| {{monzo| 0 66 -17 -23 25 -7 }}
| 231.399
| 15-odd-limit least squares
|-
|-
|
|
Line 244: Line 286:
|  
|  
| 232.258
| 232.258
|  
| 62c val
|-
|
| 129140163/1500625
| 232.418
| 9-odd-limit least squares
|-
|-
|
|
| 18/13
| 13/9
| 232.676
| 232.676
|  
|  
Line 269: Line 306:
|  
|  
| 233.333
| 233.333
|  
| 36c val
|-
|-
|
|
Line 277: Line 314:
|-
|-
|
|
| 4/3
| 3/2
| 233.985
| 233.985
|  
|  
Line 289: Line 326:
|  
|  
| 234.783
| 234.783
|  
| 46ce val
|-
|-
|
|
Line 304: Line 341:
|  
|  
| 235.714
| 235.714
|  
| 56ccee val
|-
|-
|
|
| 14/13
| 13/7
| 235.851
| 235.851
|  
|  
Line 317: Line 354:
|-
|-
|
|
| 16/13
| 13/8
| 240.528
| 240.528
|  
|  
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