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Garibaldi: Difference between revisions

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→Spectrum of garibaldi tunings by eigenmonzos: improve and standardize tuning spectra tables
Line 272: Line 272:
<nowiki>*</nowiki> in 7-limit POTE tuning
<nowiki>*</nowiki> in 7-limit POTE tuning


== Spectrum of garibaldi tunings by eigenmonzos ==
== Tuning spectra ==
=== Cassandra mapping ===
=== Cassandra ===
Gencom: [2 4/3; 225/224 275/273 325/324 385/384]
Gencom: [2 4/3; 225/224 275/273 325/324 385/384]


Gencom map: [{{val|1 2 -1 -3 13 12}}, {{val|0 -1 8 14 -23 -20}}]
Gencom map: [{{val|1 2 -1 -3 13 12}}, {{val|0 -1 8 14 -23 -20}}]


{| class="wikitable center-1 right-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
![[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! Fifth
! fifth<br>(¢)
! Comments
! comments
|-
|-
| 16/15
| 16/15
| 701.676
| 701.676
|  
|
|-
|-
| 5/4
| 5/4
| 701.711
| 701.711
|  
|
|-
|-
| {{monzo| 0 -10 17 }}
| {{monzo| 0 -10 17 }}
Line 302: Line 302:
| 10/9
| 10/9
| 701.760
| 701.760
|  
|
|-
|-
| 15/13
| 15/13
| 701.9355
| 701.9355
|  
|
|-
|-
| 13/10
| 13/10
| 701.9362
| 701.9362
|  
|
|-
|-
| 4/3
| 4/3
| 701.955
| 701.955
|  
|
|-
|-
| 16/13
| 16/13
| 702.026
| 702.026
|  
|
|-
|-
| 13/12
| 13/12
| 702.030
| 702.030
|  
|
|-
|-
| 18/13
| 18/13
| 702.034
| 702.034
|  
|
|-
|-
| 11/10
| 11/10
| 702.097
| 702.097
|  
|
|-
|-
| 15/11
| 15/11
| 702.102
| 702.102
|  
|
|-
|-
| 14/13
| 14/13
Line 370: Line 370:
| 8/7
| 8/7
| 702.227
| 702.227
|  
|
|-
|-
| 14/11
| 14/11
| 702.230
| 702.230
|  
|
|-
|-
| 11/8
| 11/8
| 702.231
| 702.231
|  
|
|-
|-
| 12/11
| 12/11
| 702.244
| 702.244
|  
|
|-
|-
| 11/9
| 11/9
| 702.258
| 702.258
|  
|
|-
|-
| 15/14
| 15/14
| 702.778
| 702.778
|  
|
|-
|-
| 7/5
| 7/5
| 702.915
| 702.915
|  
|
|-
|-
| 13/11
| 13/11
| 703.597
| 703.597
|  
|
|}
|}


=== Andromeda mapping ===
=== Andromeda ===
Gencom: [2 4/3; 100/99 105/104 196/195 245/242]
Gencom: [2 4/3; 100/99 105/104 196/195 245/242]


Gencom map: [{{val|1 2 -1 -3 -4 -5}}, {{val|0 -1 8 14 18 21}}]
Gencom map: [{{val|1 2 -1 -3 -4 -5}}, {{val|0 -1 8 14 18 21}}]


{| class="wikitable center-1 right-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! Fifth
! fifth<br>(¢)
! Comments
! comments
|-
|-
| 16/15
| 16/15
| 701.676
| 701.676
|  
|
|-
|-
| 5/4
| 5/4
| 701.711
| 701.711
|  
|
|-
|-
| 6/5
| 6/5
Line 426: Line 426:
| 10/9
| 10/9
| 701.760
| 701.760
|  
|
|-
|-
| 4/3
| 4/3
| 701.955
| 701.955
|  
|
|-
|-
| 9/7
| 9/7
Line 442: Line 442:
| 8/7
| 8/7
| 702.227
| 702.227
|  
|
|-
|-
| 11/9
| 11/9
Line 450: Line 450:
| 12/11
| 12/11
| 702.665
| 702.665
|  
|
|-
|-
| 11/8
| 11/8
| 702.705
| 702.705
|  
|
|-
|-
| 18/13
| 18/13
Line 462: Line 462:
| 15/14
| 15/14
| 702.778
| 702.778
|  
|
|-
|-
| 13/12
| 13/12
| 702.792
| 702.792
|  
|
|-
|-
| 16/13
| 16/13
| 702.832
| 702.832
|  
|
|-
|-
| 7/5
| 7/5
| 702.915
| 702.915
|  
|
|-
|-
| 15/11
| 15/11
| 703.359
| 703.359
|  
|
|-
|-
| 15/13
| 15/13
| 703.410
| 703.410
|  
|
|-
|-
| 11/10
| 11/10
| 703.500
| 703.500
|  
|
|-
|-
| 13/10
| 13/10
| 703.522
| 703.522
|  
|
|-
|-
| 13/11
| 13/11
| 703.597
| 703.597
|  
|
|-
|-
| 14/13
| 14/13
| 704.043
| 704.043
|  
|
|-
|-
| 14/11
| 14/11
| 704.377
| 704.377
|  
|
|}
|}


=== Helenus mapping ===
=== Helenus ===
Gencom: [2 4/3; 99/98 176/175 275/273 847/845]
Gencom: [2 4/3; 99/98 176/175 275/273 847/845]


Gencom map: [{{val|1 2 -1 -3 -9 -10}}, {{val|0 -1 8 14 30 33}}]
Gencom map: [{{val|1 2 -1 -3 -9 -10}}, {{val|0 -1 8 14 30 33}}]


{| class="wikitable center-1 right-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! eigenmonzo<br>(unchanged interval)
! Fifth
! fifth<br>(¢)
! Comments
! comments
|-
|-
| 14/11
| 14/11
| 701.094
| 701.094
|  
|
|-
|-
| 14/13
| 14/13
| 701.489
| 701.489
|  
|
|-
|-
| 11/10
| 11/10
| 701.591
| 701.591
|  
|
|-
|-
| 15/11
| 15/11
| 701.607
| 701.607
|  
|
|-
|-
| 11/8
| 11/8
| 701.623
| 701.623
|  
|
|-
|-
| 12/11
| 12/11
| 701.633
| 701.633
|  
|
|-
|-
| 11/9
| 11/9
Line 546: Line 546:
| 16/15
| 16/15
| 701.676
| 701.676
|  
|
|-
|-
| 5/4
| 5/4
| 701.711
| 701.711
|  
|
|-
|-
| 6/5
| 6/5
Line 558: Line 558:
| 10/9
| 10/9
| 701.760
| 701.760
|  
|
|-
|-
| 16/13
| 16/13
| 701.802
| 701.802
|  
|
|-
|-
| 13/12
| 13/12
| 701.807
| 701.807
|  
|
|-
|-
| 18/13
| 18/13
| 701.811
| 701.811
|  
|
|-
|-
| 13/10
| 13/10
| 701.831
| 701.831
|  
|
|-
|-
| 15/13
| 15/13
| 701.836
| 701.836
|  
|
|-
|-
| 4/3
| 4/3
| 701.955
| 701.955
|  
|
|-
|-
| 9/7
| 9/7
Line 594: Line 594:
| 8/7
| 8/7
| 702.227
| 702.227
|  
|
|-
|-
| 15/14
| 15/14
| 702.778
| 702.778
|  
|
|-
|-
| 7/5
| 7/5
| 702.915
| 702.915
|  
|
|-
|-
| 13/11
| 13/11
| 703.597
| 703.597
|  
|
|}
|}


Retrieved from "https://en.xen.wiki/w/Garibaldi"