User:Moremajorthanmajor/3L 1s (perfect fifth-equivalent): Difference between revisions

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1976; 2, 8
 
 
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1764; 1, 2.4
 
 
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'''1905; 1, 7.5'''
 
 
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1976; 2, 8
 
 
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2076; 1.08'''{{Overline|3}}'''
2076; 1, 12
 
 
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2234; 2, 14
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2258; 1, 4, 1.5
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2090.{{Overline|90}}
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2210; 1.9
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2206; 2, 4, 1.5
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2193; 9.{{Overline|6}}
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2188; 4.25
2188; 4, 4
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2181.{{Overline|81}}
2181.{{Overline|81}}
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|'''D'''
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'''2261; 1, 1.1{{Overline|6}}'''
'''2261; 1, 1, 6'''
|'''36\11'''
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'''2273; 1, 2.1{{Overline|6}}'''
'''2273; 1, 2, 6'''
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'''2283; 1.{{Overline|148}}'''
'''2283; 1, 6.75'''
|'''23\7'''
|'''23\7'''
'''2300'''
'''2300'''
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'''2317; 4, 7'''
'''2317; 4, 7'''
|'''33\10'''
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'''2329; 2, 2.{{Overline|3}}'''
'''2329; 2, 2, 3'''
|'''43\13'''
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'''2245.{{Overline|45}}'''
'''2245.{{Overline|45}}'''
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|D#
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2307; 1, 2, 4
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2336; 1.1875
2336; 1, 5, 3
|61\18
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2361; 3.{{Overline|4}}
2361; 3, 2, 4
| rowspan="2" |24\7
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2400
2400
|59\17
|59\17
2441; 2.{{Overline|63}}
2441; 2, 1, 1.75
|35\10
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2470; 1.7
2470; 1.7
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2446; 6.5
2446; 6.5
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2463; 6, 3
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2477; 2, 2.6
2477; 2, 2.6
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2500
2500
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2524; 7, 4
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2541; 5, 3
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2563.{{Overline|63}}
2563.{{Overline|63}}
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|E#
|E#
|54\15
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2492; 3.25
2492; 3, 4
| rowspan="2" |40\11
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2526; 3.1
2526; 3, 6
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2554; 1, 5.2
2554; 1, 5.2
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2648; 2.625
2648; 2.625
|38\10
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2682; 2.8{{Overline|3}}
2682; 2, 1.2
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2727.{{Overline|27}}
2727.{{Overline|27}}
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2538; 2.1{{Overline|6}}
2538; 2, 1
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2516; 7.75
2516; 7.75
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2500
2500
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2482; 1, 3, 7
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2470; 1.7
2470; 1.7
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'''2584; 1.625'''
'''2584; 1.625'''
|'''41\11'''
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'''2589; 2.{{Overline|1}}'''
'''2589; 2, 9'''
|'''67\18'''
|'''67\18'''
'''2593; 1, 1, 4.{{Overline|6}}'''
'''2593; 1, 1, 4, 1.5'''
|'''26\7'''
|'''26\7'''
'''2600'''
'''2600'''
|'''63\17'''
|'''63\17'''
'''2606; 1, 8.{{Overline|6}}'''
'''2606; 1, 8, 1.5'''
|'''37\10'''
|'''37\10'''
'''2611; 1, 3.25'''
'''2611; 1, 3, 4'''
|'''48\13'''
|'''48\13'''
'''2618.{{Overline|18}}'''
'''2618.{{Overline|18}}'''
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2630; 1.3
2630; 1.3
|42\11
|42\11
2652; 1.58{{Overline|3}}
2652; 1, 1, 1.4
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2670; 1.0{{Overline|3}}
2670; 1, 30
| 27\7
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2700
2700
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2731; 29
2731; 29
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2752; 1.0625
2752; 1, 16
|51\13
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2781.{{Overline|81}}
2781.{{Overline|81}}
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|F#
|F#
|58\15
|58\15
2676; 1.08{{Overline|3}}
2676; 1, 12
| rowspan="2" |43\11
| rowspan="2" |43\11
2715; 1.2{{Overline|6}}
2715; 1, 3.75
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2748; 2.58{{Overline|3}}
2748; 2, 1, 1.4
|28\7
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2800
2800
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2689; 1, 1.9
2689; 1, 1.9
|38\10
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2682; 2.8{{Overline|3}}
2682; 2, 1.2
|49\13
|49\13
2672.{{Overline|72}}
2672.{{Overline|72}}
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!0, G
!0, G
! 60\15
! 60\15
2769; 4.'''{{Overline|3}}'''
2769; 4,3
! 44\11
! 44\11
2778; 1.0{{Overline|5}}
2778; 1, 18
! 72\18
! 72\18
2787; 3.1
2787; 3.1
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2800
2800
!68\17
!68\17
2813; 1, 3.8{{Overline|3}}
2813; 1, 3, 1.2
! 40\10
! 40\10
2823; 1.{{Overline|8}}
2823; 1, 1, 8
!52\13
!52\13
2836.{{Overline|36}}
2836.{{Overline|36}}
Line 1,624: Line 1,624:
46; 6.5
46; 6.5
|1\11
|1\11
63: 6.{{Overline|3}}
63: 6, 3
|2\18
|2\18
77; 2, 2.6
77; 2, 2.6
| rowspan="2" |1\7
| rowspan="2" |1\7
100
100
|3\17
|3\17
124; 7.25
124; 7, 4
|2\10
|2\10
141; 5.{{Overline|6}}
141; 5, 1.5
|3\13
|3\13
163.{{Overline|63}}
163.{{Overline|63}}
Line 1,645: Line 1,646:
116; 7.75
116; 7.75
|2\17
|2\17
82; 1.3{{Overline|18}}
82; 1, 3, 7
|1\10
|1\10
70; 1.7
70; 1.7
Line 1,656: Line 1,657:
'''184; 1.625'''
'''184; 1.625'''
|'''3\11'''
|'''3\11'''
'''189; 2.{{Overline|1}}'''
'''189; 2, 9'''
|'''5\18'''
|'''5\18'''
'''193; 1, 1, 4.{{Overline|6}}'''
'''193; 1, 1, 4, 1.5'''
|'''2\7'''
|'''2\7'''
'''200'''
'''200'''
|'''5\17'''
|'''5\17'''
'''206; 1, 8.{{Overline|6}}'''
'''206; 1, 8, 1.5'''
|'''3\10'''
|'''3\10'''
'''211; 1, 3.25'''
'''211; 1, 3, 4'''
|'''4\13'''
|'''4\13'''
'''218.{{Overline|18}}'''
'''218.{{Overline|18}}'''
|-
|-
|G re
|G re#
|G#
|G#
| 5\15
| 5\15
230; 1.3
230; 1.3
|4\11
|4\11
252; 1.58{{Overline|3}}
252; 1, 1, 1.4
|7\18
|7\18
270; 1.0{{Overline|3}}
270; 1, 30
| rowspan="2" |3\7
| rowspan="2" |3\7
300
300
|8\17
|8\17
Line 1,686: Line 1,689:
|-
|-
|A mib
|A mib
|Ab
|Hb
|7\15
|7\15
323; 13
323; 13
|5\11
|5\11
315; 1.2{{Overline|6}}
315; 1, 3.75
| 8\18
| 8\18
309; 1, 2.1
309; 1, 2.1
Line 1,696: Line 1,699:
289; 1, 1.9
289; 1, 1.9
|4\10
|4\10
282; 2.8{{Overline|3}}
282; 2, 1.2
|5\13
|5\13
272.{{Overline|72}}
272.{{Overline|72}}
|-
|-
|A mi
|A mi
|A
|H
| 8\15
| 8\15
369; 4.{{Overline|3}}
369; 4, 3
|6\11
|6\11
378; 1.0{{Overline|5}}
378; 1, 18
|10\18
|10\18
387; 10.{{Overline|3}}
387; 10, 3
|4\7
|4\7
400
400
| 10\17
| 10\17
413; 1, 3.8{{Overline|3}}
413; 1, 3, 1.2
|6\10
|6\10
423; 1.{{Overline|8}}
423; 1, 1, 8
|8\13
|8\13
436.{{Overline|36}}
436.{{Overline|36}}
|-
|-
|A mi#
|A mi#
| A#
| H#
|9\15
|9\15
415; 2.6
415; 2.6
Line 1,726: Line 1,730:
464; 1.9375
464; 1.9375
|5\7
|5\7
500
500
| 13\17
| 13\17
537; 14.5
537; 1, 13.5
|8\10
|8\10
564; 1.41{{Overline|6}}
564; 1, 2.4
|11\13
|11\13
600
600
|-
|-
|B fa utb
|B fa utb
|Bbb
|Jbb
|10\15
|10\15
461; 1, 1, 6
461; 1, 1, 6
Line 1,741: Line 1,746:
425; 1.24
425; 1.24
|4\7
|4\7
400
400
|9\17
|9\17
372; 2.41{{Overline|6}}
372; 2, 2.4
|5\10
|5\10
352; 1, 16
352; 1, 16
Line 1,750: Line 1,756:
|-
|-
|'''B fa ut'''
|'''B fa ut'''
|'''Bb'''
|'''Jb'''  
|'''11\15'''
|'''11\15'''
'''507; 1.{{Overline|4}}'''
'''507; 1, 2, 4'''
|'''8\11'''
|'''8\11'''
'''505; 3.8'''
'''505; 3.8'''
|'''13\18'''
|'''13\18'''
'''503; 4, 2.{{Overline|3}}'''
'''503; 4, 2, 3'''
|'''5\7'''
|'''5\7'''
'''500'''
'''500'''
|'''12\17'''
|'''12\17'''
Line 1,767: Line 1,774:
|-
|-
|B fa ut#
|B fa ut#
|B
|J
| 12\15
| 12\15
553; 1.{{Overline|18}}
553; 1, 5.5
|9\11
|9\11
568; 2.375
568; 2.375
Line 1,775: Line 1,782:
580; 1.55
580; 1.55
| 6\7
| 6\7
600
600
|15\17
|15\17
Line 1,784: Line 1,792:
|-
|-
|B fa utx
|B fa utx
|B#
|J#
|13\15
|13\15
600
600
| rowspan="2" |10\11
| rowspan="2" |10\11
631; 1.{{Overline|72}}
631; 1, 1.375
|17\18
|17\18
658; 15.5
658; 15.5
|7\7
|7\7
700
700
|18\17
|18\17
744; 1.208{{Overline|3}}
744; 1, 4.8
|11\10
|11\10
776; 2, 8
776; 2, 8
Line 1,801: Line 1,814:
|-
|-
|C sol reb
|C sol reb
|Hb
|Kb
|14\15
|14\15
646; 6.5
646; 6.5
|16\18
|16\18
619; 2.{{Overline|81}}
619; 2, 1, 4.5
|6\7
|6\7
600
600
|14\17
|14\17
579; 3.{{Overline|2}}
579; 3.{{Overline|2}}
|8\10
|8\10
564; 1.41{{Overline|6}}
564; 1, 2.4
|10\13
|10\13
545.{{Overline|45}}
545.{{Overline|45}}
|-
|-
!C sol re
!C sol re
!H
!K
!'''15\15'''
!'''15\15'''
'''692; 3.25'''
'''692; 3, 4'''
!'''11\11'''
!'''11\11'''
'''694; 1, 2.8'''
'''694; 1, 2.8'''
!'''18\18'''
!'''18\18'''
'''696; 1.291'''{{Overline|6}}
'''696; 1, 3, 2, 3'''
!'''7\7'''
!'''7\7'''
'''700'''
'''700'''
!'''17\17'''
!'''17\17'''
'''703; 2, 2, 6'''
'''703; 2, 2, 6'''
!'''10\10'''
!'''10\10'''
'''705; 1.1'''{{Overline|3}}
'''705; 1, 7.5'''  
!'''13\13'''
!'''13\13'''
'''709.'''{{Overline|09}}
'''709.'''{{Overline|09}}
|-
|-
|C sol re#
|C sol re#
| Η#
| K#
|16\15
|16\15
738; 2.1{{Overline|6}}
738; 2, 6
|12\11
|12\11
757; 1, 8.5
757; 1, 8.5
|20\18
|20\18
774; 5, 6
774; 5, 6
| rowspan="2" |8\8
| rowspan="2" |8\8
800
800
|20\17
|20\17
827; 1, 1.41{{Overline|6}}
827; 1, 1, 2.4
|12\10
|12\10
847; 17
847; 17
Line 1,850: Line 1,877:
|-
|-
|D la mib  
|D la mib  
|Cb
|Lb
|18\15
|18\15
830; 1.3
830; 1.3
|13\11
|13\11
821; 19
821; 19
|21\18
|21\18
812; 1, 9.{{Overline|3}}
812; 1, 9, 3
|19\17
|19\17
786; 4.8{{Overline|3}}
786; 4, 1.2
|11\10
|11\10
776; 2, 8
776; 2, 8
Line 1,865: Line 1,896:
|-
|-
|'''D la mi'''
|'''D la mi'''
|'''C'''
|'''L'''
|'''19\15'''
|'''19\15'''
'''876; 1, 12'''
'''876; 1, 12'''
|'''14\11'''
|'''14\11'''
'''884; 4.75'''
'''884; 4.75'''
|'''23\18'''
|'''23\18'''
'''890; 3.1'''
'''890; 3.1'''
|'''9\5'''
|'''9\5'''
'''900'''
'''900'''
|'''22\17'''
|'''22\17'''
'''910; 2.9'''
'''910; 2.9'''
|'''13\10'''
|'''13\10'''
'''917; 1.{{Overline|54}}'''
'''917; 1, 1, 1.2'''
|'''17\13'''
|'''17\13'''
'''927.{{Overline|27}}'''
'''927.{{Overline|27}}'''
|-
|-
|D la mib
|D la mi#
|C#
|L#
|20\15
|20\15
923: 13
923: 13
|15\11
|15\11
947; 2, 1.4
947; 2, 1.4
|25\18
|25\18
967; 1, 2.875
967; 1, 2.875
| rowspan="2" |10\7
| rowspan="2" |10\7
1000
1000
|25\17
|25\17
1034; 2, 14
1034; 2, 14
|15\10
|15\10
1058; 1, 4.{{Overline|6}}
1058; 1, 4, 1.5
|20\13
|20\13
1090.{{Overline|90}}
1090.{{Overline|90}}
|-
|-
|E fa utb
|E fa utb
|Db
|Mb
|22\15
|22\15
1015; 2.6
1015; 2.6
|16\11
|16\11
1010; 1.9
1010; 1.9
|26\18
|26\18
1006; 2, 4.{{Overline|6}}
1006; 2, 4, 1.5
|24\17
|24\17
993; 9.{{Overline|6}}
993; 9.{{Overline|6}}
|14\10
|14\10
Line 1,914: Line 1,959:
|-
|-
|E fa ut
|E fa ut
|D
|M
|23\15
|23\15
1061; 1, 1, 6
1061; 1, 1, 6
|17\11
|17\11
1073; 1, 2, 6
1073; 1, 2, 6
|28\18
|28\18
1083; 1.{{Overline|148}}
1083; 1, 6.75
|11\7
|11\7
1100
1100
|27\17
|27\17
1117; 4, 7
1117; 4, 7
|16\10
|16\10
1129; 2, 2.{{Overline|3}}
1129; 2, 2, 3
|21\9
|21\9
1145.{{Overline|45}}
1145.{{Overline|45}}
|-
|-
|E fa ut#
|E fa ut#
|D#
|M#
|24\15
|24\15
1107; 1.{{Overline|4}}
1107; 1, 2, 4
| rowspan="2" |18\11
| rowspan="2" |18\11
1136; 1.1875
1136; 1.1875
|30\18
|30\18
1161; 3.{{Overline|4}}
1161; 3, 2, 4
|12\7
|12\7
1200
1200
|30\17
|30\17
1241; 2.{{Overline|63}}
1241; 2, 1, 1.75
|18\10
|18\10
1270; 1.7
1270; 1.7
Line 1,948: Line 2,003:
|-
|-
|F sol re utb
|F sol re utb
|Ebb
|Nbb
|25\15
|25\15
1153; 1.{{Overline|18}}
1153; 1, 5.5
|29\18
|29\18
1121; 1, 1, 2.6
1121; 1, 1, 2.6
|11\7
|11\7
1100
1100
|26\17
|26\17
1075; 1.16
1075; 1.16
|15\10
|15\10
1058; 1, 4.{{Overline|6}}
1058; 1, 4, 1.5
|19\13
|19\13
1036.{{Overline|36}}
1036.{{Overline|36}}
|-
|-
|'''F sol re ut'''
|'''F sol re ut'''
|'''Eb'''
|'''Nb'''  
|'''26\15'''
|'''26\15'''
'''1200'''
'''1200'''
|'''19\11'''
|'''19\11'''
'''1200'''
'''1200'''
|'''31\18'''
|'''31\18'''
'''1200'''
'''1200'''
|'''12\7'''
|'''12\7'''
'''1200'''
'''1200'''
|'''29\17'''
|'''29\17'''
'''1200'''
'''1200'''
|'''17\10'''
|'''17\10'''
Line 1,980: Line 2,044:
|-
|-
|F sol re ut#
|F sol re ut#
|E
|N
|27\15
|27\15
1246; 6.5
1246; 6.5
|20\11
|20\11
1263; 6.{{Overline|3}}
1263; 6, 3
|33\18
|33\18
1277; 2, 2.6
1277; 2, 2.6
|13\7
|13\7
1300
1300
|32\17
|32\17
1324; 7.25
1324; 7, 4
| 19\10
| 19\10
1341; 5.{{Overline|6}}
1341; 5, 1.5
|25\13
|25\13
1363.{{Overline|63}}
1363.{{Overline|63}}
|-
|-
|F sol re utx
|F sol re utx
| E#
| N#
|28\15
|28\15
1292; 3, 4
1292; 3, 4
| rowspan="2" |21\11
| rowspan="2" |21\11
1326; 3, 6
1326; 3, 6
|35\18
|35\18
1354; 1, 5.2
1354; 1, 5.2
|14\7
|14\7
1400
1400
|35\17
|35\17
1448; 3.625
1448; 3.625
|21\10
|21\10
1482; 2.8{{Overline|3}}
1482; 2, 1.2
|28\13
|28\13
1527.{{Overline|27}}
1527.{{Overline|27}}
|-
|-
|G la mi reb
|G la mi reb
| Fb
| Pb
| 29\15
| 29\15
1338; 2, 6
1338; 2, 6
|34\18
|34\18
1316; 7.75
1316; 7.75
|13\7
|13\7
1300
1300
|31\17
|31\17
1282; 1.3{{Overline|18}}
1282; 1, 3, 7
|18\10
|18\10
1270; 1.7
1270; 1.7
Line 2,029: Line 2,107:
|-
|-
!G la mi re
!G la mi re
!F
!P
!30\15
!30\15
1384; 1.625
1384; 1.625
! 22\11
! 22\11
1389; 2.{{Overline|1}}
1389; 2, 9
!36\18
!36\18
1393; 1, 1, 4.{{Overline|6}}
1393; 1, 1, 4, 1.5
!14\7
!14\7
1400
1400
!34\17
!34\17
1406; 1, 8.{{Overline|6}}
1406; 1, 8, 1.5
!20\10
!20\10
1411; 1, 3, 4
1411; 1, 3, 4
Line 2,046: Line 2,129:
|-
|-
|G la mi re#
|G la mi re#
|F#
|P#
|31\15
|31\15
1430; 1.3
1430; 1.3
| rowspan="2" |23\11
| rowspan="2" |23\11
1452; 1.58{{Overline|3}}
1452; 1, 1, 1.4
|38\18
|38\18
1470; 1.0{{Overline|3}}
1470; 1, 30
|15\7
|15\7
1500
1500
|37\17
|37\17
1531; 29
1531; 29
|22\10
|22\10
1552; 1, 16
1552; 1, 16
|29\13
|29\13
1581.{{Overline|81}}
1581.{{Overline|81}}
|-
|-
|A fab
|A fab
|
|Qbb
|32\15
|32\15
1476; 1, 12
1476; 1, 12
Line 2,070: Line 2,160:
|14\7
|14\7
1400
1400
|33\29
|33\17
1365; 1.9{{Overline|3}}
1365; 1, 1, 14
|19\10
|19\10
1341; 5.{{Overline|6}}
1341; 5, 1.5
|24\13
|24\13
1309.{{Overline|09}}
1309.{{Overline|09}}
|-
|-
|A fa
|A fa
|Gb
|Qb
|33\15
|33\15
1523; 13
1523; 13
|24\11
|24\11
1515; 1.2{{Overline|6}}
1515; 1, 3.75
|39\18
|39\18
1509; 1, 2.1
1509; 1, 2.1
|15\7
|15\7
1500
1500
|36\17
|36\17
1489; 1, 1.9
1489; 1, 1.9
|21\10
|21\10
1482; 2.8{{Overline|3}}
1482; 2, 1.2
|27\13
|27\13
1472.{{Overline|72}}
1472.{{Overline|72}}
|-
|-
|'''A mi'''
|'''A mi'''
|'''G'''
|'''Q'''
|'''34\15'''
|'''34\15'''
'''1569; 4.{{Overline|3}}'''
'''1569; 4, 3'''
|'''25\11'''
|'''25\11'''
'''1578; 1.0{{Overline|5}}'''
'''1578; 1, 18'''
|'''41\18'''
|'''41\18'''
'''1587; 10.{{Overline|3}}'''
'''1587; 10, 3'''
|'''16\7'''
|'''16\7'''
'''1600'''
'''1600'''
|'''39\17'''
|'''39\17'''
'''1613; 1, 3.8{{Overline|3}}'''
'''1613; 1, 3, 1.2'''
|'''23\10'''
|'''23\10'''
'''1623; 1.{{Overline|8}}'''
'''1623; 1, 1, 8'''
|'''30\13'''
|'''30\13'''
'''1636.{{Overline|36}}'''
'''1636.{{Overline|36}}'''
|-
|-
|A mi#
|A mi#
|G#
|Q#
|35\15
|35\15
1615; 2.6
1615; 2.6
|26\11
|26\11
1642; 9.5
1642; 9.5
| 43\18
| 43\18
1664; 1.9375
1664; 1, 6.75
| rowspan="2" |17\7
| rowspan="2" |17\7
1700
1700
|42\17
|42\17
1737; 14.5
1737; 1, 13.5
|25\10
|25\10
1764; 1.41{{Overline|6}}
1764; 1, 2.4
| 33\13
| 33\13
1800
1800
|-
|-
|B sol fa utb  
|B sol fa utb  
|Ab
|Rb
|37\15
|37\15
1707; 1.{{Overline|4}}
1707; 1, 2, 4
|27\11
|27\11
1705; 3.8
1705; 3.8
|44\18
|44\18
1703; 4, 2.{{Overline|3}}
1703; 4, 2, 3
|41\17
|41\17
1696; 1.8125
1696; 1.8125
|24\10
|24\10
1694; 8.5
1694; 8.5
|31\13
|31\13
1690.{{Overline|90}}
1690.{{Overline|90}}
|-
|-
| B sol fa ut
| B sol fa ut
|A
|R
| 38\15
| 38\15
1753; 1.{{Overline|18}}
1753; 1, 5.5
|28\11
|28\11
1768; 2.375
1768; 2.375
|46\18
|46\18
1780; 1.55
1780; 1.55
| 18\7
| 18\7
1800
1800
|44\17
|44\17
1820; 1.45
1820; 1.45
|26\10
|26\10
1835; 3.4
1835; 3.4
|34\13
|34\13
1854.{{Overline|54}}
1854.{{Overline|54}}
|-
|-
|B sol fa ut#
|B sol fa ut#
|A#
|R#
| 39\15
| 39\15
1800
1800
| rowspan="2" |29\11
| rowspan="2" |29\11
1831; 1.{{Overline|72}}
1831; 1, 1.375
|48\18
|48\18
1858; 15.5
1858; 15.5
|19\7
|19\7
1900
1900
| 47\17
| 47\17
1944; 1.208{{Overline|3}}
1944; 1, 4.8
|28\10
|28\10
1976; 2, 8
1976; 2, 8
|37\13
|37\13
2018.{{Overline|18}}
2018.{{Overline|18}}
|-
|-
|C la sol reb
|C la sol reb
|Bbb
|Sbb
| 40\15
| 40\15
1846; 6.5
1846; 6.5
| 47\18
| 47\18
1819; 2.{{Overline|81}}
1819; 2, 1, 4.5
|18\7
|18\7
1800
1800
|43\17
|43\17
1779; 3.{{Overline|2}}
1779; 3, 4.5
|25\10
|25\10
1764; 1.41{{Overline|6}}
1764; 1, 2.4
|32\13
|32\13
1745.{{Overline|45}}
1745.{{Overline|45}}
|-
|-
|'''C la sol re'''
|'''C la sol re'''
|'''Bb'''
|'''Sb'''
|'''41\15'''
|'''41\15'''
'''1892; 3, 4'''
'''1892; 3, 4'''
|'''30\11'''
|'''30\11'''
'''1894; 1, 2.8'''
'''1894; 1, 2.8'''
|'''49\18'''
|'''49\18'''
'''1896; 1.291{{Overline|6}}'''
'''1896; 1, 3, 2, 3'''
|'''19\7'''
|'''19\7'''
'''1900'''
'''1900'''
|'''46\17'''
|'''46\17'''
'''1903; 2, 2, 6'''
'''1903; 2, 6'''
|'''27\10'''
|'''27\10'''
'''1905; 1.1{{Overline|3}}'''
'''1905; 1, 7.5'''
|'''35\13'''
|'''35\13'''
'''1909.{{Overline|09}}'''
'''1909.{{Overline|09}}'''
|-
|-
| C la sol re#
| C la sol re#
| B
| S#
| 42\15
| 42\15
1938; 2, 6
1938; 2, 6
|31\11
|31\11
1957; 1, 8.5
1957; 1, 8.5
|51\18
|51\18
1974; 5, 6
1974; 5, 6
| 20\7
| 20\7
2000
2000
|49\17
|49\17
2027; 1, 1.41{{Overline|6}}
2027; 1, 1, 2.4
|29\10
|29\10
2047; 17
2047; 17
|38\13
|38\13
2072.{{Overline|72}}
2072.{{Overline|72}}
|-
|-
|C la sol rex
|C la sol rex
|B#
|Sx
|43\15
|43\15
1984; 1.625
1984; 1.625
| rowspan="2" |32\11
| rowspan="2" |32\11
2021; 19
2021; 19
|53\18
|53\18
2051; 1, 1, 1, 1.4
2051; 1, 1, 1, 1.4
| 21\7
| 21\7
2100
2100
|52\17
|52\17
2151; 1, 2.625
2151; 2.625
|31\10
|31\10
2188; 4.25
2188; 4, 4
|41\13
|41\13
2236.{{Overline|36}}
2236.{{Overline|36}}
|-
|-
|D la mib  
|D la mib  
| Hb
| Tb
|44\15
|44\15
2030; 1.3
2030; 1.3
|52\18
|52\18
2012; 1, 9.{{Overline|3}}
2012; 1, 9, 3
|20\7
|20\7
2000
2000
|48\17
|48\17
1986; 4.8{{Overline|3}}
1986; 4, 1.2
|28\10
|28\10
1976; 2, 8
1976; 2, 8
|36\13
|36\13
1963.{{Overline|63}}
1963.{{Overline|63}}
|-
|-
!D la mi
!D la mi
!H
!T
!45\15
!45\15
2076; 1, 12
2076; 1, 12
!33\11
!33\11
2084; 4.75
2084; 4.75
!54\18
!54\18
2090; 3.1
2090; 3.1
! 21\7
! 21\7
2100
2100
!51\17
!51\17
2110; 2.9
2110; 2.9
!30\10
!30\10
2117; 1.{{Overline|54}}
2117; 1, 1, 1.2
! 39\13
! 39\13
2127.{{Overline|27}}
2127.{{Overline|27}}
|-
|-
|D la mib  
|D la mib  
|Η#
|T#
|46\15
|46\15
2123; 13
2123; 13
Line 2,288: Line 2,459:
2234; 2, 14
2234; 2, 14
| 32\10
| 32\10
2258; 1, 4.{{Overline|6}}
2258; 1, 4, 1.5
|42\13
|42\13
2290.{{Overline|90}}
2090.{{Overline|90}}
|-
|-
|E fa utb
|E fa utb
|Cb
|Ub
|48\15
|48\15
2215; 2.6
2215; 2.6
Line 2,299: Line 2,470:
2210; 1.9
2210; 1.9
|57\18
|57\18
2206; 2, 4.{{Overline|6}}
2206; 2, 4, 1.5
|53\17
|53\17
2193; 9.{{Overline|6}}
2193; 9.{{Overline|6}}
|31\10
|31\10
2188; 4, 4
2188; 4, 4
|40\13
|40\13
Line 2,308: Line 2,480:
|-
|-
|'''E fa ut'''
|'''E fa ut'''
|'''C'''
|'''U'''
|'''49\15'''
|'''49\15'''
'''2261; 1, 1, 6'''
'''2261; 1, 1, 6'''
Line 2,314: Line 2,486:
'''2273; 1, 2, 6'''
'''2273; 1, 2, 6'''
|'''59\18'''
|'''59\18'''
'''2283; 1.{{Overline|148}}'''
'''2283; 1, 6.75'''
|'''23\7'''
|'''23\7'''
'''2300'''
'''2300'''
Line 2,320: Line 2,492:
'''2317; 4, 7'''
'''2317; 4, 7'''
|'''33\10'''
|'''33\10'''
'''2329; 2, 2.{{Overline|3}}'''
'''2329; 2, 2, 3'''
|'''43\13'''
|'''43\13'''
'''2245.{{Overline|45}}'''
'''2245.{{Overline|45}}'''
|-
|-
|E fa ut#
|E fa ut#
|C#
|U
|50\15
|50\15
2307; 1.{{Overline|4}}
2307; 1, 2, 4
|37\11
|37\11
2336; 1.1875
2336; 1, 5, 3
|61\18
|61\18
2361; 3.{{Overline|4}}
2361; 3, 2, 4
| rowspan="2" |24\7
| rowspan="2" |24\7
2400
2400
|59\17
|59\17
2441; 2.{{Overline|63}}
2441; 2, 1, 1.75
|35\10
|35\10
2470; 1.7
2470; 1.7
Line 2,342: Line 2,514:
|-
|-
|F sol re utb  
|F sol re utb  
|Db
|Vb
|52\15
|52\15
2400
2400
Line 2,357: Line 2,529:
|-
|-
|F sol re ut
|F sol re ut
|D
|V
|53\15
|53\15
2446; 6.5
2446; 6.5
|39\11
|39\11
2463; 6.{{Overline|3}}
2463; 6, 3
|64\18
|64\18
2477; 2, 2.6
2477; 2, 2.6
Line 2,367: Line 2,539:
2500
2500
|61\17
|61\17
2524; 7.25
2524; 7, 4
|36\10
|36\10
2541; 5.{{Overline|6}}
2541; 5, 3
| 47\13
| 47\13
2563.{{Overline|63}}
2563.{{Overline|63}}
|-
|-
|F sol re ut#
|F sol re ut#
|D#
|V#
|54\15
|54\15
2492; 3, 4
2492; 3, 4
| rowspan="2" |40\11
| rowspan="2" |40\11
2526; 3.1
2526; 3, 6
| 66\18
| 66\18
2554; 1, 5.2
2554; 1, 5.2
Line 2,384: Line 2,556:
2600
2600
|64\17
|64\17
2648; 3.625
2648; 2.625
|38\10
|38\10
2682; 2.8{{Overline|3}}
2682; 2, 1.2
|50\13
|50\13
2727.{{Overline|27}}
2727.{{Overline|27}}
|-
|-
|G la mi reb
|G la mi reb
|Ebb
|Wbb
|55\15
|55\15
2538; 2, 6
2538; 2, 1
|65\18
|65\18
2516; 7.75
2516; 7.75
Line 2,399: Line 2,571:
2500
2500
|60\17
|60\17
2482; 1.3{{Overline|18}}
2482; 1, 3, 7
|35\10
|35\10
2470; 1.7
2470; 1.7
Line 2,406: Line 2,578:
|-
|-
|'''G la mi re'''
|'''G la mi re'''
|'''Eb'''
|'''Wb'''  
|'''56\15'''
|'''56\15'''
'''2584; 1.625'''
'''2584; 1.625'''
|'''41\11'''
|'''41\11'''
'''2589; 2.{{Overline|1}}'''
'''2589; 2, 9'''
|'''67\18'''
|'''67\18'''
'''2593; 1, 1, 4.{{Overline|6}}'''
'''2593; 1, 1, 4, 1.5'''
|'''26\7'''
|'''26\7'''
'''2600'''
'''2600'''
|'''63\17'''
|'''63\17'''
'''2606; 1, 8.{{Overline|6}}'''
'''2606; 1, 8, 1.5'''
|'''37\10'''
|'''37\10'''
'''2611; 1, 3, 4'''
'''2611; 1, 3, 4'''
Line 2,423: Line 2,595:
|-
|-
|G la mi re#
|G la mi re#
|E
|W
|57\15
|57\15
2630; 1.3
2630; 1.3
|42\11
|42\11
2652; 1.58{{Overline|3}}
2652; 1, 1, 1.4
|69\18
|69\18
2670; 1.0{{Overline|3}}
2670; 1, 30
| 27\7
| 27\7
2700
2700
Line 2,440: Line 2,612:
|-
|-
|G la mi rex
|G la mi rex
|E#
|W#
| rowspan="2" | 58\15
| rowspan="2" | 58\15
2676; 1, 12
2676; 1, 12
|43\11
|43\11
2715; 1.2{{Overline|6}}
2715; 1, 3.75
|71\18
|71\18
2748; 2.58{{Overline|3}}
2748; 2, 1, 1.4
|28\7
|28\7
2800
2800
|69\17
|69\17
2855; 4.8
2855; 5.8
|41\10
|41\10
2894; 8.5
2894; 8.5
Line 2,457: Line 2,629:
|-
|-
|A fab
|A fab
|
|Xbb
|42\11
|42\11
2652; 1.58{{Overline|3}}
2652; 1, 1, 1.4
|68\18
|68\18
2632; 3.875
2632; 3.875
Line 2,465: Line 2,637:
2600
2600
|62\17
|62\17
2565; 1.9{{Overline|3}}
2565; 1, 1, 14
|36\10
|36\10
2541; 5.{{Overline|6}}
2541; 5, 1.5
|46\13
|46\13
2509.{{Overline|09}}
2509.{{Overline|09}}
|-
|-
|A fa
|A fa
|Fb
|Xb
|59\15
|59\15
2723; 13
2723; 13
|43\11
|43\11
2715; 1.2{{Overline|6}}
2715; 1, 3.75
|70\18
|70\18
2709; 1, 2.1
2709; 1, 2.1
Line 2,484: Line 2,656:
2689; 1, 1.9
2689; 1, 1.9
|38\10
|38\10
2682; 2.8{{Overline|3}}
2682; 2, 1.2
|49\13
|49\13
2672.{{Overline|72}}
2672.{{Overline|72}}
|-
|-
!A mi
!A mi
!F
!X
!60\15
!60\15
2769; 4.'''{{Overline|3}}'''
2769; 4, 3
!44\11
!44\11
2778; 1.0{{Overline|5}}
2778; 1, 18
!72\18
!72\18
2787; 3.1
2787; 3.1
Line 2,499: Line 2,671:
2800
2800
!68\17
!68\17
2813; 1, 3.8{{Overline|3}}
2813; 1, 3, 1.2
!40\10
!40\10
2823; 1.{{Overline|8}}
2823; 1, 1, 8
!52\13
!52\13
2836.{{Overline|36}}
2836.{{Overline|36}}
|-
|-
|A mi#
|A mi#
|
|X#
|61\15
|61\15
2815; 2.6
2815; 2.6
Line 2,516: Line 2,688:
2900
2900
|71\17
|71\17
2937; 14.5
2937; 1, 13.5
|42\10
|42\10
2964; 1.41{{Overline|6}}
2964; 1, 2.4
|55\13
|55\13
3000
3000
|-
|-
|B sol fab  
|B sol fab  
|
|Yb
|63\15
|63\15
2907; 1.{{Overline|4}}
2907; 1, 2, 4
|46\11
|46\11
2905; 3.8
2905; 3.8
|75\18
|75\18
2903; 4, 2.{{Overline|3}}
2903; 4, 2, 3
|70\17
|70\17
2896; 1.8125
2896; 1.8125
Line 2,538: Line 2,710:
|-
|-
|'''B sol fa'''
|'''B sol fa'''
|
|'''Y'''
|'''64\15'''
|'''64\15'''
'''2953; 1.{{Overline|18}}'''
'''2953; 1, 5.5'''
|'''47\11'''
|'''47\11'''
'''2968; 2.375'''
'''2968; 2.375'''
Line 2,555: Line 2,727:
|-
|-
|B sol fa#
|B sol fa#
|
|Y#
|65\15
|65\15
3000
3000
|48\11
|48\11
3031; 1.{{Overline|72}}
3031; 1, 1.375
|79\18
|79\18
3058; 15.5
3058; 15.5
Line 2,565: Line 2,737:
3100
3100
|76\17
|76\17
3144; 1.208{{Overline|3}}
3144; 1, 4.8
|45\10
|45\10
3176: 2, 8
3176: 2, 8
Line 2,572: Line 2,744:
|-
|-
|C la solb
|C la solb
|
|Zb
|67\15
|67\15
3092; 3, 4
3092; 3, 4
Line 2,578: Line 2,750:
3094; 1, 2.8
3094; 1, 2.8
|80\18
|80\18
3096; 1.291{{Overline|6}}
3096; 1, 3, 2, 3
|75\17
|75\17
3103; 2, 2, 6
3103; 2, 2, 6
|44\10
|44\10
3105; 1.1{{Overline|3}}
3105; 1, 7.5
|57\13
|57\13
3109.{{Overline|09}}
3109.{{Overline|09}}
|-
|-
|C la sol
|C la sol
|
|Z
|68\15
|68\15
3138; 2, 6
3138; 2, 6
Line 2,597: Line 2,769:
3200
3200
|78\17
|78\17
3227; 1, 1.41{{Overline|6}}
3227; 1, 1, 2.4
|46\10
|46\10
3247; 17
3247; 17
Line 2,604: Line 2,776:
|-
|-
|C la sol#
|C la sol#
|
|Z#
|69\15
|69\15
3184; 1.625
3184; 1.625
Line 2,620: Line 2,792:
3436.{{Overline|36}}
3436.{{Overline|36}}
|-
|-
|D lab
|D labb
|
|Ab
|70\15
|70\15
3230; 1.3
3230; 1.3
|83\18
|83\18
3212;  1, 9.{{Overline|3}}
3212;  1, 9, 3
|32\7
|32\7
3200
3200
|77\17
|77\17
3186; 4.{{Overline|3}}
3186; 4, 3
|45\10
|45\10
3176: 2, 8
3176: 2, 8
|58\13
|58\13
3172.{{Overline|72}}
3163.{{Overline|63}}
|-
|-
|'''D la'''
|'''D lab'''
|
|'''A'''
|'''71\15'''
|'''71\15'''
'''3276; 1, 12'''
'''3276; 1, 12'''
Line 2,648: Line 2,820:
'''3310; 2.9'''
'''3310; 2.9'''
|'''47\10'''
|'''47\10'''
'''3317; 1.5{{Overline|4}}'''
'''3317; 1, 1, 1.2'''
|'''61\13'''
|'''61\13'''
'''3327.{{Overline|27}}'''
'''3327.{{Overline|27}}'''
|-
|-
|D la#
|D la
|
|A#
|72\15
|72\15
3323; 13
3323; 13
Line 2,660: Line 2,832:
|87\18
|87\18
3367; 1, 2.875
3367; 1, 2.875
| rowspan="2" |34\7
|34\7
3400
3400
|83\17
|83\17
3434; 2, 14
3434; 2, 14
|49\10
|49\10
3458; 1, 4.{{Overline|6}}
3458; 1, 4, 1.5
|64\13
|64\13
3490.{{Overline|90}}
3490.{{Overline|90}}
|-
|D la#
|Ax
|73\15
3369; 4, 3
| rowspan="2" |54\15
3410; 1.9
|89\18
3445; 6.2
|35\7
3500
|86\17
3558; 1, 1, 1, 1.75
|51\10
3600
|67\13
3654.{{Overline|54}}
|-
|-
|F utb
|F utb
|
|Bb
|74\15
|74\15
3415; 2.6
3415; 2.6
|54\15
3410; 1.9
|88\18
|88\18
3406; 2, 4.{{Overline|6}}
3406; 2, 4, 1.5
|34\7
3400
|82\17
|82\17
3393; 9.{{Overline|6}}
3393; 9, 1.5
|48\10
|48\10
3388; 4, 4
3388; 4, 4
Line 2,685: Line 2,874:
|-
|-
!F ut
!F ut
!
!B
!75\15
!75\15
3461; 1, 1, 6
3461; 1, 1, 6
!55\11
!55\11
3473; 1, 2, 6
3473; 1, 2, 6
!90\18
!90\18
3483; 1.'''{{Overline|148}}'''
3483; 1, 6.75
!35\7
!35\7
3500
3500
Line 2,697: Line 2,886:
3517; 4, 7
3517; 4, 7
!50\10
!50\10
3529; 2, 2.{{Overline|3}}q
3529; 2, 2, 3
!65\13
!65\13
3545.{{Overline|45}}
3545.{{Overline|45}}
|}
==Intervals==
{| class="wikitable"
!Generators
!Sesquitave notation
!Interval category name
!Generators
!Notation of 3/2 inverse
!Interval category name
|-
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
|F ut#
|B#
|76\15
3507; 1, 2, 4
|56\15
3536; 1, 5, 3
|92\18
3561: 3, 2, 4
| rowspan="2" |36\7
3600
|88\17
3641; 2, 1, 1.75
|52\10
3670; 1.7
|68\13
3709.{{Overline|09}}
|-
|-
|0
|G reb
|Do, Sol
|Cb
|perfect unison
|78\15
|0
3600
|Do, Sol
|57\15
|sesquitave (just fifth)
3600
|93\18
3600
|87\17
3600
|51\10
3600
|66\13
3600
|-
|'''G re'''
|'''C'''
|'''79\15'''
'''3646; 6.5'''
|'''58\11'''
'''3663; 6, 3'''
|'''95\18'''
'''3677; 2, 2.6'''
|'''37\7'''
'''3700'''
|'''90\17'''
'''3724; 7, 4'''
|'''53\17'''
'''3741; 5, 1.5'''
|'''69\13'''
'''3763.{{Overline|63}}'''
|-
|-
|1
|G re#
|Fa, Do
|C#
|perfect fourth
|80\15
| -1
3692; 4, 3
|Re, La
|59\11
|perfect second
3726; 3, 6
|97\18
3755; 5.2
| rowspan="2" |38\7
3800
|93\17
3848; 3.625
|55\17
3882; 2, 1.2
|72\13
3927.{{Overline|27}}
|-
|-
|2
|A mib
|Mib, Sib
|Db
|minor third
|82\15
| -2
3784; 1.625
|Mi, Si
|60\11
|major third
3789; 2,9
|98\18
3793; 1, 1, 4, 1.5
|92\17
3806; 1, 8, 1.5
|54\17
3811; 1, 3, 4
|70\13
3818.{{Overline|18}}
|-
|-
| 3
|A mi
|Reb, Lab
|D
|diminished second
|83\15
| -3
3830, 1.3
|Fa#, Do#
|61\11
|augmented fourth
3852; 1, 1, 1.4
|100\18
3870; 1, 30
|39\7
3900
|95\17
3931; 29
|56\17
3952; 1, 16
|73\13
3981.{{Overline|81}}
|-
|-
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|A mi#
|D#
|84\15
3876; 1, 12
| rowspan="2" |62\11
3915; 1, 3.75
|102\18
3948; 2, 1, 1.4
|40\7
4000
|98\17
4055; 5.8
|58\10
4094; 8.5
|76\13
4145.{{Overline|45}}
|-
|-
|4
|B fa utb
|Dob, Solb
|Ebb
|diminished sesquitave
|85\15
| -4
3923; 13
| Do#, Sol#
|101\18
|augmented unison (chroma)
3909; 1, 2.1
|39\7
3900
|94\17
3889; 1, 1.9
|55\10
3882; 2, 1.2
|71\13
3872.{{Overline|72}}
|-
|'''B fa ut'''
|'''Eb'''
|'''86\15'''
'''3969; 4, 3'''
|'''63\11'''
'''3978; 1, 3.75'''
|'''103\18'''
'''3987; 10, 3'''
|'''40\7'''
'''4000'''
|'''97\17'''
'''4013; 1, 3, 1.2'''
|'''57\10'''
'''4023; 1, 1, 8'''
|'''74\13'''
'''4036.{{Overline|36}}'''
|-
|B fa ut#
|E
|87\15
4015; 2.6
|64\11
4042; 9.5
|105\18
4064; 1.9375
|41\7
4100
|100\17
4137; 1, 13.5
|59\10
4164; 1, 2.4
|77\13
4200
|-
|B fa utx
|E#
|88\15
4061; 1, 1, 6
| rowspan="2" |65\11
4105; 3.8
|107\18
4141; 1, 14.5
|42\7
4200
|103\17
4262; 14.5
|61\10
4305; 1, 7.5
|80\13
4363.{{Overline|63}}
|-
|-
|5
|C sol reb
|Fab, Dob
|Fb
|diminished fourth
|89\15
| -5
4107; 1.3
|Re#, La#
|106\18
|augmented second
4103; 4, 2, 3
|41\7
4100
|99\17
4096; 1.8125
|58\10
4094; 8.5
|75\13
4090.{{Overline|90}}
|-
|-
|6
!C sol re
|Mibb, Sibb
!F
|diminished third
!90\15
| -6
4153; 1, 5.5
|Mi#, Si#
!66\11
|augmented third
4168; 2.375
|}  
!108\18
4180; 1.55
==Genchain==
!42\7
4200
The generator chain for this scale is as follows:
!102\17
4220; 1.45
!60\10
4235; 3.4
!78\13
4254.{{Overline|54}}
|}
==Intervals==
{| class="wikitable"
{| class="wikitable"
|Mibb
!Generators
!Sesquitave notation
Sibb
!Interval category name
|Fab
!Generators
!Notation of 3/2 inverse
Dob
!Interval category name
|Dob
|-
| colspan="6" |The 4-note MOS has the following intervals (from some root):
Solb
|-
|Reb
|0
|Do, Sol
Lab
|perfect unison
|Mib
|0
|Do, Sol
Sib
|sesquitave (just fifth)
|Fa
|-
|1
Do
|Fa, Do
|Do
|perfect fourth
| -1
Sol
|Re, La
|Re
|perfect second
La
|Mi
Si
|Fa#
Do#
|Do#
Sol#
|Re#
La#
|Mi#
Si#
|-
|-
|d3
|2
|d4
|Mib, Sib
|d5
|minor third
|d2
| -2
|m3
|Mi, Si
|P4
|major third
|P1
|P2
|M3
|A4
|A1
|A2
|A3
|}
==Modes==
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
|-
!name
| 3
!pattern
|Reb, Lab
!notation
|diminished second
!2nd
| -3
!3rd
|Fa#, Do#
!4th
|augmented fourth
|-
|-
|Lydian
| colspan="6" |The chromatic 7-note MOS also has the following intervals (from some root):
|LLLs
|<nowiki>3|0</nowiki>
|P
|M
|A
|-
|-
|Major
|4
|LLsL
|Dob, Solb
|<nowiki>2|1</nowiki>
|diminished sesquitave
|P
| -4
|M
| Do#, Sol#
|P
|augmented unison (chroma)
|-
|-
|Minor
|5
|LLsL
|Fab, Dob
|<nowiki>1|2</nowiki>
|diminished fourth
|P
| -5
|m
|Re#, La#
| P
|augmented second
|-
|-
|Phrygian
|6
| sLLL
|Mibb, Sibb
|<nowiki>0|3</nowiki>
|diminished third
|d
| -6
|m
|Mi#, Si#
|P
|augmented third
|}  
|}  
==Temperaments==
==Genchain==
   
   
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
The generator chain for this scale is as follows:
==='''Napoli-Meantone'''===
{| class="wikitable"
|Mibb
   
   
[[Subgroup]]: 3/2.6/5.8/5
Sibb
|Fab
   
   
[[Comma]] list: [[81/80]]
Dob
 
|Dob
[[POL2]] generator: ~9/8 = 192.6406¢
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Optimal ET sequence]]: ~(7edf, 11edf, 18edf)
==='''Napoli-Archy'''===
   
   
[[Subgroup]]: 3/2.7/6.14/9
Solb
|Reb
   
   
[[Comma]] list: [[64/63]]
Lab
 
|Mib
[[POL2]] generator: ~8/7 = 218.6371¢
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
 
[[Optimal ET sequence]]: ~(7edf, 10edf, 13edf, 16edf)
===Scale tree===
   
   
The spectrum looks like this:
Sib
{| class="wikitable"
|Fa
! colspan="3" |Generator
   
   
(bright)
Do
!Cents<u><ref name=":03">Fractions repeating more than 4 digits written as continued fractions</ref></u>
|Do
!L
!s
Sol
!L/s
|Re
!Comments
La
|Mi
Si
|Fa#
Do#
|Do#
Sol#
|Re#
La#
|Mi#
Si#
|-
|-
|1\4
|d3
|
|d4
|
|d5
|<u>171; 2.{{Overline|3}}</u>
|d2
|1
|m3
|1
|P4
|1.000
|P1
|Equalised
|P2
|M3
|A4
|A1
|A2
|A3
|}  
==Modes==
The mode names are based on the species of fifth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
|-
|6\23
!name
|
!pattern
|
!notation
|<u>180</u>
!2nd
|6
!3rd
|5
!4th
|1.200
|
|-
|-
|
|Lydian
|11\42
|LLLs
|
|<nowiki>3|0</nowiki>
|<u>180; 1.21{{Overline|6}}</u>
|P
|11
|M
|9
|A
|1.222
|-
|
|Major
|LLsL
|<nowiki>2|1</nowiki>
|P
|M
|P
|-
|-
|5\19
|Minor
|
|LLsL
|
|<nowiki>1|2</nowiki>
|<u>181.{{Overline|81}}</u>
|P
|5
|m
|4
| P
|1.250
|
|-
|-
|Phrygian
| sLLL
|<nowiki>0|3</nowiki>
|d
|m
|P
|}
==Temperaments==
The most basic rank-2 temperament interpretation of angel is '''Napoli'''. The name "Napoli" comes from the “Neapolitan” sixth triad spelled <code>root-(p-2g)-(2p-3g)</code> (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.
==='''Napoli-Meantone'''===
[[Subgroup]]: 3/2.6/5.8/5
[[Comma]] list: [[81/80]]
[[POL2]] generator: ~9/8 = 192.6406¢
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
[[Optimal ET sequence]]: ~(7edf, 11edf, 18edf)
==='''Napoli-Archy'''===
[[Subgroup]]: 3/2.7/6.14/9
[[Comma]] list: [[64/63]]
[[POL2]] generator: ~8/7 = 218.6371¢
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -2 -3}}]
[[Optimal ET sequence]]: ~(7edf, 10edf, 13edf, 16edf)
===Scale tree===
The spectrum looks like this:
{| class="wikitable"
! colspan="3" |Generator
(bright)
!Cents<u><ref name=":03">Fractions repeating more than 4 digits written as continued fractions</ref></u>
!L
!s
!L/s
!Comments
|-
|1\4
|
|
|
|14\53
|<u>171; 2, 3</u>
|
|1
|<u>182; 1, 1.5</u>
|1
|14
|1.000
|11
|Equalised
|1.273
|
|-
|
|9\34
|
|<u>183; 19.{{Overline|6}}</u>
|9
|7
|1.286
|
|-
|4\15
|
|
|<u>184; 1.625</u>
|4
|3
|1.333
|
|-
|-
|6\23
|
|
|11\41
|
|
|<u>185, 1, 10.8{{Overline|3}}</u>
|<u>180</u>
|11
|6
|8
|5
|1.375
|1.200
|
|
|-
|-
|
|
|7\26
|11\42
|
|
|<u>186.{{Overline|6}}</u>
|<u>180; 1, 4, 1.625</u>
|7
|11
|5
|9
|1.400
|1.222
|
|
|-
|-
|5\19
|
|
|10\37
|
|
|<u>187.5</u>
|<u>181.{{Overline|81}}</u>
| 10
|5
|7
|4
|1.429
|1.250
|
|
|-
|-
|
|
|13\48
|14\53
|
|
|<u>187; 1, 19.75</u>
|<u>182; 1, 1.5</u>
|13
|14
|9
|11
|1.444
|1.273
|
|
|-
|-
|
|
|16\59
|9\34
|
|
|<u>188; 4.25</u>
|<u>183; 19, 1.5</u>
|16
|9
|11
|7
| 1.455
|1.286
|
|
|-
|-
|3\11
|4\15
|
|
|
|
|<u>189; 2.{{Overline|1}}</u>
|<u>184; 1.625</u>
|4
|3
|3
|2
|1.333
|1.500
|
|Napoli-Meantone starts here
|-
|-
|
|
|17\62
|11\41
|
|
|<u>190; 1, 1.{{Overline|12}}</u>
|<u>185, 1, 10, 1.2</u>
|17
|11
|11
|1.545
|8
|1.375
|
|
|-
|-
|
|
|14\51
|7\26
|
|
|<u>190.{{Overline|90}}</u>
|<u>186.{{Overline|6}}</u>
|14
|7
|9
|5
|1.556
|1.400
|
|
|-
|-
|
|
|11\40
|10\37
|
|
|<u>191; 3, 2.{{Overline|3}}</u>
|<u>187.5</u>
|11
| 10
|7
|7
|1.571
|1.429
|
|
|-
|-
|
|
|8\29
|13\48
|
|
|<u>192</u>
|<u>187; 1, 19.75</u>
|8
|13
|5
|9
|1.600
|1.444
|
|
|-
|-
|
|
|5\18
|16\59
|
|
|<u>193; 1, 1, 4.{{Overline|6}}</u>
|<u>188; 4, 4</u>
|5
|16
|3
|11
|1.667
| 1.455
|
|
|-
|-
|3\11
|
|
|
|
|12\43
|<u>189; 2, 9</u>
|<u>194.{{Overline|594}}</u>
|3
|12
|2
|7
|1.500
|1.714
|Napoli-Meantone starts here
|
|-
|-
|
|
|7\25
|14\51
|
|
|<u>195; 2.8{{Overline|6}}</u>
|<u>190.{{Overline|90}}</u>
|7
|14
|4
|9
|1.750
|1.556
|
|
|-
|-
|
|
|9\32
|11\40
|
|
|<u>196.{{Overline|36}}</u>
|<u>191; 3, 2, 3</u>
|9
|11
|5
|7
|1.800
|1.571
|
|
|-
|-
|
|
|11\39
|8\29
|
|
|<u>197; 67</u>
|<u>192</u>
|11
|8
|6
|5
|1.833
|1.600
|
|
|-
|-
|
|
|13\46
|5\18
|
|
|<u>197; 2.{{Overline|135}}</u>
|<u>193; 1, 1, 4, 1.5</u>
| 13
|5
|7
|3
|1.857
|1.667
|
|
|-
|-
|
|
|15\53
|
|
|<u>197; 1, 2, 1, 1.{{Overline|54}}</u>
|12\43
|15
|<u>194.{{Overline|594}}</u>
|8
|12
|1.875
|7
|1.714
|
|
|-
|-
|
|
|17\60
|7\25
|
|
|<u>198; 17.1{{Overline|6}}</u>
|<u>195; 2, 1, 6.5</u>
|17
|7
|9
|4
|1.889
|1.750
|
|
|-
|-
|
|
|19\67
|9\32
|
|
|<u>198: 3, 1, 28</u>
|<u>196.{{Overline|36}}</u>
|19
|9
|10
|5
|1.900
|1.800
|
|
|-
|-
|
|
|21\74
|11\39
|
|
|<u>198; 2.3{{Overline|518}}</u>
|<u>197; 67</u>
|21
|11
|11
|1.909
|6
|1.833
|
|
|-
|-
|
|
|23\81
|13\46
|
|
|<u>198; 1, 3, 1.7</u>
|<u>197; 2, 7.4</u>
|23
| 13
|12
|7
|1.917
|1.857
|
|
|-
|-
|
|
|25\88
|15\53
|
|
|<u>198; 1, 2, 12.25</u>
|<u>197; 1, 2, 1, 1, 1, 1.2</u>
|25
|15
|13
|8
|1.923
|1.875
|
|
|-
|-
|
|
|27\95
|17\60
|
|
|<u>198; 1, 3.{{Overline|405}}</u>
|<u>198; 17, 6</u>
|27
|17
|14
|9
|1.929
|1.889
|
|
|-
|-
|
|
|29\102
|19\67
|
|
|<u>198; 1, 1.1{{Overline|6}}</u>
|<u>198: 3, 1, 28</u>
|29
|19
|15
|10
|1.933
|1.900
|
|
|-
|-
|2\7
|
|
|21\74
|
|<u>198; 2, 2, 1.1875</u>
|21
|11
|1.909
|
|
|<u>200</u>
|2
|1
|2.000
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|-
|
|
|17\59
|23\81
|
|
|<u>201.{{Overline|9801}}</u>
|<u>198; 1, 3, 1.7</u>
|17
|23
|8
|12
|2.125
|1.917
|
|
|-
|-
|
|
|15\52
|25\88
|
|
|<u>202; 4.0{{Overline|45}}</u>
|<u>198; 1, 2, 12, 4</u>
|15
|25
|7
|13
|2.143
|1.923
|
|
|-
|-
|
|
|13\45
|27\95
|
|
|<u>202; 1, 1, 2.0{{Overline|6}}</u>
|<u>198; 1, 3, 2, 13</u>
|13
|27
|6
|14
|2.167
|1.929
|
|
|-
|-
|
|
|11\38
|29\102
|
|
|<u>203; 13</u>
|<u>198; 1, 1, 6</u>
|11
|29
|5
|15
|2.200
|1.933
|
|
|-
|-
|
|
|9\31
|31\109
|
|
|<u>203; 1, 3.41{{Overline|6}}</u>
|<u>198; 1, 13, 2.6</u>
|9
|31
|4
|16
|2.250
|1.9375
|
|
|-
|-
|
|
| 7\24
|33\116
|
|
|<u>204; 1. 7.2</u>
|<u>198; 1, 198</u>
| 7
|33
|3
|17
|2.333
|1.941
|
|
|-
|-
|2\7
|
|
|
|
|12\41
|<u>200</u>
|<u>205; 1.4</u>
|2
|12
|1
|5
|2.000
|2.400
|Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|
|
|-
|17\59
|
|
|5\17
|<u>201.{{Overline|9801}}</u>
|17
|8
|2.125
|
|
|<u>206; 1, 8.{{Overline|6}}</u>
|5
|2
|2.500
|Napoli-Neogothic heartland is from here…
|-
|-
|
|
|15\52
|
|
|18\61
|<u>202; 4, 22</u>
|<u>207; 1.{{Overline|4}}</u>
|15
|18
|7
|7
|2.571
|2.143
|
|
|-
|-
|
|
|13\45
|
|
|13\44
|<u>202; 1, 1, 2, 15</u>
|<u>208</u>
|13
|13
|5
|6
|2.600
|2.167
|
|
|-
|-
|
|
|8\27
|11\38
|
|
|<u>208; 1.4375</u>
|<u>203; 13</u>
|8
|3
|2.667
|…to here
|-
|
|11\37
|
|<u>209; 1.{{Overline|90}}</u>
|11
|11
|4
|5
|2.750
|2.200
|
|
|-
|-
|
|
|14\47
|9\31
|
|
|<u>210</u>
|<u>203; 1, 3, 2.4</u>
|14
|9
|5
|4
|2.800
|2.250
|
|
|-
|-
|
|
|17\57
| 7\24
|
|
|<u>210; 3.2{{Overline|3}}</u>
|<u>204; 1. 7.2</u>
|17
| 7
|6
|3
|2.833
|2.333
|
|
|-
|-
|
|
|20\67
|
|
|<u>210; 1.9</u>
|12\41
|20
|<u>205; 1.4</u>
|7
|12
|2.857
|5
|2.400
|
|
|-
|-
|
|
|23\77
|5\17
|
|
|<u>210; 1.4{{Overline|5}}</u>
|<u>206; 1, 8, 1.5</u>
|23
|5
|2
|2.500
|Napoli-Neogothic heartland is from here…
|-
|
|
|18\61
|<u>207; 1, 2, 4</u>
|18
|7
|2.571
|
|-
|
|8\27
|
|<u>208; 1, 5, 3</u>
|8
|8
|2.875
|3
|2.667
|…to here
|-
|
|11\37
|
|<u>209; 1, 1.1</u>
|11
|4
|2.750
|
|-
|
|14\47
|
|<u>210</u>
|14
|5
|2.800
|
|
|-
|-
Line 3,341: Line 3,716:
|
|
|
|
|<u>211; 1, 3.25</u>
|<u>211; 1, 3, 4</u>
|3
|3
|1
|1
Line 3,350: Line 3,725:
|22\73
|22\73
|
|
|<u>212; 1, 9.{{Overline|3}}</u>
|<u>212; 1, 9, 3</u>
|22
|22
|7
|7
Line 3,359: Line 3,734:
|19\63
|19\63
|
|
|<u>213; 11.{{Overline|8}}</u>
|<u>213; 11, 1, 8</u>
|19
|19
|6
|6
Line 3,377: Line 3,752:
|13\43
|13\43
|
|
|<u>213; 1, 2.3{{Overline|18}}</u>
|<u>213; 1, 2, 3, 7</u>
|13
|13
|4
|4
Line 3,404: Line 3,779:
|11\36
|11\36
|
|
|<u>216; 2.541{{Overline|6}}</u>
|<u>216; 2, 1, 1, 5.5</u>
|11
|11
|3
|3
Line 3,413: Line 3,788:
|15\49
|15\49
|
|
|<u>216; 1.152{{Overline|7}}</u>
|<u>216; 1, 6, 1, 1.2</u>
|15
|15
|4
|4
Line 3,476: Line 3,851:
|16\51
|16\51
|
|
|<u>223; 3.{{Overline|90}}</u>
|<u>223; 3, 1.1</u>
|16
|16
|3
|3
Line 3,492: Line 3,867:
|-
|-
|
|
|17\54
|17\54
|
|
|<u>224; 5.7{{Overline|2}}</u>
|<u>224; 5, 1, 2.6</u>
| 17
| 17
|3
|3
|5.667
|5.667
|
|
|-
|-
|6\19
|6\19
|
|
|
|
|<u>225</u>
|<u>225</u>
|6
|6
|1
|1
|6.000
|6.000
|
|
|-
|-
|1\3
|1\3
|
|
|
|
|<u>240</u>
|<u>240</u>
|1
|1
|0
|0
|→ inf
|→ inf
|Paucitonic
|Paucitonic
|}
|}
 
 
==See also==
==See also==
[[3L 1s (3/2-equivalent)]] - idealized tuning
[[3L 1s (3/2-equivalent)]] - idealized tuning
 
[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone
 
[[6L 2s (52/23-equivalent)]] - Neapolitan gentle temperament
 
[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy
 
[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone
 
[[9L 3s (22/13-equivalent]]) - Bijou gentle temperament
 
[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy
 
[[12L 4s (5/1-equivalent)]] - Hex meantone
 
[[12L 4s (56/11-equivalent)]] - Hextone gentle temperament


[[6L 2s (20/9-equivalent)]] - Neapolitan 1/2-comma meantone
[[12L 4s (36/7-equivalent)]] - Hextone 1/4-comma archy


[[6L 2s (52/23-equivalent)]] - Neapolitan gentle temperament
[[15L 5s (15/2-equivalent)]] - Guidotonic major 1/5-comma meantone


[[6L 2s (16/7-equivalent)]] - Neapolitan 1/2-comma archy
[[15L 5s (84/11-equivalent)]] - Guidotonic major gentle temperament


[[9L 3s (10/3-equivalent)]] - Bijou 1/3-comma meantone
[[15L 5s (54/7-equivalent)]] - Guidotonic major 1/5-comma archy


[[9L 3s (22/13-equivalent]]) - Bijou gentle temperament
[[18L 6s (11/1-equivalent)]] - Subdozenal harmonic tuning


[[9L 3s (24/7-equivalent)]] - Bijou 1/3-comma archy
[[18L 6s (56/5-equivalent)]] - Subdozenal low septimal tuning
 
[[12L 4s (5/1-equivalent)]] - Hex meantone


[[12L 4s (56/11-equivalent)]] - Hextone gentle temperament
[[18L 6s (80/7-equivalent)]] - Subdozenal high septimal tuning


[[12L 4s (36/7-equivalent)]] - Hextone 1/4-comma archy<references />
[[18L 6s (128/11-equivalent)]] - Subdozenal subharmonic tuning<references />

Revision as of 03:39, 9 July 2023

3L 1s<perfect fifth> is constructed by repeating the fifth-spanning pattern LLLs of the ordinary diatonic mos (5L 2s) at the equave of 3/2. The so-called "Super Ultra Hyper Mega Meta Lydian" is one mode of this mos.

The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating 3L 1s. The name of the period interval is called the sesquitave (by analogy to the tritave). The generator range is 171.4 to 240 cents, placing it near the diatonic major second, usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fifth complement (480 to 514.3 cents).

In the fifth-repeating version of the diatonic scale, each tone has a 3/2 perfect fifth above it. The scale has two major chords and two minor chords.

Angel is a proposed name for this mos. Basic Angel is in 7edf, which is a very good fifth-based equal tuning similar to 12edo.

Notation

There are 4 main ways to notate the angel scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate angel scales as repeating at the double, triple, quadruple, quintuple or sextuple sesquitave (major ninth, thirteenth, seventeenth i. e. ~pentave or twenty-first or augmented twenty-fifth), however it does make navigating the genchain harder. This way, 5/3 is its own pitch class, distinct from 10/9. Notating this way produces a major ninth which is the Aeolian mode of Napoli[6L 2s], a major thirteenth which is the Dorian mode of Bijou[9L 3s], an ~pentave which is the Mixolydian mode of Hextone[12L 4s], a major twenty-first which is the Ionian mode of Guidotonic[15L 5s] or an augmented twenty-fifth which is the Lydian mode of Subdozenal[18L 6s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation, 16 in quadruple sesquitave notation, 20 in quintuple sesquitave notation and 24 in sextuple sesquitave notation, letters A-H (FGABHCDEF), dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F molle), the Guidonian names with F as the lowest ut or letters except I and O may be used.

Cents[1]
Notation Supersoft Soft Semisoft Basic Semihard Hard Superhard
Diatonic Napoli Bijou Hextone ~15edf ~11edf ~18edf ~7edf ~17edf ~10edf ~13edf
Do#, Sol# F# 0#, D# 0#, G# 1\15

46; 6.5

1\11

63: 6, 3

2\18

77; 2, 2.6

1\7

100

3\17

124; 7, 4

2\10

141; 5, 1.5

3\13

163.63

Reb, Lab Gb 1b, 1c 1f 3\15

138; 3, 4

2\11

126; 3, 6

3\18

116; 7.75

2\17

82; 1, 3, 7

1\10

70; 1.7

1\13

54.54

Re, La G 1 1 4\15

184; 1.625

3\11

189; 2, 9

5\18

193; 1, 1, 4, 1.5

2\7

200

5\17

206; 1, 8, 1.5

3\10

211; 1, 3, 4

4\13

218.18

Re#, La# G# 1# 1# 5\15

230; 1.3

4\11

252; 1, 1, 1.4

7\18

270; 1, 30

3\7

300

8\17

331; 29

5\10

352; 1, 16

7\13

381.81

Mib, Sib Ab 2b, 2c 2f 7\15

323; 13

5\11

315; 1, 3.75

8\18

309; 1, 2.1

7\17

289; 1, 1.9

4\10

282; 2, 1.2

5\13

272.72

Mi, Si A 2 2 8\15

369; 4, 3

6\11

378; 1, 18

10\18

387; 10, 3

4\7

400

10\17

413; 1, 3, 1.2

6\10

423; 1, 1, 8

8\13

436.36

Mi#, Si# A# 2# 2# 9\15

415; 2.6

7\11

442; 9.5

12\18

464; 1.9375

5\7

500

13\17

537; 14.5

8\10

564; 1, 2.4

11\13

600

Fab, Dob Bbb 3b, 3c 3f 10\15

461; 1, 1, 6

11\18

425; 1.24

4\7

400

9\17

372; 2, 2.4

5\10

352; 1, 16

6\13

327.27

Fa, Do Bb 3 3 11\15

507; 1, 2, 4

8\11

505; 3.8

13\18

503; 4, 2, 3

5\7

500

12\17

496; 1.8125

7\10

494; 8.5

9\13

490.90

Fa#, Do# B 3# 3# 12\15

553; 1, 5.5

9\11

568; 2.375

15\18

580; 1.55

6\7

600

15\17

620; 1.45

9\10

635; 3.4

12\13

654.54

Fax, Dox B# 3x 3x 13\15

600

10\11

631; 1, 1.375

17\18

658; 15.5

7\7

700

18\17

744; 1, 4.8

11\10

776; 2, 8

15\13

818.18

Dob, Solb Hb 4b, 4c 4f 14\15

646; 6.5

16\18

619; 2, 1, 4.5

6\7

600

14\17

579; 3.2

8\10

564; 1, 2.4

10\13

545.45

Do, Sol H 4 4 15\15

692; 3, 4

11\11

694; 1, 2.8

18\18

696; 1, 3, 2, 3

7\7

700

17\17

703; 2, 2, 6

10\10

705; 1, 7.5

13\13

709.09

Do#, Sol# Η# 4# 4# 16\15

738; 2, 6

12\11

757; 1, 8.5

20\18

774; 5, 6

8\8

800

20\17

827; 1, 1, 2.4

12\10

847; 17

16\13

872.72

Reb, Lab Cb 5b, 5c 5 18\15

830; 1.3

13\11

821; 19

21\18

812; 1, 9, 3

19\17

786; 4, 1.2

11\10

776; 2, 8

14\13

763.63

Re, La C 5 5 19\15

876; 1, 12

14\11

884; 4.75

23\18

890; 3.1

9\5

900

22\17

910; 2.9

13\10

917; 1, 1, 1.2

17\13

927.27

Re#, La# C# 5# 5# 20\15

923: 13

15\11

947; 2, 1.4

25\18

967; 1, 2.875

10\7

1000

25\17

1034; 2, 14

15\10

1058; 1, 4, 1.5

20\13

1090.90

Mib, Sib Db 6b, 6c 6f 22\15

1015; 2.6

16\11

1010; 1.9

26\18

1006; 2, 4, 1.5

24\17

993; 9.6

14\10

988; 4, 4

18\13

981.81

Mi, Si D 6 6 23\15

1061; 1, 1, 6

17\11

1073; 1, 2, 6

28\18

1083; 1, 6.75

11\7

1100

27\17

1117; 4, 7

16\10

1129; 2, 2, 3

21\9

1145.45

Mi#, Si# D# 6# 6# 24\15

1107; 1, 2, 4

18\11

1136; 1.1875

30\18

1161; 3, 2, 4

12\7

1200

30\17

1241; 2, 1, 1.75

18\10

1270; 1.7

24\13

1309.09

Fab, Dob Ebb 7b, 7c 7f 25\15

1153; 1, 5.5

29\18

1121; 1, 1, 2.6

11\7

1100

26\17

1075; 1.16

15\10

1058; 1, 4, 1.5

19\13

1036.36

Fa, Do Eb 7 7 26\15

1200

19\11

1200

31\18

1200

12\7

1200

29\17

1200

17\10

1200

22\13

1200

Fa#, Do# E 7# 7# 27\15

1246; 6.5

20\11

1263; 6, 3

33\18

1277; 2, 2.6

13\7

1300

32\17

1324; 7, 4

19\10

1341; 5, 1.5

25\13

1363.63

Fax, Dox E# 7x 7x 28\15

1292; 3, 4

21\11

1326; 3, 6

35\18

1354; 1, 5.2

14\7

1400

35\17

1448; 3.625

21\10

1482; 2, 1.2

28\13

1527.27

Dob, Solb Fb 8b, Fc 8f 29\15

1338; 2, 6

34\18

1316; 7.75

13\7

1300

31\17

1282; 1, 3, 7

18\10

1270; 1.7

23\13

1254.54

Do, Sol F 8, F 8 30\15

1384; 1.625

22\11

1389; 2, 9

36\18

1393; 1, 1, 4, 1.5

14\7

1400

34\17

1406; 1, 8, 1.5

20\10

1411; 1, 3, 4

26\13

1418.18

Do#, Sol# F# 8#, F# 8# 31\15

1430; 1.3

23\11

1452; 1, 1, 1.4

38\18

1470; 1, 30

15\7

1500

37\17

1531; 29

22\10

1552; 1, 16

29\13

1581.81

Reb, Lab Gb 9b, Gc 9f 33\15

1523; 13

24\11

1515; 1, 3.75

39\18

1509; 1, 2.1

36\17

1489; 1, 1.9

21\10

1482; 2, 1.2

27\13

1472.72

Re, La G 9, G 9 34\15

1569; 4, 3

25\11

1578; 1, 18

41\18

1587; 10, 3

16\7

1600

39\17

1613; 1, 3, 1.2

23\10

1623; 1, 1, 8

30\13

1636.36

Re#, La# G# 9#, G# 9# 35\15

1615; 2.6

26\11

1642; 9.5

43\18

1664; 1, 6.75

17\7

1700

42\17

1737; 14.5

25\10

1764; 1, 2.4

33\13

1800

Mib, Sib Ab Xb, Ac Af 37\15

1707; 1, 2, 4

27\11

1705; 3.8

44\18

1703; 4, 2, 3

41\17

1696; 1.8125

24\10

1694; 8.5

31\13

1690.90

Mi, Si A X, A A 38\15

1753; 1, 5.5

28\11

1768; 2.375

46\18

1780; 1.55

18\7

1800

44\17

1820; 1.45

26\10

1835; 3.4

34\13

1854.54

Mi#, Si# A# X#, A# A# 39\15

1800

29\11

1831; 1, 1. 375

48\18

1858; 15.5

19\7

1900

47\17

1944; 1, 4.8

28\10

1976; 2, 8

37\13

2018.18

Fab, Dob Bbb Ebb, Ccc Bf 40\15

1846; 6.5

47\18

1819; 2, 1, 4.5

18\7

1800

43\17

1779; 3, 4.5

25\10

1764; 1, 2.4

32\13

1745.45

Fa, Do Bb Eb, Cc B 41\15

1892; 3, 4

30\11

1894; 1, 2.8

49\18

1896; 1, 3, 2, 3

19\7

1900

46\17

1903; 2, 6

27\10

1905; 1, 7.5

35\13

1909.09

Fa#, Do# B E, C B# 42\15

1938; 2, 6

31\11

1957; 1, 8.5

51\18

1974; 5, 6

20\7

2000

49\17

2027; 1, 1, 2.4

29\10

2047; 17

38\13

2072.72

Fax, Dox B# Ex, Cx Bx 43\15

1984; 1.625

32\11

2021; 19

53\18

2051; 1, 1, 1, 1.4

21\7

2100

52\17

2151; 2.625

31\10

2188; 4, 4

41\13

2236.36

Dob, Solb Hb 0b, Dc Cf 44\15

2030; 1.3

52\18

2012; 1, 9, 3

20\7

2000

48\17

1986; 4, 1.2

28\10

1976; 2, 8

36\13

1963.63

Do, Sol H 0, D C 45\15

2076; 1, 12

33\11

2084; 4.75

54\18

2090; 3.1

21\7

2100

51\17

2110; 2.9

30\10

2117; 1, 1, 1.2

39\13

2127.27

Do#, Sol# Η# 0#, D# C# 46\15

2123; 13

34\11

2147; 2, 1.4

56\18

2167; 1, 2.875

22\7

2200

54\17

2234; 2, 14

32\10

2258; 1, 4, 1.5

42\13

2090.90

Reb, Lab Cb 1b, 1c Df 48\15

2215; 2.6

35\11

2210; 1.9

57\18

2206; 2, 4, 1.5

53\17

2193; 9.6

31\10

2188; 4, 4

40\13

2181.81

Re, La C 1 D 49\15

2261; 1, 1, 6

36\11

2273; 1, 2, 6

59\18

2283; 1, 6.75

23\7

2300

56\17

2317; 4, 7

33\10

2329; 2, 2, 3

43\13

2245.45

Re#, La# C# 1# D# 50\15

2307; 1, 2, 4

37\11

2336; 1, 5, 3

61\18

2361; 3, 2, 4

24\7

2400

59\17

2441; 2, 1, 1.75

35\10

2470; 1.7

46\13

2509.09

Mib, Sib Db 2b, 2c Ef 52\15

2400

38\11

2400

62\18

2400

58\17

2400

34\10

2400

44\13

2400

Mi, Si D 2 E 53\15

2446; 6.5

39\11

2463; 6, 3

64\18

2477; 2, 2.6

25\7

2500

61\17

2524; 7, 4

36\10

2541; 5, 3

47\13

2563.63

Mi#, Si# D# 2# E# 54\15

2492; 3, 4

40\11

2526; 3, 6

66\18

2554; 1, 5.2

26\7

2600

64\17

2648; 2.625

38\10

2682; 2, 1.2

50\13

2727.27

Fab, Dob Ebb 3b, 3c Fff 55\15

2538; 2, 1

65\18

2516; 7.75

25\7

2500

60\17

2482; 1, 3, 7

35\10

2470; 1.7

45\13

2454.54

Fa, Do Eb 3 Ff 56\15

2584; 1.625

41\11

2589; 2, 9

67\18

2593; 1, 1, 4, 1.5

26\7

2600

63\17

2606; 1, 8, 1.5

37\10

2611; 1, 3, 4

48\13

2618.18

Fa#, Do# E 3# F 57\15

2630; 1.3

42\11

2652; 1, 1, 1.4

69\18

2670; 1, 30

27\7

2700

66\17

2731; 29

39\10

2752; 1, 16

51\13

2781.81

Fax, Dox E# 3x F# 58\15

2676; 1, 12

43\11

2715; 1, 3.75

71\18

2748; 2, 1, 1.4

28\7

2800

69\17

2855; 4.8

41\10

2894; 8.5

54\13

2945.45

Dob, Solb Fb 4b, 4c 0f, Gf 59\15

2723; 13

70\18

2709; 1, 2.1

27\7

2700

65\17

2689; 1, 1.9

38\10

2682; 2, 1.2

49\13

2672.72

Do, Sol F 4 0, G 60\15

2769; 4,3

44\11

2778; 1, 18

72\18

2787; 3.1

28\7

2800

68\17

2813; 1, 3, 1.2

40\10

2823; 1, 1, 8

52\13

2836.36

Cents[2]
Notation Supersoft Soft Semisoft Basic Semihard Hard Superhard
Guidotonic Subdozenal ~15edf ~11edf ~18edf ~7edf ~17edf ~10edf ~13edf
F ut# F# 1\15

46; 6.5

1\11

63: 6, 3

2\18

77; 2, 2.6

1\7

100

3\17

124; 7, 4

2\10

141; 5, 1.5

3\13

163.63

G reb Gb 3\15

138; 3, 4

2\11

126; 3, 6

3\18

116; 7.75

2\17

82; 1, 3, 7

1\10

70; 1.7

1\13

54.54

G re G 4\15

184; 1.625

3\11

189; 2, 9

5\18

193; 1, 1, 4, 1.5

2\7

200

5\17

206; 1, 8, 1.5

3\10

211; 1, 3, 4

4\13

218.18

G re# G# 5\15

230; 1.3

4\11

252; 1, 1, 1.4

7\18

270; 1, 30

3\7

300

8\17

331; 29

5\10

352; 1, 16

7\13

381.81

A mib Hb 7\15

323; 13

5\11

315; 1, 3.75

8\18

309; 1, 2.1

7\17

289; 1, 1.9

4\10

282; 2, 1.2

5\13

272.72

A mi H 8\15

369; 4, 3

6\11

378; 1, 18

10\18

387; 10, 3

4\7

400

10\17

413; 1, 3, 1.2

6\10

423; 1, 1, 8

8\13

436.36

A mi# H# 9\15

415; 2.6

7\11

442; 9.5

12\18

464; 1.9375

5\7

500

13\17

537; 1, 13.5

8\10

564; 1, 2.4

11\13

600

B fa utb Jbb 10\15

461; 1, 1, 6

11\18

425; 1.24

4\7

400

9\17

372; 2, 2.4

5\10

352; 1, 16

6\13

327.27

B fa ut Jb 11\15

507; 1, 2, 4

8\11

505; 3.8

13\18

503; 4, 2, 3

5\7

500

12\17

496; 1.8125

7\10

494; 8.5

9\13

490.90

B fa ut# J 12\15

553; 1, 5.5

9\11

568; 2.375

15\18

580; 1.55

6\7

600

15\17

620; 1.45

9\10

635; 3.4

12\13

654.54

B fa utx J# 13\15

600

10\11

631; 1, 1.375

17\18

658; 15.5

7\7

700

18\17

744; 1, 4.8

11\10

776; 2, 8

15\13

818.18

C sol reb Kb 14\15

646; 6.5

16\18

619; 2, 1, 4.5

6\7

600

14\17

579; 3.2

8\10

564; 1, 2.4

10\13

545.45

C sol re K 15\15

692; 3, 4

11\11

694; 1, 2.8

18\18

696; 1, 3, 2, 3

7\7

700

17\17

703; 2, 2, 6

10\10

705; 1, 7.5

13\13

709.09

C sol re# K# 16\15

738; 2, 6

12\11

757; 1, 8.5

20\18

774; 5, 6

8\8

800

20\17

827; 1, 1, 2.4

12\10

847; 17

16\13

872.72

D la mib Lb 18\15

830; 1.3

13\11

821; 19

21\18

812; 1, 9, 3

19\17

786; 4, 1.2

11\10

776; 2, 8

14\13

763.63

D la mi L 19\15

876; 1, 12

14\11

884; 4.75

23\18

890; 3.1

9\5

900

22\17

910; 2.9

13\10

917; 1, 1, 1.2

17\13

927.27

D la mi# L# 20\15

923: 13

15\11

947; 2, 1.4

25\18

967; 1, 2.875

10\7

1000

25\17

1034; 2, 14

15\10

1058; 1, 4, 1.5

20\13

1090.90

E fa utb Mb 22\15

1015; 2.6

16\11

1010; 1.9

26\18

1006; 2, 4, 1.5

24\17

993; 9.6

14\10

988; 4, 4

18\13

981.81

E fa ut M 23\15

1061; 1, 1, 6

17\11

1073; 1, 2, 6

28\18

1083; 1, 6.75

11\7

1100

27\17

1117; 4, 7

16\10

1129; 2, 2, 3

21\9

1145.45

E fa ut# M# 24\15

1107; 1, 2, 4

18\11

1136; 1.1875

30\18

1161; 3, 2, 4

12\7

1200

30\17

1241; 2, 1, 1.75

18\10

1270; 1.7

24\13

1309.09

F sol re utb Nbb 25\15

1153; 1, 5.5

29\18

1121; 1, 1, 2.6

11\7

1100

26\17

1075; 1.16

15\10

1058; 1, 4, 1.5

19\13

1036.36

F sol re ut Nb 26\15

1200

19\11

1200

31\18

1200

12\7

1200

29\17

1200

17\10

1200

22\13

1200

F sol re ut# N 27\15

1246; 6.5

20\11

1263; 6, 3

33\18

1277; 2, 2.6

13\7

1300

32\17

1324; 7, 4

19\10

1341; 5, 1.5

25\13

1363.63

F sol re utx N# 28\15

1292; 3, 4

21\11

1326; 3, 6

35\18

1354; 1, 5.2

14\7

1400

35\17

1448; 3.625

21\10

1482; 2, 1.2

28\13

1527.27

G la mi reb Pb 29\15

1338; 2, 6

34\18

1316; 7.75

13\7

1300

31\17

1282; 1, 3, 7

18\10

1270; 1.7

23\13

1254.54

G la mi re P 30\15

1384; 1.625

22\11

1389; 2, 9

36\18

1393; 1, 1, 4, 1.5

14\7

1400

34\17

1406; 1, 8, 1.5

20\10

1411; 1, 3, 4

26\13

1418.18

G la mi re# P# 31\15

1430; 1.3

23\11

1452; 1, 1, 1.4

38\18

1470; 1, 30

15\7

1500

37\17

1531; 29

22\10

1552; 1, 16

29\13

1581.81

A fab Qbb 32\15

1476; 1, 12

37\18

1432; 3.875

14\7

1400

33\17

1365; 1, 1, 14

19\10

1341; 5, 1.5

24\13

1309.09

A fa Qb 33\15

1523; 13

24\11

1515; 1, 3.75

39\18

1509; 1, 2.1

15\7

1500

36\17

1489; 1, 1.9

21\10

1482; 2, 1.2

27\13

1472.72

A mi Q 34\15

1569; 4, 3

25\11

1578; 1, 18

41\18

1587; 10, 3

16\7

1600

39\17

1613; 1, 3, 1.2

23\10

1623; 1, 1, 8

30\13

1636.36

A mi# Q# 35\15

1615; 2.6

26\11

1642; 9.5

43\18

1664; 1, 6.75

17\7

1700

42\17

1737; 1, 13.5

25\10

1764; 1, 2.4

33\13

1800

B sol fa utb Rb 37\15

1707; 1, 2, 4

27\11

1705; 3.8

44\18

1703; 4, 2, 3

41\17

1696; 1.8125

24\10

1694; 8.5

31\13

1690.90

B sol fa ut R 38\15

1753; 1, 5.5

28\11

1768; 2.375

46\18

1780; 1.55

18\7

1800

44\17

1820; 1.45

26\10

1835; 3.4

34\13

1854.54

B sol fa ut# R# 39\15

1800

29\11

1831; 1, 1.375

48\18

1858; 15.5

19\7

1900

47\17

1944; 1, 4.8

28\10

1976; 2, 8

37\13

2018.18

C la sol reb Sbb 40\15

1846; 6.5

47\18

1819; 2, 1, 4.5

18\7

1800

43\17

1779; 3, 4.5

25\10

1764; 1, 2.4

32\13

1745.45

C la sol re Sb 41\15

1892; 3, 4

30\11

1894; 1, 2.8

49\18

1896; 1, 3, 2, 3

19\7

1900

46\17

1903; 2, 6

27\10

1905; 1, 7.5

35\13

1909.09

C la sol re# S# 42\15

1938; 2, 6

31\11

1957; 1, 8.5

51\18

1974; 5, 6

20\7

2000

49\17

2027; 1, 1, 2.4

29\10

2047; 17

38\13

2072.72

C la sol rex Sx 43\15

1984; 1.625

32\11

2021; 19

53\18

2051; 1, 1, 1, 1.4

21\7

2100

52\17

2151; 2.625

31\10

2188; 4, 4

41\13

2236.36

D la mib Tb 44\15

2030; 1.3

52\18

2012; 1, 9, 3

20\7

2000

48\17

1986; 4, 1.2

28\10

1976; 2, 8

36\13

1963.63

D la mi T 45\15

2076; 1, 12

33\11

2084; 4.75

54\18

2090; 3.1

21\7

2100

51\17

2110; 2.9

30\10

2117; 1, 1, 1.2

39\13

2127.27

D la mib T# 46\15

2123; 13

34\11

2147; 2, 1.4

56\18

2167; 1, 2.875

22\7

2200

54\17

2234; 2, 14

32\10

2258; 1, 4, 1.5

42\13

2090.90

E fa utb Ub 48\15

2215; 2.6

35\11

2210; 1.9

57\18

2206; 2, 4, 1.5

53\17

2193; 9.6

31\10

2188; 4, 4

40\13

2181.81

E fa ut U 49\15

2261; 1, 1, 6

36\11

2273; 1, 2, 6

59\18

2283; 1, 6.75

23\7

2300

56\17

2317; 4, 7

33\10

2329; 2, 2, 3

43\13

2245.45

E fa ut# U 50\15

2307; 1, 2, 4

37\11

2336; 1, 5, 3

61\18

2361; 3, 2, 4

24\7

2400

59\17

2441; 2, 1, 1.75

35\10

2470; 1.7

46\13

2509.09

F sol re utb Vb 52\15

2400

38\11

2400

62\18

2400

58\17

2400

34\10

2400

44\13

2400

F sol re ut V 53\15

2446; 6.5

39\11

2463; 6, 3

64\18

2477; 2, 2.6

25\7

2500

61\17

2524; 7, 4

36\10

2541; 5, 3

47\13

2563.63

F sol re ut# V# 54\15

2492; 3, 4

40\11

2526; 3, 6

66\18

2554; 1, 5.2

26\7

2600

64\17

2648; 2.625

38\10

2682; 2, 1.2

50\13

2727.27

G la mi reb Wbb 55\15

2538; 2, 1

65\18

2516; 7.75

25\7

2500

60\17

2482; 1, 3, 7

35\10

2470; 1.7

45\13

2454.54

G la mi re Wb 56\15

2584; 1.625

41\11

2589; 2, 9

67\18

2593; 1, 1, 4, 1.5

26\7

2600

63\17

2606; 1, 8, 1.5

37\10

2611; 1, 3, 4

48\13

2618.18

G la mi re# W 57\15

2630; 1.3

42\11

2652; 1, 1, 1.4

69\18

2670; 1, 30

27\7

2700

66\17

2731; 29

39\10

2752; 1, 16

51\13

2781.81

G la mi rex W# 58\15

2676; 1, 12

43\11

2715; 1, 3.75

71\18

2748; 2, 1, 1.4

28\7

2800

69\17

2855; 5.8

41\10

2894; 8.5

54\13

2945.45

A fab Xbb 42\11

2652; 1, 1, 1.4

68\18

2632; 3.875

26\7

2600

62\17

2565; 1, 1, 14

36\10

2541; 5, 1.5

46\13

2509.09

A fa Xb 59\15

2723; 13

43\11

2715; 1, 3.75

70\18

2709; 1, 2.1

27\7

2700

65\17

2689; 1, 1.9

38\10

2682; 2, 1.2

49\13

2672.72

A mi X 60\15

2769; 4, 3

44\11

2778; 1, 18

72\18

2787; 3.1

28\7

2800

68\17

2813; 1, 3, 1.2

40\10

2823; 1, 1, 8

52\13

2836.36

A mi# X# 61\15

2815; 2.6

45\11

2842; 9.5

74\18

2864; 1.9375

29\7

2900

71\17

2937; 1, 13.5

42\10

2964; 1, 2.4

55\13

3000

B sol fab Yb 63\15

2907; 1, 2, 4

46\11

2905; 3.8

75\18

2903; 4, 2, 3

70\17

2896; 1.8125

41\10

2894; 8.5

53\13

2890.90

B sol fa Y 64\15

2953; 1, 5.5

47\11

2968; 2.375

77\18

2980; 1.55

30\7

3000

73\17

3020; 1.45

43\10

3035; 3.4

56\13

3054.54

B sol fa# Y# 65\15

3000

48\11

3031; 1, 1.375

79\18

3058; 15.5

31\7

3100

76\17

3144; 1, 4.8

45\10

3176: 2, 8

59\13

3218.18

C la solb Zb 67\15

3092; 3, 4

49\11

3094; 1, 2.8

80\18

3096; 1, 3, 2, 3

75\17

3103; 2, 2, 6

44\10

3105; 1, 7.5

57\13

3109.09

C la sol Z 68\15

3138; 2, 6

50\11

3157; 1, 8.5

82\18

3174; 5, 6

32\7

3200

78\17

3227; 1, 1, 2.4

46\10

3247; 17

60\13

3272.72

C la sol# Z# 69\15

3184; 1.625

51\11

3221: 19

84\18

3251; 1, 1, 1, 1.4

33\7

3300

81\17

3351; 1, 2.625

48\10

3388; 4, 4

63\13

3436.36

D labb Ab 70\15

3230; 1.3

83\18

3212; 1, 9, 3

32\7

3200

77\17

3186; 4, 3

45\10

3176: 2, 8

58\13

3163.63

D lab A 71\15

3276; 1, 12

52\11

3284; 4.75

85\18

3290; 3.1

33\7

3300

80\17

3310; 2.9

47\10

3317; 1, 1, 1.2

61\13

3327.27

D la A# 72\15

3323; 13

53\11

3347; 2, 1.4

87\18

3367; 1, 2.875

34\7

3400

83\17

3434; 2, 14

49\10

3458; 1, 4, 1.5

64\13

3490.90

D la# Ax 73\15

3369; 4, 3

54\15

3410; 1.9

89\18

3445; 6.2

35\7

3500

86\17

3558; 1, 1, 1, 1.75

51\10

3600

67\13

3654.54

F utb Bb 74\15

3415; 2.6

88\18

3406; 2, 4, 1.5

34\7

3400

82\17

3393; 9, 1.5

48\10

3388; 4, 4

62\13

3381.81

F ut B 75\15

3461; 1, 1, 6

55\11

3473; 1, 2, 6

90\18

3483; 1, 6.75

35\7

3500

85\17

3517; 4, 7

50\10

3529; 2, 2, 3

65\13

3545.45

F ut# B# 76\15

3507; 1, 2, 4

56\15

3536; 1, 5, 3

92\18

3561: 3, 2, 4

36\7

3600

88\17

3641; 2, 1, 1.75

52\10

3670; 1.7

68\13

3709.09

G reb Cb 78\15

3600

57\15

3600

93\18

3600

87\17

3600

51\10

3600

66\13

3600

G re C 79\15

3646; 6.5

58\11

3663; 6, 3

95\18

3677; 2, 2.6

37\7

3700

90\17

3724; 7, 4

53\17

3741; 5, 1.5

69\13

3763.63

G re# C# 80\15

3692; 4, 3

59\11

3726; 3, 6

97\18

3755; 5.2

38\7

3800

93\17

3848; 3.625

55\17

3882; 2, 1.2

72\13

3927.27

A mib Db 82\15

3784; 1.625

60\11

3789; 2,9

98\18

3793; 1, 1, 4, 1.5

92\17

3806; 1, 8, 1.5

54\17

3811; 1, 3, 4

70\13

3818.18

A mi D 83\15

3830, 1.3

61\11

3852; 1, 1, 1.4

100\18

3870; 1, 30

39\7

3900

95\17

3931; 29

56\17

3952; 1, 16

73\13

3981.81

A mi# D# 84\15

3876; 1, 12

62\11

3915; 1, 3.75

102\18

3948; 2, 1, 1.4

40\7

4000

98\17

4055; 5.8

58\10

4094; 8.5

76\13

4145.45

B fa utb Ebb 85\15

3923; 13

101\18

3909; 1, 2.1

39\7

3900

94\17

3889; 1, 1.9

55\10

3882; 2, 1.2

71\13

3872.72

B fa ut Eb 86\15

3969; 4, 3

63\11

3978; 1, 3.75

103\18

3987; 10, 3

40\7

4000

97\17

4013; 1, 3, 1.2

57\10

4023; 1, 1, 8

74\13

4036.36

B fa ut# E 87\15

4015; 2.6

64\11

4042; 9.5

105\18

4064; 1.9375

41\7

4100

100\17

4137; 1, 13.5

59\10

4164; 1, 2.4

77\13

4200

B fa utx E# 88\15

4061; 1, 1, 6

65\11

4105; 3.8

107\18

4141; 1, 14.5

42\7

4200

103\17

4262; 14.5

61\10

4305; 1, 7.5

80\13

4363.63

C sol reb Fb 89\15

4107; 1.3

106\18

4103; 4, 2, 3

41\7

4100

99\17

4096; 1.8125

58\10

4094; 8.5

75\13

4090.90

C sol re F 90\15

4153; 1, 5.5

66\11

4168; 2.375

108\18

4180; 1.55

42\7

4200

102\17

4220; 1.45

60\10

4235; 3.4

78\13

4254.54

Intervals

Generators Sesquitave notation Interval category name Generators Notation of 3/2 inverse Interval category name
The 4-note MOS has the following intervals (from some root):
0 Do, Sol perfect unison 0 Do, Sol sesquitave (just fifth)
1 Fa, Do perfect fourth -1 Re, La perfect second
2 Mib, Sib minor third -2 Mi, Si major third
3 Reb, Lab diminished second -3 Fa#, Do# augmented fourth
The chromatic 7-note MOS also has the following intervals (from some root):
4 Dob, Solb diminished sesquitave -4 Do#, Sol# augmented unison (chroma)
5 Fab, Dob diminished fourth -5 Re#, La# augmented second
6 Mibb, Sibb diminished third -6 Mi#, Si# augmented third

Genchain

The generator chain for this scale is as follows:

Mibb

Sibb

Fab

Dob

Dob

Solb

Reb

Lab

Mib

Sib

Fa

Do

Do

Sol

Re

La

Mi

Si

Fa#

Do#

Do#

Sol#

Re#

La#

Mi#

Si#

d3 d4 d5 d2 m3 P4 P1 P2 M3 A4 A1 A2 A3

Modes

The mode names are based on the species of fifth:

Mode Scale UDP Interval type
name pattern notation 2nd 3rd 4th
Lydian LLLs 3|0 P M A
Major LLsL 2|1 P M P
Minor LLsL 1|2 P m P
Phrygian sLLL 0|3 d m P

Temperaments

The most basic rank-2 temperament interpretation of angel is Napoli. The name "Napoli" comes from the “Neapolitan” sixth triad spelled root-(p-2g)-(2p-3g) (p = 3/2, g = the whole tone) which serves as its minor triad approximating 5:6:8 in pental interpretations or 18:21:28 in septimal ones. Basic ~7edf fits both interpretations.

Napoli-Meantone

Subgroup: 3/2.6/5.8/5

Comma list: 81/80

POL2 generator: ~9/8 = 192.6406¢

Mapping: [⟨1 1 2], ⟨0 -2 -3]]

Optimal ET sequence: ~(7edf, 11edf, 18edf)

Napoli-Archy

Subgroup: 3/2.7/6.14/9

Comma list: 64/63

POL2 generator: ~8/7 = 218.6371¢

Mapping: [⟨1 1 2], ⟨0 -2 -3]]

Optimal ET sequence: ~(7edf, 10edf, 13edf, 16edf)

Scale tree

The spectrum looks like this:

Generator

(bright)

Cents[3] L s L/s Comments
1\4 171; 2, 3 1 1 1.000 Equalised
6\23 180 6 5 1.200
11\42 180; 1, 4, 1.625 11 9 1.222
5\19 181.81 5 4 1.250
14\53 182; 1, 1.5 14 11 1.273
9\34 183; 19, 1.5 9 7 1.286
4\15 184; 1.625 4 3 1.333
11\41 185, 1, 10, 1.2 11 8 1.375
7\26 186.6 7 5 1.400
10\37 187.5 10 7 1.429
13\48 187; 1, 19.75 13 9 1.444
16\59 188; 4, 4 16 11 1.455
3\11 189; 2, 9 3 2 1.500 Napoli-Meantone starts here
14\51 190.90 14 9 1.556
11\40 191; 3, 2, 3 11 7 1.571
8\29 192 8 5 1.600
5\18 193; 1, 1, 4, 1.5 5 3 1.667
12\43 194.594 12 7 1.714
7\25 195; 2, 1, 6.5 7 4 1.750
9\32 196.36 9 5 1.800
11\39 197; 67 11 6 1.833
13\46 197; 2, 7.4 13 7 1.857
15\53 197; 1, 2, 1, 1, 1, 1.2 15 8 1.875
17\60 198; 17, 6 17 9 1.889
19\67 198: 3, 1, 28 19 10 1.900
21\74 198; 2, 2, 1.1875 21 11 1.909
23\81 198; 1, 3, 1.7 23 12 1.917
25\88 198; 1, 2, 12, 4 25 13 1.923
27\95 198; 1, 3, 2, 13 27 14 1.929
29\102 198; 1, 1, 6 29 15 1.933
31\109 198; 1, 13, 2.6 31 16 1.9375
33\116 198; 1, 198 33 17 1.941
2\7 200 2 1 2.000 Napoli-Meantone ends, Napoli-Pythagorean begins
17\59 201.9801 17 8 2.125
15\52 202; 4, 22 15 7 2.143
13\45 202; 1, 1, 2, 15 13 6 2.167
11\38 203; 13 11 5 2.200
9\31 203; 1, 3, 2.4 9 4 2.250
7\24 204; 1. 7.2 7 3 2.333
12\41 205; 1.4 12 5 2.400
5\17 206; 1, 8, 1.5 5 2 2.500 Napoli-Neogothic heartland is from here…
18\61 207; 1, 2, 4 18 7 2.571
8\27 208; 1, 5, 3 8 3 2.667 …to here
11\37 209; 1, 1.1 11 4 2.750
14\47 210 14 5 2.800
3\10 211; 1, 3, 4 3 1 3.000 Napoli-Pythagorean ends, Napoli-Archy begins
22\73 212; 1, 9, 3 22 7 3.143
19\63 213; 11, 1, 8 19 6 3.167
16\53 213.3 16 5 3.200
13\43 213; 1, 2, 3, 7 13 4 3.250
10\33 214; 3.5 10 3 3.333
7\23 215; 2.6 7 2 3.500
11\36 216; 2, 1, 1, 5.5 11 3 3.667
15\49 216; 1, 6, 1, 1.2 15 4 3.750
19\62 217; 7 19 5 3.800
4\13 218.18 4 1 4.000
13\42 219; 1, 2.55 13 3 4.333
9\29 220; 2.45 9 2 4.500
14\45 221; 19 14 3 4.667
5\16 222.2 5 1 5.000 Napoli-Archy ends
16\51 223; 3, 1.1 16 3 5.333
11\35 223; 1, 2.6875 11 2 5.500
17\54 224; 5, 1, 2.6 17 3 5.667
6\19 225 6 1 6.000
1\3 240 1 0 → inf Paucitonic

See also

3L 1s (3/2-equivalent) - idealized tuning

6L 2s (20/9-equivalent) - Neapolitan 1/2-comma meantone

6L 2s (52/23-equivalent) - Neapolitan gentle temperament

6L 2s (16/7-equivalent) - Neapolitan 1/2-comma archy

9L 3s (10/3-equivalent) - Bijou 1/3-comma meantone

9L 3s (22/13-equivalent) - Bijou gentle temperament

9L 3s (24/7-equivalent) - Bijou 1/3-comma archy

12L 4s (5/1-equivalent) - Hex meantone

12L 4s (56/11-equivalent) - Hextone gentle temperament

12L 4s (36/7-equivalent) - Hextone 1/4-comma archy

15L 5s (15/2-equivalent) - Guidotonic major 1/5-comma meantone

15L 5s (84/11-equivalent) - Guidotonic major gentle temperament

15L 5s (54/7-equivalent) - Guidotonic major 1/5-comma archy

18L 6s (11/1-equivalent) - Subdozenal harmonic tuning

18L 6s (56/5-equivalent) - Subdozenal low septimal tuning

18L 6s (80/7-equivalent) - Subdozenal high septimal tuning

18L 6s (128/11-equivalent) - Subdozenal subharmonic tuning

  1. ↑ Fractions repeating more than 4 digits written as continued fractions
  2. ↑ Fractions repeating more than 4 digits written as continued fractions
  3. ↑ Fractions repeating more than 4 digits written as continued fractions
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