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

Moremajorthanmajor (talk | contribs)
Moremajorthanmajor (talk | contribs)
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124; 7, 4
 
 
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'''193; 1, 1, 4, 1.5'''
 
 
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461; 1, 1, 6
 
 
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|'''11\15'''
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553; 1, 5.5
 
 
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631; 1.{{Overline|72}}
631; 1, 1.375
 
 
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744; 1.208{{Overline|3}}
744; 1, 4.8
 
 
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776; 2.125
776; 2, 8
 
 
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564; 1, 2.4
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!'''15\15'''
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'''692; 3.25'''
'''692; 3, 4'''
 
 
!'''11\11'''
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!'''18\18'''
 
 
'''696; 1.291'''{{Overline|6}}
'''696; 1, 3, 2, 3'''
 
 
!'''7\7'''
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!'''17\17'''
 
 
'''703; 2, 2.1'''{{Overline|6}}
'''703; 2, 2, 6'''
 
 
!'''10\10'''
!'''10\10'''
 
 
'''705; 1.1'''{{Overline|3}}
'''705; 1, 7.5'''
 
 
!'''13\13'''
!'''13\13'''
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738; 2.1{{Overline|6}}
738; 2, 6
 
 
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812; 1, 9.{{Overline|3}}
812; 1, 9, 3
 
 
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786; 4.8{{Overline|3}}
786; 4, 1.2
 
 
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776; 2.125
776; 2, 8
 
 
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'''876; 1, 12'''
 
 
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1326; 3, 6
 
 
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1393; 1, 1, 4, 1.5
 
 
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1406; 1, 8, 1.5
 
 
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1411; 1, 3, 4
 
 
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1470; 1, 30
 
 
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'''1569; 4.{{Overline|3}}'''
'''1569; 4, 3'''
 
 
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'''1578; 1.0{{Overline|5}}'''
'''1578; 1, 18'''
 
 
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'''1587; 10.{{Overline|3}}'''
'''1587; 10, 3'''
 
 
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'''1613; 1, 3, 1.2'''
 
 
|'''23\10'''
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'''1623; 1.{{Overline|8}}'''
'''1623; 1, 1, 8'''
 
 
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1664; 1.0625
1664; 1, 6.75
 
 
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1764; 1, 2.4
 
 
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1707; 1, 2, 4
 
 
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1831; 1.{{Overline|72}}
1831; 1, 1. 375
 
 
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1944; 1.208{{Overline|3}}
1944; 1, 4.8
 
 
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1976; 2.125
1976; 2, 8
 
 
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1819; 2.{{Overline|81}}
1819; 2, 1, 4.5
 
 
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1779; 3.{{Overline|2}}
1779; 3, 4.5
 
 
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1764; 1.41{{Overline|6}}
1764; 1, 2.4
 
 
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|'''41\15'''
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'''1892; 3.25'''
'''1892; 3, 4'''
 
 
|'''30\11'''
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|'''49\18'''
|'''49\18'''
 
 
'''1896; 1.291{{Overline|6}}'''
'''1896; 1, 3, 2, 3'''
 
 
|'''19\7'''
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|'''46\17'''
|'''46\17'''
 
 
'''1903; 2.1{{Overline|6}}'''
'''1903; 2, 6'''
 
 
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|'''27\10'''
 
 
'''1905; 1.1{{Overline|3}}'''
'''1905; 1, 7.5'''
 
 
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1938; 2.1{{Overline|6}}
1938; 2, 6
 
 
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1974; 5.1{{Overline|6}}
1974; 5, 6
 
 
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2027; 1, 1.41{{Overline|6}}
2027; 1, 1, 2.4
 
 
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2188; 4.25
2188; 4, 4
 
 
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2012; 1, 9,{{Overline|3}}
2012; 1, 9, 3
 
 
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1986; 4.8{{Overline|3}}
1986; 4, 1.2
 
 
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1976; 2.125
1976; 2, 8
 
 
|36\13
|36\13
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! 45\15
! 45\15
 
 
2076; 1.08'''{{Overline|3}}'''
2076; 1, 12
 
 
!33\11
!33\11
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!30\10
!30\10
 
 
2117; 1.{{Overline|54}}
2117; 1, 1, 1.2
 
 
!39\13
!39\13
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2234; 2, 14
2234; 2, 14
| 32\10
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2258; 1, 4.{{Overline|6}}
2258; 1, 4, 1.5
|42\13
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2090.{{Overline|90}}
2090.{{Overline|90}}
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2210; 1.9
2210; 1.9
|57\18
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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; 4.25
2188; 4, 4
|40\13
|40\13
2181.{{Overline|81}}
2181.{{Overline|81}}
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|'''D'''
|'''D'''
|'''49\15'''
|'''49\15'''
'''2261; 1, 1.1{{Overline|6}}'''
'''2261; 1, 1, 6'''
|'''36\11'''
|'''36\11'''
'''2273; 1, 2.1{{Overline|6}}'''
'''2273; 1, 2, 6'''
|'''59\18'''
|'''59\18'''
'''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'''
|'''33\10'''
'''2329; 2, 2.{{Overline|3}}'''
'''2329; 2, 2, 3'''
|'''43\13'''
|'''43\13'''
'''2245.{{Overline|45}}'''
'''2245.{{Overline|45}}'''
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|D#
|D#
|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
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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
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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}}
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|E#
|E#
|54\15
|54\15
2492; 3.25
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
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2648; 2.625
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}}
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|Fff
|Fff
|55\15
|55\15
2538; 2.1{{Overline|6}}
2538; 2, 1
|65\18
|65\18
2516; 7.75
2516; 7.75
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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 1,512: Line 1,512:
'''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, 3.25'''
'''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
|69\18
|69\18
2670; 1.0{{Overline|3}}
2670; 1, 30
| 27\7
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2700
2700
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2731; 29
2731; 29
|39\10
|39\10
2752; 1.0625
2752; 1, 16
|51\13
|51\13
2781.{{Overline|81}}
2781.{{Overline|81}}
Line 1,548: Line 1,548:
|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
|71\18
|71\18
2748; 2.58{{Overline|3}}
2748; 2, 1, 1.4
|28\7
|28\7
2800
2800
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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}}
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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 />