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

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Redirected page to 3L 1s (3/2-equivalent)
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#redirect [[3L 1s (3/2-equivalent)]]
{{Infobox MOS
 
| Name =
| Equave = 3/2
| nLargeSteps = 3
| nSmallSteps = 1
| Equalized = 2
| Collapsed = 1
 
| Pattern = LLLs
}}'''3L 1s<3/2>''', is a fifth-repeating MOS scale. 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 [[9/8|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.
 
[[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 or quadruple sesquitave (major ninth, thirteenth or seventeenth i. e. ~pentave), however it does make navigating the [[Generator|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] or an ~pentave which is the Mixolydian mode of Hextone[12L 4s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation and 16 in quadruple sesquitave notation, letters A-H (FGABHCDEF) or dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F molle) may be used.
{| class="wikitable"
|+
Cents<ref name=":0">Fractions repeating more than 4 digits written as continued fractions</ref>
! colspan="4" |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.{{Overline|3}}
|2\18
77; 2, 2.6
| rowspan="2" |1\7
100
|3\17
124; 7.25
|2\10
141; 5.{{Overline|6}}
|3\13
163.{{Overline|63}}
|-
|Reb, Lab
|Gb
|1b, 1c
|1f
|3\15
138; 3.25
|2\11
126; 3.1{{Overline|6}}
|3\18
116; 7.75
|2\17
82; 1.3{{Overline|18}}
|1\10
70; 1.7
|1\13
54.{{Overline|54}}
|-
|'''Re, La'''
|'''G'''
|'''1'''
|'''1'''
|'''4\15'''
'''184; 1.625'''
|'''3\11'''
'''189; 2.{{Overline|1}}'''
|'''5\18'''
'''193; 1, 1, 4.{{Overline|6}}'''
|'''2\7'''
'''200'''
|'''5\17'''
'''206; 1, 8.{{Overline|6}}'''
|'''3\10'''
'''211; 1, 3.25'''
|'''4\13'''
'''218.{{Overline|18}}'''
|-
|Re#, La#
|G#
|1#
|1#
|5\15
230; 1.3
|4\11
252; 1.58{{Overline|3}}
|7\18
270; 1.0{{Overline|3}}
| rowspan="2" |3\7
300
|8\17
331; 29
|5\10
352; 1.0625
|7\13
381.{{Overline|81}}
|-
|Mib, Sib
|Ab
|2b, 2c
|2f
|7\15
323; 13
|5\11
315; 1.2{{Overline|6}}
|8\18
309; 1, 2.1
|7\17
289; 1, 1.9
|4\10
282; 2.8{{Overline|3}}
|5\13
272.{{Overline|72}}
|-
|Mi, Si
|A
|2
|2
|8\15
369; 4.{{Overline|3}}
|6\11
378; 1.0{{Overline|5}}
|10\18
387; 10.{{Overline|3}}
|4\7
400
|10\17
413; 1, 3.8{{Overline|3}}
|6\10
423; 1.{{Overline|8}}
|8\13
436.{{Overline|36}}
|-
|Mi#, Si#
|A#
|2#
|2#
|9\15
415; 2.6
| rowspan="2" |7\11
442; 9.5
|12\18
464; 1.0625
|5\7
500
|13\17
537; 14.5
|8\10
564; 1.41{{Overline|6}}
|11\13
600
|-
|Fab, Dob
|Bbb
|3b, 3c
|3f
|10\15
461; 1, 1.1{{Overline|6}}
|11\18
425; 1.24
|4\7
400
|9\17
372; 2.41{{Overline|6}}
|5\10
352; 1.0625
|6\13
327.{{Overline|27}}
|-
|'''Fa, Do'''
|'''Bb'''
|'''3'''
|'''3'''
|'''11\15'''
'''507; 1.{{Overline|4}}'''
|'''8\11'''
'''505; 3.8'''
|'''13\18'''
'''503; 4, 2.{{Overline|3}}'''
|'''5\7'''
'''500'''
|'''12\17'''
'''496; 1.8125'''
|'''7\10'''
'''494; 8.5'''
|'''9\13'''
'''490.{{Overline|90}}'''
|-
|Fa#, Do#
|B
|3#
|3#
|12\15
553; 1.{{Overline|18}}
|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.{{Overline|54}}
|-
|Fax, Dox
|B#
|3x
|3x
|13\15
600
| rowspan="2" |10\11
631; 1.{{Overline|72}}
|17\18
658; 15.5
|7\7
700
|18\17
744; 1.208{{Overline|3}}
|11\10
776; 2.125
|15\13
818.{{Overline|18}}
|-
|Dob, Solb
|Hb
| 4b, 4c
|4f
|14\15
646; 6.5
|16\18
619; 2.{{Overline|81}}
|6\7
600
|14\17
579; 3.{{Overline|2}}
|8\10
564; 1.41{{Overline|6}}
|10\13
545.{{Overline|45}}
|-
!Do, Sol
!H
!4
!4
!'''15\15'''
'''692; 3.25'''
!'''11\11'''
'''694; 1, 2.8'''
!'''18\18'''
'''696; 1.291'''{{Overline|6}}
!'''7\7'''
'''700'''
!'''17\17'''
'''703; 2, 2.1'''{{Overline|6}}
!'''10\10'''
'''705; 1.1'''{{Overline|3}}
!'''13\13'''
'''709.'''{{Overline|09}}
|-
|Do#, Sol#
|Η#
|4#
|4#
|16\15
738; 2.1{{Overline|6}}
|12\11
757; 1, 8.5
| 20\18
774; 5, 6
| rowspan="2" | 8\8
800
|20\17
827; 1, 1.41{{Overline|6}}
|12\10
847; 17
| 16\13
872.{{Overline|72}}
|-
|Reb, Lab
|Cb
|5b, 5c
|5
|18\15
830; 1.3
|13\11
821; 19
| 21\18
812; 1, 9.{{Overline|3}}
| 19\17
786; 4.8{{Overline|3}}
| 11\10
776; 2.125
| 14\13
763.{{Overline|63}}
|-
|'''Re, La'''
|'''C'''
|'''5'''
|'''5'''
|'''19\15'''
'''876; 1.08{{Overline|3}}'''
|'''14\11'''
'''884; 4.75'''
|'''23\18'''
'''890; 3.1'''
|'''9\5'''
'''900'''
|'''22\17'''
'''910; 2.9'''
|'''13\10'''
'''917; 1.{{Overline|54}}'''
|'''17\13'''
'''927.{{Overline|27}}'''
|-
| Re#, La#
|C#
| 5#
|5#
|20\15
923: 13
|15\11
947; 2, 1.4
|25\18
967; 1, 2.875
| rowspan="2" |10\7
1000
|25\17
1034; 2, 14
| 15\10
1058; 1, 4.{{Overline|6}}
|20\13
1090.{{Overline|90}}
|-
|Mib, Sib
|Db
|6b, 6c
|6f
|22\15
1015; 2.6
|16\11
1010; 1.9
| 26\18
1006; 2, 4.{{Overline|6}}
|24\17
993; 9.{{Overline|6}}
|14\10
988; 4.25
|18\13
981.{{Overline|81}}
|-
|Mi, Si
|D
|6
|6
|23\15
1061; 1, 1.1{{Overline|6}}
|17\11
1073; 1, 2.1{{Overline|6}}
| 28\18
1083; 1.{{Overline|148}}
|11\7
1100
| 27\17
1117; 4, 7
| 16\10
1129; 2, 2.{{Overline|3}}
| 21\9
1145.{{Overline|45}}
|-
|Mi#, Si#
| D#
|6#
|6#
| 24\15
1107; 1.{{Overline|4}}
| rowspan="2" | 18\11
1136; 1.1875
|30\18
1161; 3.{{Overline|4}}
| 12\7
1200
|30\17
1241; 2.{{Overline|63}}
|18\10
1270; 1.7
|24\13
1309.{{Overline|09}}
|-
|Fab, Dob
|Ebb
|7b, 7c
|7f
|25\15
1153; 1.{{Overline|18}}
|29\18
1121; 1, 1, 2.6
| 11\7
1100
|26\17
1075; 1.16
|15\10
1058; 1, 4.{{Overline|6}}
|19\13
1036.{{Overline|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.{{Overline|3}}
| 33\18
1277; 2, 2.6
|13\7
1300
|32\17
1324; 7.25
|19\10
1341; 5.{{Overline|6}}
|25\13
1363.{{Overline|63}}
|-
|Fax, Dox
|E#
|7x
|7x
|28\15
1292; 3.25
| rowspan="2" |21\11
1326; 3.1{{Overline|6}}
|35\18
1354; 1, 5.2
| 14\7
1400
|35\17
1448; 3.625
|21\10
1482; 2.8{{Overline|3}}
|28\13
1527.{{Overline|27}}
|-
|Dob, Solb
|Fb
|8b, Fc
|8f
|29\15
1338; 2.1{{Overline|6}}
|34\18
1316; 7.75
|13\7
1300
|31\17
1282; 1.3{{Overline|18}}
|18\10
1270; 1.7
| 23\13
1254.{{Overline|54}}
|-
!Do, Sol
!F
! 8, F
!8
! 30\15
1384; 1.625
! 22\11
1389; 2.{{Overline|1}}
!36\18
1393; 1, 1, 4.{{Overline|6}}
!14\7
1400
! 34\17
1406; 1, 8.{{Overline|6}}
! 20\10
1411; 1, 3.25
!26\13
1418.{{Overline|18}}
|-
|Do#, Sol#
|F#
|8#, F#
|8#
|31\15
1430; 1.3
| 23\11
1452; 1.58{{Overline|3}}
|38\18
1470; 1.0{{Overline|3}}
| rowspan="2" |15\7
1500
| 37\17
1531; 29
| 22\10
1552; 1.0625
|29\13
1581.{{Overline|81}}
|-
| Reb, Lab
|Gb
|9b, Gc
|9f
|33\15
1523; 13
|24\11
1515; 1.2{{Overline|6}}
| 39\18
1509; 1, 2.1
|36\17
1489; 1, 1.9
|21\10
1482; 2.8{{Overline|3}}
|27\13
1472.{{Overline|72}}
|-
|'''Re, La'''
|'''G'''
|'''9, G'''
|9
|'''34\15'''
'''1569; 4.{{Overline|3}}'''
|'''25\11'''
'''1578; 1.0{{Overline|5}}'''
|'''41\18'''
'''1587; 10.{{Overline|3}}'''
|'''16\7'''
'''1600'''
|'''39\17'''
'''1613; 1, 3.8{{Overline|3}}'''
|'''23\10'''
'''1623; 1.{{Overline|8}}'''
|'''30\13'''
'''1636.{{Overline|36}}'''
|-
|Re#, La#
|G#
|9#, G#
|9#
|35\15
1615; 2.6
|26\11
1642; 9.5
| 43\18
1664; 1.0625
| rowspan="2" | 17\7
1700
|42\17
1737; 14.5
|25\10
1764; 1.41{{Overline|6}}
|33\13
1800
|-
|Mib, Sib
|Ab
|Xb, Ac
|Af
|37\15
1707; 1.{{Overline|4}}
|27\11
1705; 3.8
|44\18
1703; 4, 2.{{Overline|3}}
|41\17
1696; 1.8125
|24\10
1694; 8.5
|31\13
1690.{{Overline|90}}
|-
|Mi, Si
|A
|X, A
|A
|38\15
1753; 1.{{Overline|18}}
|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.{{Overline|54}}
|-
|Mi#, Si#
| A#
|X#, A#
|A#
|39\15
1800
| rowspan="2" |29\11
1831; 1.{{Overline|72}}
|48\18
1858; 15.5
|19\7
1900
|47\17
1944; 1.208{{Overline|3}}
|28\10
1976; 2.125
| 37\13
2018.{{Overline|18}}
|-
|Fab, Dob
|Bbb
|Ebb, Ccc
|Bf
|40\15
1846; 6.5
|47\18
1819; 2.{{Overline|81}}
| 18\7
1800
|43\17
1779; 3.{{Overline|2}}
|25\10
1764; 1.41{{Overline|6}}
| 32\13
1745.{{Overline|45}}
|-
|'''Fa, Do'''
|'''Bb'''
|'''Eb, Cc'''
|'''B'''
|'''41\15'''
'''1892; 3.25'''
|'''30\11'''
'''1894; 1, 2.8'''
|'''49\18'''
'''1896; 1.291{{Overline|6}}'''
|'''19\7'''
'''1900'''
|'''46\17'''
'''1903; 2.1{{Overline|6}}'''
|'''27\10'''
'''1905; 1.1{{Overline|3}}'''
|'''35\13'''
'''1909.{{Overline|09}}'''
|-
|Fa#, Do#
| B
|E, C
|B#
|42\15
1938; 2.1{{Overline|6}}
|31\11
1957; 1, 8.5
| 51\18
1974; 5.1{{Overline|6}}
|20\7
2000
|49\17
2027; 1, 1.41{{Overline|6}}
|29\10
2047; 17
|38\13
2072.{{Overline|72}}
|-
|Fax, Dox
|B#
|Ex, Cx
|Bx
|43\15
1984; 1.625
| rowspan="2" |32\11
2021; 19
|53\18
2051; 1, 1, 1, 1.4
|21\7
2100
|52\17
2151; 2.625
|31\10
2188; 4.25
|41\13
2236.{{Overline|36}}
|-
|Dob, Solb
|Hb
|0b, Dc
|Cf
|44\15
2030; 1.3
|52\18
2012; 1, 9,{{Overline|3}}
|20\7
2000
|48\17
1986; 4.8{{Overline|3}}
|28\10
1976; 2.125
|36\13
1963.{{Overline|63}}
|-
!Do, Sol
!H
!0, D
!C
!45\15
2076; 1.08'''{{Overline|3}}'''
!33\11
2084; 4.75
!54\18
2090; 3.1
!21\7
2100
!51\17
2110; 2.9
!30\10
2117; 1.{{Overline|54}}
!39\13
2127.{{Overline|27}}
|-
|Do#, Sol#
|Η#
|0#, D#
|C#
|46\15
2123; 13
|34\11
2147; 2, 1.4
|56\18
2167; 1, 2.875
| rowspan="2" |22\7
2200
|54\17
2234; 2, 14
|32\10
2258; 1, 4.{{Overline|6}}
|42\13
2090.{{Overline|90}}
|-
|Reb, Lab
|Cb
|1b, 1c
|Df
|48\15
2215; 2.6
|35\11
2210; 1.9
|57\18
2206; 2, 4.{{Overline|6}}
|53\17
2193; 9.{{Overline|6}}
|31\10
2188; 4.25
|40\13
2181.{{Overline|81}}
|-
|'''Re, La'''
|'''C'''
|'''1'''
|'''D'''
|'''49\15'''
'''2261; 1, 1.1{{Overline|6}}'''
|'''36\11'''
'''2273; 1, 2.1{{Overline|6}}'''
|'''59\18'''
'''2283; 1.{{Overline|148}}'''
|'''23\7'''
'''2300'''
|'''56\17'''
'''2317; 4, 7'''
|'''33\10'''
'''2329; 2, 2.{{Overline|3}}'''
|'''43\13'''
'''2245.{{Overline|45}}'''
|-
|Re#, La#
|C#
|1#
|D#
|50\15
2307; 1.{{Overline|4}}
|37\11
2336; 1.1875
|61\18
2361; 3.{{Overline|4}}
| rowspan="2" |24\7
2400
|59\17
2441; 2.{{Overline|63}}
|35\10
2470; 1.7
|46\13
2509.{{Overline|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.{{Overline|3}}
|64\18
2477; 2, 2.6
|25\7
2500
|61\17
2524; 7.25
|36\10
2541; 5.{{Overline|6}}
|47\13
2563.{{Overline|63}}
|-
|Mi#, Si#
|D#
|2#
|E#
|54\15
2492; 3.25
| rowspan="2" |40\11
2526; 3.1
|66\18
2554; 1, 5.2
|26\7
2600
|64\17
2648; 2.625
|38\10
2682; 2.8{{Overline|3}}
|50\13
2727.{{Overline|27}}
|-
|Fab, Dob
|Ebb
|3b, 3c
|Fff
|55\15
2538; 2.1{{Overline|6}}
|65\18
2516; 7.75
|25\7
2500
|60\17
2482; 1.3{{Overline|18}}
|35\10
2470; 1.7
|45\13
2454.{{Overline|54}}
|-
|'''Fa, Do'''
|'''Eb'''
|'''3'''
|'''Ff'''
|'''56\15'''
'''2584; 1.625'''
|'''41\11'''
'''2589; 2.{{Overline|1}}'''
|'''67\18'''
'''2593; 1, 1, 4.{{Overline|6}}'''
|'''26\7'''
'''2600'''
|'''63\17'''
'''2606; 1, 8.{{Overline|6}}'''
|'''37\10'''
'''2611; 1, 3.25'''
|'''48\13'''
'''2618.{{Overline|18}}'''
|-
|Fa#, Do#
|E
|3#
|F
|57\15
2630; 1.3
|42\11
2652; 1.58{{Overline|3}}
|69\18
2670; 1.0{{Overline|3}}
|27\7
2700
|66\17
2731; 29
|39\10
2752; 1.0625
|51\13
2781.{{Overline|81}}
|-
|Fax, Dox
|E#
|3x
|F#
|58\15
2676; 1.08{{Overline|3}}
| rowspan="2" |43\11
2715; 1.2{{Overline|6}}
|71\18
2748; 2.58{{Overline|3}}
|28\7
2800
|69\17
2855; 4.8
|41\10
2894; 8.5
|54\13
2945.{{Overline|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; 2.8{{Overline|3}}
|49\13
2672.{{Overline|72}}
|-
!Do, Sol
!F
!4
!0, G
!60\15
2769; 4.'''{{Overline|3}}'''
!44\11
2778; 1.0{{Overline|5}}
!72\18
2787; 3.1
!28\7
2800
!68\17
2813; 1, 3.8{{Overline|3}}
!40\10
2823; 1.{{Overline|8}}
!52\13
2836.{{Overline|36}}
|}
{| class="wikitable"
|+Relative cents<ref name=":02">Fractions repeating more than 4 digits written as continued fractions</ref>
! colspan="4" | 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.{{Overline|6}}''
|1\11
''63.{{Overline|63}}''
|2\18
''77.7̄''
| rowspan="2" |1\7
''100''
| 3\17
''123; 1.{{Overline|8}}''
| 2\10
''140''
|3\13
''161; 1, 1.1{{Overline|6}}''
|-
|Reb, Lab
| Gb
|1b, 1c
|1f
|3\15
''140''
|2\11
''127.{{Overline|27}}''
|3\18
''116.{{Overline|6}}''
| 2\17
''82; 2.8{{Overline|3}}''
|1\10
''70''
|1\13
''53; 1.{{Overline|18}}''
|-
|'''Re, La'''
|'''G'''
|'''1'''
|'''1'''
|'''4\15'''
'''''186.{{Overline|6}}'''''
|'''3\11'''
'''''190.{{Overline|90}}'''''
|'''5\18'''
'''''194.{{Overline|4}}'''''
|'''2\7'''
'''''200'''''
|'''5\17'''
'''''205; 1.1{{Overline|3}}'''''
|'''3\10'''
'''''210'''''
|'''4\13'''
'''''215; 2.6'''''
|-
|Re#, La#
| G#
| 1#
|1#
|5\15
''233.{{Overline|3}}''
|4\11
''254.{{Overline|54}}''
|7\18
''272.2̄''
| rowspan="2" |3\7
''300''
|8\17
''329; 2, 2.{{Overline|3}}''
|5\10
''350''
|7\13
''376; 1.08{{Overline|3}}''
|-
|Mib, Sib
|Ab
|2b, 2c
|2f
|7\15
''326.{{Overline|6}}''
|5\11
''318.{{Overline|18}}''
| 8\18
''311.{{Overline|1}}''
|7\17
''288; 4.25''
| 4\10
''280''
|5\13
''269; 4.{{Overline|3}}''
|-
|Mi, Si
|A
| 2
|2
|8\15
''373.{{Overline|3}}''
|6\11
''381.{{Overline|81}}''
|10\18
''388.{{Overline|8}}''
|4\7
''400''
|10\17
''411; 1, 3.25''
|6\10
''420''
|8\13
''430; 1.3''
|-
|Mi#, Si#
|A#
|2#
|2#
|9\15
''420''
| rowspan="2" |7\11
''445.{{Overline|45}}''
|12\18
''466.{{Overline|6}}''
|5\7
''500''
|13\17
''535; 3.4''
|8\10
''560''
|11\13
''592; 3.25''
|-
|Fab, Dob
|Bbb
|3b, 3c
|3f
|10\15
''466.{{Overline|6}}''
|11\18
''427.{{Overline|7}}''
|4\7
''400''
|9\17
''370; 1.7''
|5\10
''350''
|6\13
''323; 13''
|-
|'''Fa, Do'''
|'''Bb'''
|'''3'''
|'''3'''
|'''11\15'''
'''''513.{{Overline|3}}'''''
|'''8\11'''
'''''509.{{Overline|09}}'''''
|'''13\18'''
'''''505.{{Overline|5}}'''''
|'''5\7'''
'''''500'''''
|'''12\17'''
'''''494; 8.5'''''
|'''7\10'''
'''''490'''''
|'''9\13'''
'''''484; 1.625'''''
|-
|Fa#, Do#
| B
|3#
|3#
|12\15
''560''
|9\11
''572.{{Overline|72}}''
| 15\18
''583.{{Overline|3}}''
|6\7
''600''
|15\17
''617; 1.41{{Overline|6}}''
|9\10
''630''
|12\13
''646; 6.5''
|-
| Fax, Dox
|B#
|3x
|3x
|13\15
''606.{{Overline|6}}''
| rowspan="2" |10\11
''636.{{Overline|36}}''
|17\18
''661.{{Overline|1}}''
|7\7
''700''
|18\17
''741; 5.{{Overline|6}}''
|11\10
''770''
|15\13
''807; 1.{{Overline|4}}''
|-
|Dob, Solb
|Hb
|4b, 4c
|4f
|14\15
''653.{{Overline|3}}''
|16\18
''622.{{Overline|2}}''
|6\7
''600''
| 14\17
''576; 2.125''
| 8\10
''560''
|10\13
''538; 2.1{{Overline|6}}''
|-
!Do, Sol
!H
!4
!4
! colspan="7" |''700''
|-
|Do#, Sol#
|Η#
|4#
|4#
|16\15
''746.{{Overline|6}}''
|12\11
''763.{{Overline|63}}''
|20\18
''777.{{Overline|7}}''
| rowspan="2" |8\7
''800''
|20\17
''823; 1.{{Overline|8}}''
|12\10
''840''
|16\13
''861; 1, 1.1{{Overline|6}}''
|-
|Reb, Lab
|Cb
|5b, 5c
|5
|18\15
''840''
|13\11
''827.{{Overline|27}}''
|21\18
''816.{{Overline|6}}''
| 19\17
''782; 2.8{{Overline|3}}''
|11\10
''770''
|14\13
''753; 1.{{Overline|18}}''
|-
|'''Re, La'''
|'''C'''
|'''5'''
|'''5'''
|'''19\15'''
'''''886.{{Overline|6}}'''''
|'''14\11'''
'''''890.{{Overline|90}}'''''
|'''23\18'''
'''''894.{{Overline|4}}'''''
|'''9\7'''
'''''900'''''
|'''22\17'''
'''''905; 1.1{{Overline|3}}'''''
|'''13\10'''
'''''910'''''
|'''17\13'''
'''''915; 2.6'''''
|-
| Re#, La#
|C#
|5#
|5#
|20\15
''933.{{Overline|3}}''
|15\11
''954.{{Overline|54}}''
|25\18
''972.{{Overline|2}}''
| rowspan="2" | 10\7
''1000''
|25\17
''1029; 2, 2.{{Overline|3}}''
|15\10
''1050''
|20\13
''1076; 1.08{{Overline|3}}''
|-
|Mib, Sib
|Db
|6b, 6c
|6f
|22\15
''1026.{{Overline|6}}''
|16\11
''1018.{{Overline|18}}''
|26\18
''1011.{{Overline|1}}''
|24\17
''988; 4.25''
|14\10
''980''
|18\13
''969; 4.{{Overline|3}}''
|-
|Mi, Si
|D
|6
|6
| 23\15
''1073.{{Overline|3}}''
|17\11
''1081.{{Overline|81}}''
|28\18
''1088.{{Overline|8}}''
|11\7
''1100''
|27\17
''1111; 1, 3.25''
|16\10
''1120''
|21\13
''1130; 1.3''
|-
|Mi#, Si#
| D#
|6#
|6#
|24\15
''1120''
| rowspan="2" | 18\11
''1145.{{Overline|45}}''
|30\18
''1166.{{Overline|6}}''
|12\7
''1200''
| 30\17
''1235; 3.4''
|18\10
''1260''
|24\13
''1292; 3.25''
|-
| Fab, Dob
| Ebb
| 7b, 7c
|7f
|25\15
''1166.{{Overline|6}}''
|29\18
''1127.{{Overline|7}}''
|11\7
''1100''
|26\17
''1070; 1.7''
|15\10
''1050''
|19\13
''1023; 13''
|-
|'''Fa, Do'''
|'''Eb'''
|'''7'''
|'''7'''
|'''26\15'''
'''''1213.{{Overline|3}}'''''
|'''19\11'''
'''''1209.{{Overline|09}}'''''
|'''31\18'''
'''''1205.{{Overline|5}}'''''
|'''12\7'''
'''''1200'''''
|'''29\17'''
'''''1194; 8.5'''''
|'''17\10'''
'''''1190'''''
|'''22\13'''
'''''1184; 1.625'''''
|-
|Fa#, Do#
|E
|7#
|7#
|27\15
''1260''
|20\11
''1272.{{Overline|72}}''
| 33\18
''1283.{{Overline|3}}''
|13\7
''1300''
|32\17
''1317; 1.41{{Overline|6}}''
|19\10
''1330''
| 25\13
''1346; 6.5''
|-
|Fax, Dox
|E#
|7x
|7x
|28\15
''1306.{{Overline|6}}''
| rowspan="2" |21\11
''1336.{{Overline|36}}''
|35\18
''1361.{{Overline|1}}''
|14\7
''1400''
|35\17
''1441; 5.{{Overline|6}}''
|21\10
''1470''
|28\13
''1507; 1.{{Overline|4}}''
|-
|Dob, Solb
|Fb
|8b, Fc
|8f
|29\15
''1333.{{Overline|3}}''
|34\18
''1322.{{Overline|2}}''
|13\7
''1300''
|31\17
''1276; 2.125''
|18\10
''1260''
|23\13
''1238; 2.1{{Overline|6}}''
|-
!Do, Sol
!F
!8, F
!8
! colspan="7" |''1400''
|-
|Do#, Sol#
|F#
|8#, F#
|8#
|31\15
''1446.{{Overline|6}}''
|23\11
''1463.{{Overline|63}}''
|38\18
''1477.7̄''
| rowspan="2" |15\7
''1500''
|37\17
''1523; 1.{{Overline|8}}''
|22\10
''1540''
| 29\13
''1561; 1, 1.1{{Overline|6}}''
|-
|Reb, Lab
|Gb
| 9b, Gc
|9f
|33\15
''1540''
|24\11
''1527.{{Overline|27}}''
|39\18
''1516.{{Overline|6}}''
| 36\17
''1482; 2.8{{Overline|3}}''
|21\10
''1470''
|27\13
''1453; 1.{{Overline|18}}''
|-
|'''Re, La'''
|'''G'''
|'''9, G'''
|9
|'''34\15'''
'''''1586.{{Overline|6}}'''''
|'''25\11'''
'''''1590.{{Overline|90}}'''''
|'''41\18'''
'''''1594.{{Overline|4}}'''''
|'''16\7'''
'''''1600'''''
|'''39\17'''
'''''1605; 1.1{{Overline|3}}'''''
|'''23\10'''
'''''1610'''''
|'''30\13'''
'''''1615; 2.6'''''
|-
|Re#, La#
|G#
|9#, G#
|9#
|35\15
''1633.{{Overline|3}}''
|26\11
''1654.{{Overline|54}}''
|43\18
''1672.{{Overline|2}}''
| rowspan="2" |17\7
''1700''
|42\17
''1729; 2, 2.{{Overline|3}}''
|25\10
''1750''
|33\13
''1776; 1.08{{Overline|3}}''
|-
|Mib, Sib
| Ab
|Xb, Ac
|Af
|37\15
''1726.{{Overline|6}}''
| 27\11
''1718.{{Overline|18}}''
|44\18
''1711.{{Overline|1}}''
|41\17
''1688; 4.25''
| 24\10
''1680''
|31\13
''1669; 4.{{Overline|3}}''
|-
|Mi, Si
|A
|X, A
|A
|38\15
''1773.{{Overline|3}}''
|28\11
''1781.{{Overline|81}}''
|46\18
''1788.{{Overline|8}}''
|18\7
''1800''
| 44\17
''1811; 1, 3.25''
|26\10
''1820''
|34\13
''1830; 1.3''
|-
|Mi#, Si#
|A#
|X#, A#
|A#
|39\15
''1820''
| rowspan="2" |29\11
''1845.{{Overline|45}}''
|48\18
''1866.{{Overline|6}}''
|19\7
''1900''
|47\17
''1935; 3.4''
|28\10
''1960''
| 37\13
''1992; 3.25''
|-
|Fab, Dob
|Bbb
|Ebb, Ccc
|Bf
|40\15
''1866.{{Overline|6}}''
|47\18
''1827.{{Overline|7}}''
|18\7
''1800''
|43\17
''1770; 1.7''
|25\10
''1750''
|32\13
''1723; 13''
|-
|'''Fa, Do'''
|'''Bb'''
|Eb, Cc
|'''B'''
|'''41\15'''
'''''1913.{{Overline|3}}'''''
|'''30\11'''
'''''1909.{{Overline|09}}'''''
|'''49\18'''
'''''1905.{{Overline|5}}'''''
|'''19\7'''
'''''1900'''''
|'''46\17'''
'''''1894; 8.5'''''
|'''27\10'''
'''''1890'''''
|'''35\13'''
'''''1884; 1.625'''''
|-
|Fa#, Do#
|B
|E, C
|B#
| 42\15
''1960''
|31\11
''1972.{{Overline|72}}''
|51\18
''1983.{{Overline|3}}''
|20\7
''2000''
|49\17
''2017; 1.41{{Overline|6}}''
|29\10
''2030''
|38\13
''2046; 6.5''
|-
|Fax, Dox
|B#
|Ex, Cx
|Bx
|43\15
''2006.{{Overline|6}}''
| rowspan="2" |32\11
''2036.{{Overline|36}}''
|53\18
''2061.{{Overline|1}}''
|21\7
''2100''
|52\17
''2141; 5.{{Overline|6}}''
|31\10
''2170''
|41\13
''2207; 1.{{Overline|4}}''
|-
| Dob, Solb
|Hb
|0b, Dc
|Cf
|44\15
''2053.{{Overline|3}}''
|52\18
''2022.{{Overline|2}}''
|20\7
''2000''
|48\17
''1976; 2.125''
|28\10
''1960''
| 36\13
''1938; 2.1{{Overline|6}}''
|-
!Do, Sol
!H
!0, D
!C
! colspan="7" |''2100''
|-
|Do#, Sol#
|Η#
|0#, D#
|C#
|46\15
''2146.{{Overline|6}}''
|34\11
''2163.{{Overline|63}}''
|56\18
''2177.{{Overline|7}}''
| rowspan="2" |22\7
''2200''
|54\17
''2223; 1.{{Overline|8}}''
|32\10
''2240''
|42\13
''2261; 1, 1.1{{Overline|6}}''
|-
|Reb, Lab
|Cb
|1b, 1c
|Df
|48\15
''2240''
|35\11
''2227.{{Overline|27}}''
|57\18
''2216.{{Overline|6}}''
|53\17
''2182; 2.8{{Overline|3}}''
|31\10
''2170''
|40\13
''2153; 1.{{Overline|18}}''
|-
|'''Re, La'''
|'''C'''
|'''1'''
|'''D'''
|'''49\15'''
'''''2286.{{Overline|6}}'''''
|'''36\11'''
'''''2290.{{Overline|90}}'''''
|'''59\18'''
'''''2294.{{Overline|4}}'''''
|'''23\7'''
'''''2300'''''
|'''56\17'''
'''''2305; 1.1{{Overline|3}}'''''
|'''33\10'''
'''2310'''
|'''43\13'''
'''''2315; 2.6'''''
|-
|Re#, La#
|C#
|1#
|D#
|50\15
''2223.{{Overline|3}}''
|37\11
''2354.{{Overline|54}}''
|61\18
''2372.''{{Overline|2}}
| rowspan="2" |24\7
''2400''
|59\17
''2429; 2, 2.{{Overline|3}}''
|35\10
''2450''
|46\13
''2476; 1.08{{Overline|3}}''
|-
|Mib, Sib
|Db
|2b, 2c
|Ef
|52\15
''2426.{{Overline|6}}''
|38\11
''2418.{{Overline|18}}''
|62\18
''2411.{{Overline|1}}''
|58\17
''2388; 4.25''
|34\10
''2380''
|44\13
''2369; 4.{{Overline|3}}''
|-
|Mi, Si
|D
|2
|E
|53\15
''2473,{{Overline|3}}''
|39\11
''2481.{{Overline|81}}''
|64\11
''2488.{{Overline|8}}''
|25\7
''2500''
|61\17
''2511; 1, 3.25''
|36\10
''2520''
|47\13
''2530; 1.3''
|-
|Mi#, Si#
|D#
|2#
|E#
|54\15
''2520''
| rowspan="2" |40\11
''2545.{{Overline|45}}''
|66\18
''2566.{{Overline|6}}''
|26\7
''2600''
|64\17
''2635; 3.4''
|38\10
''2660''
|50\13
''2692; 3.25''
|-
|Fab, Dob
|Ebb
|3b, 3c
|Fff
|55\15
''2566.{{Overline|6}}''
|65\18
''2527.{{Overline|7}}''
|25\7
''2500''
|60\17
''2470; 1.7''
|35\10
''2450''
|45\13
''2423; 13''
|-
|'''Fa, Do'''
|'''Eb'''
|'''3'''
|'''Ff'''
|'''56\15'''
'''''2613.{{Overline|3}}'''''
|'''41\11'''
'''''2609.{{Overline|09}}'''''
|'''67\18'''
'''''2605.{{Overline|5}}'''''
|'''26\7'''
'''''2600'''''
|'''63\17'''
'''''2594; 8.5'''''
|'''37\10'''
'''''2590'''''
|'''48\13'''
'''''2584; 1.625'''''
|-
|Fa#, Do#
|E
|3#
|F
|57\15
''2660''
|42\11
''2672.{{Overline|72}}''
|69\18
''2683.{{Overline|3}}''
|27\7
''2700''
|66\17
''2717; 1.41{{Overline|6}}''
|39\10
''2730''
|51\13
''2746; 6.5''
|-
|Fax, Dox
|E#
|3x
|F#
|58\15
''2706.{{Overline|6}}''
| rowspan="2" |43\11
''2736.{{Overline|36}}''
|71\18
''2761.{{Overline|1}}''
|28\7
''2800''
|69\17
''2841; 5.{{Overline|6}}''
|41\10
''2870''
|54\13
''2907; 1.{{Overline|4}}''
|-
|Dob, Solb
|Fb
|4b, 4c
|0f, Gf
|59\15
''2753.{{Overline|3}}''
|70\18
''2722.{{Overline|2}}''
|27\7
''2700''
|65\17
''2676; 2.125''
|38\10
''2660''
|49\13
''2638; 2.1{{Overline|6}}''
|-
!Do, Sol
!F
!4
!0, G
! colspan="7" |''2800''
|}
==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):
|-
|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
|-
| colspan="6" |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:
{| class="wikitable"
|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:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="3" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
|-
|Lydian
|LLLs
|<nowiki>3|0</nowiki>
|P
|M
| A
|-
|Major
|LLsL
|<nowiki>2|1</nowiki>
|P
|M
|P
|-
| Minor
|LLsL
|<nowiki>1|2</nowiki>
| P
|m
|P
|-
|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-Superpyth'''===
[[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" rowspan="2" |Generator
(bright)
! colspan="2" |Cents
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" | Comments
|-
!<u>Normalised<ref name=":03">Fractions repeating more than 4 digits written as continued fractions</ref></u>
!''ed7\12<ref name=":04">Fractions repeating more than 4 digits written as continued fractions</ref>''
|-
| 1\4
|
|
|<u>171; 2.{{Overline|3}}</u>
|''175''
|1
|1
|1.000
|Equalised
|-
|6\23
|
|
|<u>180</u>
|''182; 1, 1.{{Overline|5}}''
|6
|5
|1.200
|
|-
|
| 11\42
|
|<u>180; 1.21{{Overline|6}}</u>
|''183.{{Overline|3}}''
|11
|9
|1.222
|
|-
|5\19
|
|
|<u>181.{{Overline|81}}</u>
|''184; 4.75''
|5
|4
|1.250
|
|-
|
|14\53
|
|<u>182; 1, 1.5</u>
|''184; 1, 9.6''
|14
|11
|1.273
|
|-
|
|9\34
|
|<u>183; 19.{{Overline|6}}</u>
|''185; 3.4''
| 9
|7
|1.286
|
|-
|4\15
|
|
|<u>184; 1.625</u>
|''186.{{Overline|6}}''
|4
|3
|1.333
|
|-
|
|11\41
|
|<u>185, 1, 10.8{{Overline|3}}</u>
|''187; 1.{{Overline|24}}''
|11
| 8
|1.375
|
|-
|
|7\26
|
|<u>186.{{Overline|6}}</u>
|''188; 2.1{{Overline|6}}''
|7
|5
|1.400
|
|-
|
|10\37
|
|<u>187.5</u>
|''189.{{Overline|189}}''
|10
| 7
| 1.429
|
|-
|
|13\48
|
|<u>187; 1, 19.75</u>
|''189.58{{Overline|3}}''
|13
|9
|1.444
|
|-
|
|16\59
|
|<u>188; 4.25</u>
|''189; 1, 4.9''
|16
|11
|1.455
|
|-
| 3\11
|
|
|<u>189; 2.{{Overline|1}}</u>
|''190.{{Overline|90}}''
| 3
|2
|1.500
|Napoli-Meantone starts here
|-
|
|17\62
|
|<u>190; 1, 1.{{Overline|12}}</u>
|''191; 1, 14.5''
|17
|11
|1.545
|
|-
|
|14\51
|
|<u>190.{{Overline|90}}</u>
|''192; 8.375''
|14
| 9
| 1.556
|
|-
|
|11\40
|
|<u>191; 3, 2.{{Overline|3}}</u>
|''192.5''
|11
| 7
| 1.571
|
|-
|
|8\29
|
|<u>192</u>
|''193; 9.{{Overline|6}}''
| 8
| 5
|1.600
|
|-
|
|5\18
|
|<u>193; 1, 1, 4.{{Overline|6}}</u>
|''194.{{Overline|4}}''
|5
|3
|1.667
|
|-
|
|
|12\43
|<u>194.{{Overline|594}}</u>
|''195; 2.8{{Overline|6}}''
| 12
| 7
|1.714
|
|-
|
|7\25
|
|<u>195; 2.8{{Overline|6}}</u>
|''196''
|7
|4
|1.750
|
|-
|
|9\32
|
|<u>196.{{Overline|36}}</u>
|''196.875''
|9
|5
|1.800
|
|-
|
|11\39
|
|<u>197; 67</u>
|''197; 2, 3.4''
|11
| 6
|1.833
|
|-
|
|13\46
|
|<u>197; 2.{{Overline|135}}</u>
|''197; 1, 4.75''
| 13
| 7
| 1.857
|
|-
|
|15\53
|
|<u>197; 1, 2, 1, 1.{{Overline|54}}</u>
|''198; 8.8{{Overline|3}}''
|15
|8
|1.875
|
|-
|
| 17\60
|
|<u>198; 17.1{{Overline|6}}</u>
|''198.{{Overline|3}}''
|17
| 9
| 1.889
|
|-
|
|19\67
|
|<u>198: 3, 1, 28</u>
|''198, 1, 1.{{Overline|03}}''
|19
| 10
|1.900
|
|-
|
|21\74
|
|<u>198; 2.3{{Overline|518}}</u>
| ''198.{{Overline |''198.{{Overline|648}}''
|21
| 11
|1.909
|
|-
|
|23\81
|
|<u>198; 1, 3, 1.7</u>
|''198; 1, 3, 3.8''
|23
|12
| 1.917
|
|-
|
| 25\88
|
|<u>198; 1, 2, 12.25</u>
|''198.8{{Overline|63}}''
|25
| 13
|1.923
|
|-
|
|27\95
|
|<u>198; 1, 3.{{Overline|405}}</u>
|''198; 1.0{{Overline|5}}''
|27
|14
|1.929
|
|-
|
|29\102
|
|<u>198; 1, 1.1{{Overline|6}}</u>
|''199; 51''
|29
|15
|1.933
|
|-
|2\7
|
|
|<u>200</u>
|''200''
|2
|1
|2.000
| Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|
|17\59
|
|<u>201.{{Overline|9801}}</u>
|''201; 1, 2.2{{Overline|7}}''
|17
|8
|2.125
|
|-
|
| 15\52
|
|<u>202; 4.0{{Overline|45}}</u>
|''201; 1.08{{Overline|3}}''
|15
|7
|2.143
|
|-
|
|13\45
|
|<u>202; 1, 1, 2.0{{Overline|6}}</u>
|''202.{{Overline|2}}''
|13
|6
|2.167
|
|-
|
|11\38
|
|<u>203; 13</u>
|''202; 1.58{{Overline|3}}''
|11
|5
|2.200
|
|-
|
|9\31
|
|<u>203; 1, 3.41{{Overline|6}}</u>
|''203; 4, 2.{{Overline|3}}''
|9
|4
| 2.250
|
|-
|
|7\24
|
|<u>204; 1. 7.2</u>
|''204.1{{Overline|6}}''
| 7
|3
|2.333
|
|-
|
|
|12\41
|<u>205; 1.4</u>
|''204; 1. 7.2''
|12
|5
|2.400
|
|-
|
|5\17
|
|<u>206; 1, 8.{{Overline|6}}</u>
|''205; 1.1{{Overline|3}}''
|5
|2
|2.500
|Napoli-Neogothic heartland is from here…
|-
|
|
|18\61
|<u>207; 1.{{Overline|4}}</u>
|''206; 1.{{Overline|259}}''
|18
|7
| 2.571
|
|-
|
|
|13\44
|<u>208</u>
|''206.{{Overline|81}}''
|13
| 5
| 2.600
|
|-
|
|8\27
|
|<u>208; 1.4375</u>
|''207.{{Overline|407}}''
| 8
|3
|2.667
|…to here
|-
|
|11\37
|
|<u>209; 1.{{Overline|90}}</u>
|''208.{{Overline|108}}''
|11
|4
| 2.750
|
|-
|
|14\47
|
|<u>210</u>
|''208; 1.958{{Overline|3}}''
| 14
| 5
|2.800
|
|-
|
|17\57
|
|<u>210; 3.2{{Overline|3}}</u>
|''208; 1.29{{Overline|54}}''
|17
|6
|2.833
|
|-
|
| 20\67
|
|<u>210; 1.9</u>
|''208; 1, 21.{{Overline|3}}''
| 20
|7
|2.857
|
|-
|
| 23\77
|
|<u>210; 1.4{{Overline|5}}</u>
|''209.{{Overline|09}}''
|23
|8
|2.875
|
|-
|3\10
|
|
|<u>211; 1, 3.25</u>
|''210''
|3
| 1
|3.000
|Napoli-Pythagorean ends, Napoli-Superpyth begins
|-
|
|22\73
|
|<u>212; 1, 9.{{Overline|3}}</u>
|''210; 1, 23.{{Overline|3}}''
|22
|7
|3.143
|
|-
|
|19\63
|
|<u>213; 11.{{Overline|8}}</u>
|''211.{{Overline|1}}''
|19
|6
|3.167
|
|-
|
|16\53
|
|<u>213.{{Overline|3}}</u>
|''211; 3, 8.5''
|16
|5
|3.200
|
|-
|
|13\43
|
|<u>213; 1, 2.3{{Overline|18}}</u>
|''211; 1.{{Overline|592}}''
|13
|4
|3.250
|
|-
|
| 10\33
|
|<u>214; 3.5</u>
|''212.{{Overline|12}}''
|10
|3
|3.333
|
|-
|
|7\23
|
|<u>215; 2.6</u>
|''213; 23''
|7
|2
|3.500
|
|-
|
|11\36
|
|<u>216; 2.541{{Overline|6}}</u>
|''213.{{Overline|3}}''
| 11
|3
|3.667
|
|-
|
|15\49
|
|<u>216; 1.152{{Overline|7}}</u>
|''214; 3.5''
|15
|4
|3.750
|
|-
|
|19\62
|
|<u>217; 7</u>
|''214; 1.9375''
|19
|5
|3.800
|
|-
|4\13
|
|
|<u>218.{{Overline|18}}</u>
|''215; 2.6''
|4
|1
|4.000
|
|-
|
|13\42
|
|<u>219; 1, 2.55</u>
|''216.{{Overline|6}}''
|13
|3
|4.333
|
|-
|
|9\29
|
|<u>220; 2.45</u>
|''217; 4, 7''
|9
|2
|4.500
|
|-
|
|14\45
|
|<u>221; 19</u>
|''217.{{Overline|7}}''
|14
| 3
| 4.667
|
|-
|5\16
|
|
|<u>222.{{Overline|2}}</u>
|''218.75''
|5
| 1
|5.000
|Napoli-Superpyth ends
|-
|
|16\51
|
|<u>223; 3.{{Overline|90}}</u>
|''219; 1, 1.55''
|16
|3
|5.333
|
|-
|
|11\35
|
|<u>223; 1, 2.6875</u>
|''220''
|11
|2
|5.500
|
|-
|
|17\54
|
|<u>224; 5.7{{Overline|2}}</u>
|''220.{{Overline|370}}''
| 17
| 3
|5.667
|
|-
|6\19
|
|
|<u>225</u>
|''221; 19''
|6
|1
|6.000
|
|-
|1\3
|
|
|<u>240</u>
|''233.{{Overline|3}}''
|1
|0
|→ inf
|Paucitonic
|}

Revision as of 00:30, 23 May 2023

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