3L 1s (3/2-equivalent): Difference between revisions

'''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]].

   

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.

! 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

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