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

{{Infobox MOS

}}'''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).  

There are 3 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 diatonic scales as repeating at the double or triple sesquitave (major ninth or thirteenth), 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] or a major thirteenth which is the Dorian mode of Bijou[9L 3s]. Since there are exactly 8 naturals in double sesquitave notation and 12 in triple sesquitave notation, letters A-H (FGABHCDEF) or dozenal digits (0123456789XE0 or D1234567FGACD with flats written C molle) may be used.

! colspan="3" |Notation

| 23\18

|Eb, Cc

|Do#, Sol#

|F#

|0#, D#

|1\15

''46.{{Overline|6}}''

|1\11

''63.{{Overline|63}}''

|2\18

''77.7̄''

| rowspan="2" |1\7

| 3\17

''123.529…''

| 2\10

|3\13

|Reb, Lab

| Gb

|1b, 1c

|3\15

|2\11

''127.{{Overline|27}}''

|3\18

''116.{{Overline|6}}''

| 2\17

''82.352…''

|1\10

|1\13

''53.846…''

|'''Re, La'''

|'''G'''

|'''1'''

|'''4\15'''

'''''186.{{Overline|6}}'''''

|'''3\11'''

'''''190.{{Overline|90}}'''''

|'''5\18'''

'''''194.{{Overline|4}}'''''

|'''2\7'''

'''''200'''''

|'''5\17'''

'''''205.882…'''''

|'''3\10'''

'''''210'''''

|'''4\13'''

'''''215.384…'''''

|Re#, La#

| G#

| 1#

|5\15

|4\11

''254.{{Overline|54}}''

|7\18

''272.2̄''

| rowspan="2" |3\7

|8\17

''329.411…''

|5\10

|7\13

''376.923…''

|Mib, Sib

|2b, 2c

|7\15

''326.{{Overline|6}}''

|5\11

''318.{{Overline|18}}''

| 8\18

''311.{{Overline|1}}''

|7\17

''288.235…''

| 4\10

''280''

|5\13

''269.230…''

|Mi, Si

|A

| 2

|8\15

''373.{{Overline|3}}''

|6\11

''381.{{Overline|81}}''

|10\18

''388.{{Overline|8}}''

|4\7

''400''

|10\17

''411.764…''

|6\10

''420''

''430.769…''

|Mi#, Si#

|A#

|2#

|9\15

''420''

| rowspan="2" |7\11

''445.{{Overline|45}}''

|12\18

''466.{{Overline|6}}''

|5\7

''500''

|13\17

''535.294…''

|8\10

''560''

|11\13

''592.307…''

|Fab, Dob

|Bbb

|3b, 3c

|10\15

''466.{{Overline|6}}''

|11\18

''427.{{Overline|7}}''

|4\7

''400''

|9\17

''370.588…''

|6\13

''323.076.…''

|'''Fa, Do'''

|'''Bb'''

|'''3'''

|'''11\15'''

'''''513.{{Overline|3}}'''''

|'''8\11'''

'''''509.{{Overline|09}}'''''

|'''13\18'''

'''''505.{{Overline|5}}'''''

|'''5\7'''

'''''500'''''

|'''12\17'''

'''''494.117…'''''

|'''7\10'''

'''''490'''''

'''''484.615…'''''

|Fa#, Do#

| B

|3#

|12\15

''560''

|9\11

''572.{{Overline|72}}''

| 15\18

''583.{{Overline|3}}''

|6\7

''600''

|15\17

''617.647…''

|9\10

''630''

|12\13

''646.153…''

| Fax, Dox

|B#

|3x

|13\15

''606. {{Overline|6}}''

| rowspan="2" |10\11

''636.{{Overline|36}}''

|17\18

''661.{{Overline|1}}''

|7\7

''700''

|18\17

''741.176…''

|11\10

''770''

|15\13

''807.692…''

|Dob, Solb

|Hb

|4b, 4c

|14\15

''653.{{Overline|3}}''

|16\18

''622.{{Overline|2}}''

|6\7

''600''

| 14\17

''576.470…''

| 8\10

''560''

|10\13

''538.461…''

!Do, Sol

! colspan="7" |''700''

|-

|Do#, Sol#

|Η#

|16\15

''746.{{Overline|6}}''

|12\11

''763.{{Overline|63}}''

|20\18

''777.{{Overline|7}}''

| rowspan="2" |8\7

''800''

|20\17

''823.529…''

|12\10

''840''

|16\13

''861.538…''

|Reb, Lab

|Cb

|5b, 5c

|18\15

''840''

|13\11

''827.{{Overline|27}}''

|21\18

''816.{{Overline|6}}''

| 19\17

''782.352…''

|11\10

''770''

|14\13

''753.846…''

|'''Re, La'''

|'''C'''

|'''5'''

|'''19\15'''

   

'''''886.{{Overline|6}}'''''

|'''14\11'''

'''''890.{{Overline|90}}'''''

|'''23\18'''

'''''894.{{Overline|4}}'''''

|'''9\7'''

'''''900'''''

|'''22\17'''

'''''905.882…'''''

|'''13\10'''

'''''910'''''

|'''17\13'''

'''''915.384…'''''

| Re#, La#

|C#

|5#

|20\15

''933.{{Overline|3}}''

|15\11

''954.{{Overline|54}}''

|25\18

''972.{{Overline|2}}''

| rowspan="2" | 10\7

''1000''

|25\17

''1029.411…''

|15\10

''1050''

''1076.923…''

|Mib, Sib

|Db

|6b, 6c

|22\15

''1026.{{Overline|6}}''

|16\11

''1018.{{Overline|18}}''

|26\18

''1011. {{Overline|1}}''

|24\17

''988.235…''

|14\10

''980''

|18\13

''969.230…''

|Mi, Si

|D

|6

| 23\15

''1073.{{Overline|3}}''

|17\11

''1081.{{Overline|81}}''

|28\18

''1088.{{Overline|8}}''

|11\7

''1100''

|27\17

''1111.764…''

|16\10

''1120''

|21\13

''1130.769…''

|6#

|24\15

''1120''

| rowspan="2" | 18\11

''1145.{{Overline|45}}''

|30\18

''1166.{{Overline|6}}''

|12\7

''1200''

| 30\17

''1235.294…''

|18\10

''1260''

|24\13

''1292.307…''

|-

|25\15

''1166.{{Overline|6}}''

|29\18

''1127.{{Overline|7}}''

|11\7

''1100''

|26\17

''1070.588…''

|19\13

''1023.076…''

|'''Fa, Do'''

|'''Eb'''

|'''7'''

|'''26\15'''

'''''1213.{{Overline|3}}'''''

|'''19\11'''

'''''1209.{{Overline|09}}'''''

|'''31\18'''

'''''1205.{{Overline|5}}'''''

|'''12\7'''

'''''1200'''''

|'''29\17'''

'''''1194.117…'''''

|'''17\10'''

'''''1190'''''

|'''22\13'''

'''''1184.615…'''''

|-

|27\15

''1260''

|20\11

''1272.{{Overline|72}}''

| 33\18