User:Moremajorthanmajor/4L 1s (5/3-equivalent): Difference between revisions

[[Basic]] diatonic is in [[9ed5/3]], which is a very good minor sixth-based equal tuning similar to [[12edo]].

==Notation==

There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (minor sixth) repeating notation consisting of 5 naturals (Do, Re, Mi, Fa, Sol or Sol, La, Si, Do, Re). Given that 1-5/4-3/2 is major sixth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate these diatonic scales as repeating at the double sextave (augmented eleventh~twelfth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 10\9. Notating this way produces a twelfth which is the Scala Francisci[8L 2s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.

{| class="wikitable"

738.4615

|12\14

|20\23

774.194

|Α#

|''1\19''

|''1\14''

|''2\23''

| rowspan="2" |''1\9''

''100''

''122.{{Overline|72}}''

|''2\13''

|''3\17''

|-

|Reb, Lab

|Βb

|''3\19''

|''2\14''

|''3\23''

|''2\22''

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

|''1\13''

|''1\17''

|-

|'''Re, La'''

|Β

|'''''4\19'''''

|'''''3\14'''''

|'''''5\23'''''

|'''''2\9'''''

'''''200'''''

'''''204.{{Overline|54}}'''''

|'''''3\13'''''

|'''''4\17'''''

|-

|Re#, La#

|Β#

|''5\19''

|''4\14''

|''7\23''

''273.913''

''327.{{Overline|27}}''

|''5\13''

|''7\17''

|-

|Mib, Sib

|Γb

|''7\19''

|''5\14''

|''8\23''

|''7\22''

''286.{{Overline|36}}''

|''4\13''

|''5\17''

|-

|Mi, Si

|Γ

|''8\19''

|''6\14''

|''10\23''

''391.304''

''409.{{Overline|09}}''

|''6\13''

|''8\17''

|-

|Mi#, Si#

|Γ#

|''9\19''

| rowspan="2" |''7\14''

''450''

|''12\23''

|''5\9''

''500''

''531.{{Overline|81}}''

|''8\13''

|''11\17''

|-

|Fab, Dob

|Δb

|''10\19''

|''11\23''

|''4\9''

''400''

|''9\22''

|''5\13''

|''6\17''

|-

|Fa, Do

|Δ

|''11\19''

|''8\14''

|''13\23''

''508.696''

''490.{{Overline|90}}''

|''7\13''

|''9\17''

|-

|Fa#, Do#

|Δ#

|''12\19''

|''9\14''

|''15\23''

| rowspan="2" |''6\9''

''600''

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

|''9\13''

|''12\17''

|-

|Solb, Reb

|Εb

|''14\19''

|''10\14''

|''16\23''

''626.087''

|''14\22''

|''8\13''

|''10\17''

|-

|'''Sol, Re'''

|'''Ε'''

|'''''15\19'''''

|'''''11\14'''''

|'''''18\23'''''

|'''''7\8'''''

'''''700'''''

'''''695.{{Overline|45}}'''''

|'''''10\13'''''

|'''''13\17'''''

|-

|Sol#, Re#

|Ε#

|''16\19''

|''12\14''

|''20\23''

| rowspan="2" |''8\8''

''800''

''818.{{Overline|18}}''

|''12\13''

|-

|Dob, Solb

|Ϛb/Ϝb

|''18\19''

|''13\14''

|''21\23''

|''19\22''

''777.{{Overline|27}}''

|''11\13''

|''14\17''

|-

!Do, Sol

|Ϛ#/Ϝ#

|''20\19''

|''15\14''

|''25\23''

| rowspan="2" |''10\9''

''1000''

|Ζb

|''22\19''

|''16\14''

|''26\23''

|''24\22''

''981.{{Overline|81}}''

|''14\13''

|''18\17''

|-

|'''Re, La'''

|'''Ζ'''

|'''''23\19'''''

|'''''17\14'''''

|'''''28\23'''''

|'''''11\9'''''

'''''1100'''''

'''''1104.{{Overline|54}}'''''

|'''''16\13'''''

|'''''21\17'''''

|-

|Re#, La#

|Ζ#

|''24\19''

|''18\14''

|''30\23''

''1173.913''

''1227.{{Overline|27}}''

|''18\13''

|''24\14''

|-

|Mib, Sib

|Ηb

|''26\19''

|''19\14''

|''31\23''

''1213.0345''

''1186.{{Overline|36}}''

|''17\13''

|''22\17''

|-

|Mi, Si

|Η

|''27\19''

|''20\14''

|''33\23''

''1291.304''

''1309.{{Overline|09}}''

|''19\13''

|''25\17''

|-

|Mi#, Si#

|Η#

|''28\19''

| rowspan="2" |''21\14''

''1350''

|''35\23''

|''14\9''

''1400''

''1431.{{Overline|81}}''

|''21\13''

|''28\17''

|-

|Fab, Dob

|Θb

|''29\19''

|''34\23''

|''13\9''

''1300''

''1368.{{Overline|18}}''

|''18\13''

|''23\17''

|-

|Fa, Do

|Θ

|''30\19''

|''22\14''

|''36\23''

''1408.696''

''1390.{{Overline|90}}''

|''20\13''

|''26\17''

|-

|Fa#, Do#

|Θ#

|''31\19''

|''23\14''

|''38\23''

''1487.9655''

''1513.{{Overline|63}}''

|''22\13''

|''29\17''

|-

|Solb, Reb

|Ιb

|''33\19''

|''24\14''

|''39\23''

''1526.087''

''1472.{{Overline|72}}''

|''21\13''

|''27\17''

|-

|'''Sol, Re'''

|'''Ι'''

|'''''34\19'''''

|'''''25\14'''''

|'''''41\23'''''

|'''''16\9'''''

'''''1600'''''

'''''1595.{{Overline|45}}'''''

|'''''23\13'''''

|'''''30\17'''''

|-

|Sol#, Re#

|Ι#

|''35\19''

|''26\14''

|''43\23''

| rowspan="2" |''17\9''

''1700''

|''42\22''

|''25\13''

|''33\17''

|-

|Dob, Solb

|Αb

|''37\19''

|''27\14''

|''44\23''

|''41\22''

''1677.{{Overline|27}}''

''1661.5385''

|''31\17''

|-

!Do, Sol

|5

|1.600

|

|-

|3

|1.667

|

|-

|201.77

|700.885

|19

|9

|202.247

|701.123

|15

|7

|213.084

|706.542

|19

|6

|216.867

|708.434

|15

|4

|712.088

|''215.492''

|17

|3