User:Moremajorthanmajor/4L 1s (5/3-equivalent): Difference between revisions
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'''4L 1s<5/3>''' (sometimes called '''diatonic'''), is a minor sixth-repeating MOS scale. The notation "<5/3>" means the period of the MOS is 5/3, disambiguating it from octave-repeating [[4L 1s]]. The name of the period interval is called the '''sextave''' (by analogy to the [[tritave]]). | '''4L 1s<5/3>''' (sometimes called '''diatonic'''), is a minor sixth-repeating MOS scale. The notation "<5/3>" means the period of the MOS is 5/3, disambiguating it from octave-repeating [[4L 1s]]. The name of the period interval is called the '''sextave''' (by analogy to the [[tritave]]). | ||
The generator range is 171.4 to 240 cents, placing it on the diatonic major second, usually representing a major second of some type (like [[8/7]]). The bright (chroma-positive) generator is, however, its major sixth complement (685.7 to 720 cents). | The generator range is 171.4 to 240 cents, placing it on the diatonic major second, usually representing a major second of some type (like [[8/7]]). The bright (chroma-positive) generator is, however, its major sixth complement (685.7 to 720 cents). | ||
Because this diatonic is a | Because this diatonic is a minor sixth-repeating scale, each tone has a 5/3 minor sixth above it. The scale has one augmented chord, two major chords, two minor chords. This diatonic also has two dominant 7th chords, making it a warped Neapolitan minor scale. | ||
[[Basic]] diatonic is in [[9ed5/3]], which is a very good minor sixth-based equal tuning similar to [[12edo]]. | [[Basic]] diatonic is in [[9ed5/3]], which is a very good minor sixth-based equal tuning similar to [[12edo]]. | ||
| Line 43: | Line 43: | ||
100 | 100 | ||
|3\22 | |3\22 | ||
124.1379 | |||
|2\13 | |2\13 | ||
141.1765 | |||
|3\17 | |3\17 | ||
163.{{Overline|63}} | 163.{{Overline|63}} | ||
| Line 52: | Line 52: | ||
|Βb | |Βb | ||
|3\19 | |3\19 | ||
138.4615 | |||
|2\14 | |2\14 | ||
126.3158 | |||
|3\23 | |3\23 | ||
116.129 | 116.129 | ||
| Line 67: | Line 67: | ||
|'''Β''' | |'''Β''' | ||
|'''4\19''' | |'''4\19''' | ||
''' | '''184.6154''' | ||
|'''3\14''' | |'''3\14''' | ||
''' | '''189.4736''' | ||
|'''5\23''' | |'''5\23''' | ||
''' | '''193.5484''' | ||
|'''2\9''' | |'''2\9''' | ||
'''200''' | '''200''' | ||
| Line 77: | Line 77: | ||
'''206.89655''' | '''206.89655''' | ||
|'''3\13''' | |'''3\13''' | ||
''' | '''211.7647''' | ||
|'''4\17''' | |'''4\17''' | ||
'''218.{{Overline|18}}''' | '''218.{{Overline|18}}''' | ||
| Line 84: | Line 84: | ||
|Β# | |Β# | ||
|5\19 | |5\19 | ||
230.7692 | |||
|4\14 | |4\14 | ||
252.6316 | |||
|7\23 | |7\23 | ||
270.9677 | |||
| rowspan="2" |3\9 | | rowspan="2" |3\9 | ||
300 | 300 | ||
|8\22 | |8\22 | ||
331.0345 | |||
|5\13 | |5\13 | ||
352.9412 | |||
|7\17 | |7\17 | ||
381.{{Overline|81}} | 381.{{Overline|81}} | ||
| Line 101: | Line 101: | ||
|Γb | |Γb | ||
|7\19 | |7\19 | ||
323.0769 | |||
|5\14 | |5\14 | ||
315.7895 | |||
|8\23 | |8\23 | ||
309.6774 | |||
|7\22 | |7\22 | ||
289.6552 | |||
|4\13 | |4\13 | ||
282.3529 | |||
|5\17 | |5\17 | ||
272.{{Overline|72}} | 272.{{Overline|72}} | ||
| Line 116: | Line 116: | ||
|Γ | |Γ | ||
|8\19 | |8\19 | ||
369.2308 | |||
|6\14 | |6\14 | ||
378.9474 | |||
|10\23 | |10\23 | ||
387.0968 | |||
|4\9 | |4\9 | ||
400 | 400 | ||
|10\22 | |10\22 | ||
413.7931 | |||
|6\13 | |6\13 | ||
423.5294 | |||
|8\17 | |8\17 | ||
436.{{Overline|36}} | 436.{{Overline|36}} | ||
| Line 134: | Line 134: | ||
|Γ# | |Γ# | ||
|9\19 | |9\19 | ||
415.3846 | |||
| rowspan="2" |7\14 | | rowspan="2" |7\14 | ||
442.1053 | |||
|12\23 | |12\23 | ||
464.5161 | |||
|5\9 | |5\9 | ||
500 | 500 | ||
| Line 144: | Line 144: | ||
537.931 | 537.931 | ||
|8\13 | |8\13 | ||
564.7059 | |||
|11\17 | |11\17 | ||
600 | 600 | ||
| Line 151: | Line 151: | ||
|Δb | |Δb | ||
|10\19 | |10\19 | ||
461.5385 | |||
|11\23 | |11\23 | ||
425.80645 | 425.80645 | ||
| Line 157: | Line 157: | ||
400 | 400 | ||
|9\22 | |9\22 | ||
372.4138 | |||
|5\13 | |5\13 | ||
352.9412 | |||
|6\17 | |6\17 | ||
327.{{Overline|27}} | 327.{{Overline|27}} | ||
| Line 166: | Line 166: | ||
|Δ | |Δ | ||
|11\19 | |11\19 | ||
507.6923 | |||
|8\14 | |8\14 | ||
505.2632 | |||
|13\23 | |13\23 | ||
503.2259 | |||
|5\9 | |5\9 | ||
500 | 500 | ||
|12\22 | |12\22 | ||
496.5517 | |||
|7\13 | |7\13 | ||
494.11765 | 494.11765 | ||
| Line 187: | Line 187: | ||
568.42105 | 568.42105 | ||
|15\23 | |15\23 | ||
580.6452 | |||
| rowspan="2" |6\9 | | rowspan="2" |6\9 | ||
600 | 600 | ||
|15\22 | |15\22 | ||
620.6897 | |||
|9\13 | |9\13 | ||
635.2941 | |||
|12\17 | |12\17 | ||
654.{{Overline|54}} | 654.{{Overline|54}} | ||
| Line 204: | Line 204: | ||
631.57895 | 631.57895 | ||
|16\23 | |16\23 | ||
619.3548 | |||
|14\22 | |14\22 | ||
579.3103 | |||
|8\13 | |8\13 | ||
564.7059 | |||
|10\17 | |10\17 | ||
545.{{Overline|45}} | 545.{{Overline|45}} | ||
| Line 215: | Line 215: | ||
|'''Ε''' | |'''Ε''' | ||
|'''15\19''' | |'''15\19''' | ||
''' | '''692.3077''' | ||
|'''11\14''' | |'''11\14''' | ||
''' | '''694.7368''' | ||
|'''18\23''' | |'''18\23''' | ||
''' | '''696.7742''' | ||
|'''7\8''' | |'''7\8''' | ||
'''700''' | '''700''' | ||
|'''17\22''' | |'''17\22''' | ||
''' | '''703.4483''' | ||
|'''10\13''' | |'''10\13''' | ||
'''705.88235''' | '''705.88235''' | ||
| Line 232: | Line 232: | ||
|Ε# | |Ε# | ||
|16\19 | |16\19 | ||
738.4615 | |||
|12\14 | |12\14 | ||
757.8947 | |||
|20\23 | |20\23 | ||
774.19355 | 774.19355 | ||
| Line 240: | Line 240: | ||
800 | 800 | ||
|20\22 | |20\22 | ||
827.5862 | |||
|12\13 | |12\13 | ||
847.0588 | |||
|16\14 | |16\14 | ||
872.{{Overline|72}} | 872.{{Overline|72}} | ||
| Line 249: | Line 249: | ||
|Ϛb/Ϝb | |Ϛb/Ϝb | ||
|18\19 | |18\19 | ||
830.7692 | |||
|13\14 | |13\14 | ||
821.0526 | |||
|21\23 | |21\23 | ||
812.9032 | |||
|19\22 | |19\22 | ||
786.2069 | |||
|11\13 | |11\13 | ||
776.6471 | |||
|14\17 | |14\17 | ||
763.{{Overline|63}} | 763.{{Overline|63}} | ||
| Line 264: | Line 264: | ||
!Ϛ/Ϝ | !Ϛ/Ϝ | ||
!19\19 | !19\19 | ||
876.9231 | |||
!14\14 | !14\14 | ||
884.2105 | |||
!23\23 | !23\23 | ||
890.3226 | |||
!9\9 | !9\9 | ||
900 | 900 | ||
!22\22 | !22\22 | ||
910.3448 | |||
!13\13 | !13\13 | ||
917.6471 | |||
!17\17 | !17\17 | ||
927.{{Overline|27}} | 927.{{Overline|27}} | ||
| Line 281: | Line 281: | ||
|Ϛ#/Ϝ# | |Ϛ#/Ϝ# | ||
|20\19 | |20\19 | ||
923.0769 | |||
|15\14 | |15\14 | ||
947.3684 | |||
|24\23 | |24\23 | ||
929.0323 | |||
| rowspan="2" |10\9 | | rowspan="2" |10\9 | ||
1000 | 1000 | ||
| Line 306: | Line 306: | ||
993.10345 | 993.10345 | ||
|14\13 | |14\13 | ||
988.2353 | |||
|18\17 | |18\17 | ||
981.{{Overline|81}} | 981.{{Overline|81}} | ||
| Line 559: | Line 559: | ||
''122.{{Overline|72}}'' | ''122.{{Overline|72}}'' | ||
|''2\13'' | |''2\13'' | ||
'' | ''138.4615'' | ||
|''3\17'' | |''3\17'' | ||
'' | ''158.8235'' | ||
|- | |- | ||
|Reb, Lab | |Reb, Lab | ||
|Βb | |Βb | ||
|''3\19'' | |''3\19'' | ||
'' | ''142.1053'' | ||
|''2\14'' | |''2\14'' | ||
'' | ''128.5714'' | ||
|''3\23'' | |''3\23'' | ||
'' | ''117.3913'' | ||
|''2\22'' | |''2\22'' | ||
''81.{{Overline|81}}'' | ''81.{{Overline|81}}'' | ||
| Line 581: | Line 581: | ||
|Β | |Β | ||
|'''''4\19''''' | |'''''4\19''''' | ||
''''' | '''''189.4737''''' | ||
|'''''3\14''''' | |'''''3\14''''' | ||
''''' | '''''192.8571''''' | ||
|'''''5\23''''' | |'''''5\23''''' | ||
''''' | '''''195.6522''''' | ||
|'''''2\9''''' | |'''''2\9''''' | ||
'''''200''''' | '''''200''''' | ||
| Line 591: | Line 591: | ||
'''''204.{{Overline|54}}''''' | '''''204.{{Overline|54}}''''' | ||
|'''''3\13''''' | |'''''3\13''''' | ||
''''' | '''''207.6923''''' | ||
|'''''4\17''''' | |'''''4\17''''' | ||
''''' | '''''211.7647''''' | ||
|- | |- | ||
|Re#, La# | |Re#, La# | ||
|Β# | |Β# | ||
|''5\19'' | |''5\19'' | ||
'' | ''236.8421'' | ||
|''4\14'' | |''4\14'' | ||
'' | ''257.1429'' | ||
|''7\23'' | |''7\23'' | ||
''273.913'' | ''273.913'' | ||
| Line 610: | Line 610: | ||
''346.15385'' | ''346.15385'' | ||
|''7\17'' | |''7\17'' | ||
'' | ''370.5882'' | ||
|- | |- | ||
|Mib, Sib | |Mib, Sib | ||
| Line 617: | Line 617: | ||
''331.57895'' | ''331.57895'' | ||
|''5\14'' | |''5\14'' | ||
'' | ''321.4286'' | ||
|''8\23'' | |''8\23'' | ||
'' | ''313.0345'' | ||
|''7\22'' | |''7\22'' | ||
''286.{{Overline|36}}'' | ''286.{{Overline|36}}'' | ||
|''4\13'' | |''4\13'' | ||
'' | ''276.9231'' | ||
|''5\17'' | |''5\17'' | ||
'' | ''264.7059'' | ||
|- | |- | ||
|Mi, Si | |Mi, Si | ||
|Γ | |Γ | ||
|''8\19'' | |''8\19'' | ||
'' | ''378.9474'' | ||
|''6\14'' | |''6\14'' | ||
'' | ''385.7143'' | ||
|''10\23'' | |''10\23'' | ||
''391.304'' | ''391.304'' | ||
| Line 641: | Line 641: | ||
''409.{{Overline|09}}'' | ''409.{{Overline|09}}'' | ||
|''6\13'' | |''6\13'' | ||
'' | ''415.3846'' | ||
|''8\17'' | |''8\17'' | ||
'' | ''423.5294'' | ||
|- | |- | ||
|Mi#, Si# | |Mi#, Si# | ||
|Γ# | |Γ# | ||
|''9\19'' | |''9\19'' | ||
'' | ''426.3158'' | ||
| rowspan="2" |''7\14'' | | rowspan="2" |''7\14'' | ||
''450'' | ''450'' | ||
|''12\23'' | |''12\23'' | ||
'' | ''469.5652'' | ||
|''5\9'' | |''5\9'' | ||
''500'' | ''500'' | ||
| Line 660: | Line 660: | ||
''553.84615'' | ''553.84615'' | ||
|''11\17'' | |''11\17'' | ||
'' | ''582.3529'' | ||
|- | |- | ||
|Fab, Dob | |Fab, Dob | ||
|Δb | |Δb | ||
|''10\19'' | |''10\19'' | ||
'' | ''473.6842'' | ||
|''11\23'' | |''11\23'' | ||
'' | ''430.7692'' | ||
|''4\9'' | |''4\9'' | ||
''400'' | ''400'' | ||
| Line 675: | Line 675: | ||
''346.15385'' | ''346.15385'' | ||
|''6\17'' | |''6\17'' | ||
'' | ''317.6471'' | ||
|- | |- | ||
|Fa, Do | |Fa, Do | ||
|Δ | |Δ | ||
|''11\19'' | |''11\19'' | ||
'' | ''521.0526'' | ||
|''8\14'' | |''8\14'' | ||
'' | ''514.2857'' | ||
|''13\23'' | |''13\23'' | ||
''508.696'' | ''508.696'' | ||
| Line 690: | Line 690: | ||
''490.{{Overline|90}}'' | ''490.{{Overline|90}}'' | ||
|''7\13'' | |''7\13'' | ||
'' | ''484.6154'' | ||
|''9\17'' | |''9\17'' | ||
'' | ''476.4706'' | ||
|- | |- | ||
|Fa#, Do# | |Fa#, Do# | ||
| Line 699: | Line 699: | ||
''568.42105'' | ''568.42105'' | ||
|''9\14'' | |''9\14'' | ||
'' | ''578.5714'' | ||
|''15\23'' | |''15\23'' | ||
'' | ''587.9655'' | ||
| rowspan="2" |''6\9'' | | rowspan="2" |''6\9'' | ||
''600'' | ''600'' | ||
| Line 707: | Line 707: | ||
''613.{{Overline|63}}'' | ''613.{{Overline|63}}'' | ||
|''9\13'' | |''9\13'' | ||
'' | ''623.0769'' | ||
|''12\17'' | |''12\17'' | ||
'' | ''635.2931'' | ||
|- | |- | ||
|Solb, Reb | |Solb, Reb | ||
|Εb | |Εb | ||
|''14\19'' | |''14\19'' | ||
'' | ''663.1579'' | ||
|''10\14'' | |''10\14'' | ||
'' | ''642.8571'' | ||
|''16\23'' | |''16\23'' | ||
''626.087'' | ''626.087'' | ||
| Line 724: | Line 724: | ||
''553.84615'' | ''553.84615'' | ||
|''10\17'' | |''10\17'' | ||
'' | ''529.4118'' | ||
|- | |- | ||
|'''Sol, Re''' | |'''Sol, Re''' | ||
|'''Ε''' | |'''Ε''' | ||
|'''''15\19''''' | |'''''15\19''''' | ||
''''' | '''''710.5263''''' | ||
|'''''11\14''''' | |'''''11\14''''' | ||
''''' | '''''707.1429''''' | ||
|'''''18\23''''' | |'''''18\23''''' | ||
''''' | '''''704.3478''''' | ||
|'''''7\8''''' | |'''''7\8''''' | ||
'''''700''''' | '''''700''''' | ||
| Line 739: | Line 739: | ||
'''''695.{{Overline|45}}''''' | '''''695.{{Overline|45}}''''' | ||
|'''''10\13''''' | |'''''10\13''''' | ||
''''' | '''''692.3077''''' | ||
|'''''13\17''''' | |'''''13\17''''' | ||
''''' | '''''688.2353''''' | ||
|- | |- | ||
|Sol#, Re# | |Sol#, Re# | ||
|Ε# | |Ε# | ||
|''16\19'' | |''16\19'' | ||
'' | ''757.8947'' | ||
|''12\14'' | |''12\14'' | ||
'' | ''771.4286'' | ||
|''20\23'' | |''20\23'' | ||
'' | ''782.6087'' | ||
| rowspan="2" |''8\8'' | | rowspan="2" |''8\8'' | ||
''800'' | ''800'' | ||
| Line 756: | Line 756: | ||
''818.{{Overline|18}}'' | ''818.{{Overline|18}}'' | ||
|''12\13'' | |''12\13'' | ||
'' | ''830.7692'' | ||
|''16\14'' | |''16\14'' | ||
'' | ''847.0588'' | ||
|- | |- | ||
|Dob, Solb | |Dob, Solb | ||
|Ϛb/Ϝb | |Ϛb/Ϝb | ||
|''18\19'' | |''18\19'' | ||
'' | ''852.6316'' | ||
|''13\14'' | |''13\14'' | ||
'' | ''835.7143'' | ||
|''21\23'' | |''21\23'' | ||
'' | ''821.7391'' | ||
|''19\22'' | |''19\22'' | ||
''777.{{Overline|27}}'' | ''777.{{Overline|27}}'' | ||
|''11\13'' | |''11\13'' | ||
'' | ''761.5385'' | ||
|''14\17'' | |''14\17'' | ||
'' | ''741.1765'' | ||
|- | |- | ||
!Do, Sol | !Do, Sol | ||
| Line 782: | Line 782: | ||
|Ϛ#/Ϝ# | |Ϛ#/Ϝ# | ||
|''20\19'' | |''20\19'' | ||
'' | ''947.3684'' | ||
|''15\14'' | |''15\14'' | ||
'' | ''964.2857'' | ||
|''25\23'' | |''25\23'' | ||
'' | ''978.2609'' | ||
| rowspan="2" |''10\9'' | | rowspan="2" |''10\9'' | ||
''1000'' | ''1000'' | ||
| Line 807: | Line 807: | ||
''981.{{Overline|81}}'' | ''981.{{Overline|81}}'' | ||
|''14\13'' | |''14\13'' | ||
'' | ''969.2308'' | ||
|''18\17'' | |''18\17'' | ||
'' | ''952.9412'' | ||
|- | |- | ||
|'''Re, La''' | |'''Re, La''' | ||
| Line 1,209: | Line 1,209: | ||
[[Comma]] list: [[81/80]] | [[Comma]] list: [[81/80]] | ||
[[POL2]] generator: ~9/8 = | [[POL2]] generator: ~9/8 = 193.8419 | ||
[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}] | [[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}] | ||
| Line 1,219: | Line 1,219: | ||
[[Comma]] list: [[64/63]] | [[Comma]] list: [[64/63]] | ||
[[POL2]] generator: ~9/8 = | [[POL2]] generator: ~9/8 = 216.5781 | ||
[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}] | [[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}] | ||
| Line 1,582: | Line 1,582: | ||
|201.77 | |201.77 | ||
|700.885 | |700.885 | ||
|'' | |''201.1765'' | ||
|'' | |''698.8235'' | ||
|19 | |19 | ||
|9 | |9 | ||
| Line 1,606: | Line 1,606: | ||
|202.247 | |202.247 | ||
|701.123 | |701.123 | ||
|'' | |''201.4925'' | ||
|'' | |''698.5075'' | ||
|15 | |15 | ||
|7 | |7 | ||
| Line 1,762: | Line 1,762: | ||
|213.084 | |213.084 | ||
|706.542 | |706.542 | ||
|'' | |''208.5365'' | ||
|'' | |''691.4635'' | ||
|19 | |19 | ||
|6 | |6 | ||
| Line 1,834: | Line 1,834: | ||
|216.867 | |216.867 | ||
|708.434 | |708.434 | ||
|'' | |''210.9375'' | ||
|'' | |''689.0625'' | ||
|15 | |15 | ||
|4 | |4 | ||