User:Moremajorthanmajor/4L 1s (5/3-equivalent): Difference between revisions
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{{Infobox MOS|Equalized=1|Equave=5/3|Name=|Collapsed=1|Pattern=LLLLs|nLargeSteps=4|nSmallSteps=1}} | {{Infobox MOS|Equalized=1|Equave=5/3|Name=|Collapsed=1|Pattern=LLLLs|nLargeSteps=4|nSmallSteps=1}} | ||
'''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 | 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 major sixth-repeating scale, each tone has a 5/3 major sixth above it. The scale has one augmented chord, two major chords and 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]]. | ||
==Notation== | ==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[6L 4s]. Since there are exactly 10 naturals in double | 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[6L 4s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 43: | Line 43: | ||
100 | 100 | ||
|3\22 | |3\22 | ||
124.1379 | [[Tel:124.1379|124.1379]] | ||
|2\13 | |2\13 | ||
141.1765 | [[Tel:141.1765|141.1765]] | ||
|3\17 | |3\17 | ||
163.{{Overline|63}} | 163.{{Overline|63}} | ||
| Line 52: | Line 52: | ||
|Βb | |Βb | ||
|3\19 | |3\19 | ||
138.4615 | [[Tel:138.4615|138.4615]] | ||
|2\14 | |2\14 | ||
126.3158 | [[Tel:126.3158|126.3158]] | ||
|3\23 | |3\23 | ||
116.129 | 116.129 | ||
| Line 67: | Line 67: | ||
|'''Β''' | |'''Β''' | ||
|'''4\19''' | |'''4\19''' | ||
'''184.6154''' | '''[[Tel:184.6154|184.6154]]''' | ||
|'''3\14''' | |'''3\14''' | ||
'''189.4736''' | '''[[Tel:189.4736|189.4736]]''' | ||
|'''5\23''' | |'''5\23''' | ||
'''193.5484''' | '''[[Tel:193.5484|193.5484]]''' | ||
|'''2\9''' | |'''2\9''' | ||
'''200''' | '''200''' | ||
| Line 77: | Line 77: | ||
'''206.89655''' | '''206.89655''' | ||
|'''3\13''' | |'''3\13''' | ||
'''211.7647''' | '''[[Tel:211.7647|211.7647]]''' | ||
|'''4\17''' | |'''4\17''' | ||
'''218.{{Overline|18}}''' | '''218.{{Overline|18}}''' | ||
| Line 84: | Line 84: | ||
|Β# | |Β# | ||
|5\19 | |5\19 | ||
230.7692 | [[Tel:230.7692|230.7692]] | ||
|4\14 | |4\14 | ||
252.6316 | [[Tel:252.6316|252.6316]] | ||
|7\23 | |7\23 | ||
270.9677 | [[Tel:270.9677|270.9677]] | ||
| rowspan="2" |3\9 | | rowspan="2" |3\9 | ||
300 | 300 | ||
|8\22 | |8\22 | ||
331.0345 | [[Tel:331.0345|331.0345]] | ||
|5\13 | |5\13 | ||
352.9412 | [[Tel:352.9412|352.9412]] | ||
|7\17 | |7\17 | ||
381.{{Overline|81}} | 381.{{Overline|81}} | ||
| Line 101: | Line 101: | ||
|Γb | |Γb | ||
|7\19 | |7\19 | ||
323.0769 | [[Tel:323.0769|323.0769]] | ||
|5\14 | |5\14 | ||
315.7895 | [[Tel:315.7895|315.7895]] | ||
|8\23 | |8\23 | ||
309.6774 | [[Tel:309.6774|309.6774]] | ||
|7\22 | |7\22 | ||
289.6552 | [[Tel:289.6552|289.6552]] | ||
|4\13 | |4\13 | ||
282.3529 | [[Tel:282.3529|282.3529]] | ||
|5\17 | |5\17 | ||
272.{{Overline|72}} | 272.{{Overline|72}} | ||
| Line 116: | Line 116: | ||
|Γ | |Γ | ||
|8\19 | |8\19 | ||
369.2308 | [[Tel:369.2308|369.2308]] | ||
|6\14 | |6\14 | ||
378.9474 | [[Tel:378.9474|378.9474]] | ||
|10\23 | |10\23 | ||
387.0968 | [[Tel:387.0968|387.0968]] | ||
|4\9 | |4\9 | ||
400 | 400 | ||
|10\22 | |10\22 | ||
413.7931 | [[Tel:413.7931|413.7931]] | ||
|6\13 | |6\13 | ||
423.5294 | [[Tel:423.5294|423.5294]] | ||
|8\17 | |8\17 | ||
436.{{Overline|36}} | 436.{{Overline|36}} | ||
| Line 134: | Line 134: | ||
|Γ# | |Γ# | ||
|9\19 | |9\19 | ||
415.3846 | [[Tel:415.3846|415.3846]] | ||
| rowspan="2" |7\14 | | rowspan="2" |7\14 | ||
442.1053 | [[Tel:442.1053|442.1053]] | ||
|12\23 | |12\23 | ||
464.5161 | [[Tel:464.5161|464.5161]] | ||
|5\9 | |5\9 | ||
500 | 500 | ||
| Line 144: | Line 144: | ||
537.931 | 537.931 | ||
|8\13 | |8\13 | ||
564.7059 | [[Tel:564.7059|564.7059]] | ||
|11\17 | |11\17 | ||
600 | 600 | ||
| Line 151: | Line 151: | ||
|Δb | |Δb | ||
|10\19 | |10\19 | ||
461.5385 | [[Tel:461.5385|461.5385]] | ||
|11\23 | |11\23 | ||
425.80645 | 425.80645 | ||
| Line 157: | Line 157: | ||
400 | 400 | ||
|9\22 | |9\22 | ||
372.4138 | [[Tel:372.4138|372.4138]] | ||
|5\13 | |5\13 | ||
352.9412 | [[Tel:352.9412|352.9412]] | ||
|6\17 | |6\17 | ||
327.{{Overline|27}} | 327.{{Overline|27}} | ||
| Line 166: | Line 166: | ||
|Δ | |Δ | ||
|11\19 | |11\19 | ||
507.6923 | [[Tel:507.6923|507.6923]] | ||
|8\14 | |8\14 | ||
505.2632 | [[Tel:505.2632|505.2632]] | ||
|13\23 | |13\23 | ||
503.2259 | [[Tel:503.2259|503.2259]] | ||
|5\9 | |5\9 | ||
500 | 500 | ||
|12\22 | |12\22 | ||
496.5517 | [[Tel:496.5517|496.5517]] | ||
|7\13 | |7\13 | ||
494.11765 | 494.11765 | ||
| Line 187: | Line 187: | ||
568.42105 | 568.42105 | ||
|15\23 | |15\23 | ||
580.6452 | [[Tel:580.6452|580.6452]] | ||
| rowspan="2" |6\9 | | rowspan="2" |6\9 | ||
600 | 600 | ||
|15\22 | |15\22 | ||
620.6897 | [[Tel:620.6897|620.6897]] | ||
|9\13 | |9\13 | ||
635.2941 | [[Tel:635.2941|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 | [[Tel:619.3548|619.3548]] | ||
|14\22 | |14\22 | ||
579.3103 | [[Tel:579.3103|579.3103]] | ||
|8\13 | |8\13 | ||
564.7059 | [[Tel:564.7059|564.7059]] | ||
|10\17 | |10\17 | ||
545.{{Overline|45}} | 545.{{Overline|45}} | ||
| Line 215: | Line 215: | ||
|'''Ε''' | |'''Ε''' | ||
|'''15\19''' | |'''15\19''' | ||
'''692.3077''' | '''[[Tel:692.3077|692.3077]]''' | ||
|'''11\14''' | |'''11\14''' | ||
'''694.7368''' | '''[[Tel:694.7368|694.7368]]''' | ||
|'''18\23''' | |'''18\23''' | ||
'''696.7742''' | '''[[Tel:696.7742|696.7742]]''' | ||
|'''7\8''' | |'''7\8''' | ||
'''700''' | '''700''' | ||
|'''17\22''' | |'''17\22''' | ||
'''703.4483''' | '''[[Tel:703.4483|703.4483]]''' | ||
|'''10\13''' | |'''10\13''' | ||
'''705.88235''' | '''705.88235''' | ||
| Line 232: | Line 232: | ||
|Ε# | |Ε# | ||
|16\19 | |16\19 | ||
738.4615 | [[Tel:738.4615|738.4615]] | ||
|12\14 | |12\14 | ||
757.8947 | [[Tel:757.8947|757.8947]] | ||
|20\23 | |20\23 | ||
774.19355 | 774.19355 | ||
| Line 240: | Line 240: | ||
800 | 800 | ||
|20\22 | |20\22 | ||
827.5862 | [[Tel:827.5862|827.5862]] | ||
|12\13 | |12\13 | ||
847.0588 | [[Tel:847.0588|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 | [[Tel:830.7692|830.7692]] | ||
|13\14 | |13\14 | ||
821.0526 | [[Tel:821.0526|821.0526]] | ||
|21\23 | |21\23 | ||
812.9032 | [[Tel:812.9032|812.9032]] | ||
|19\22 | |19\22 | ||
786.2069 | [[Tel:786.2069|786.2069]] | ||
|11\13 | |11\13 | ||
776.6471 | [[Tel:776.6471|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 | [[Tel:876.9231|876.9231]] | ||
!14\14 | !14\14 | ||
884.2105 | [[Tel:884.2105|884.2105]] | ||
!23\23 | !23\23 | ||
890.3226 | [[Tel:890.3226|890.3226]] | ||
!9\9 | !9\9 | ||
900 | 900 | ||
!22\22 | !22\22 | ||
910.3448 | [[Tel:910.3448|910.3448]] | ||
!13\13 | !13\13 | ||
917.6471 | [[Tel:917.6471|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 | [[Tel:923.0769|923.0769]] | ||
|15\14 | |15\14 | ||
947.3684 | [[Tel:947.3684|947.3684]] | ||
|24\23 | |24\23 | ||
929.0323 | [[Tel:929.0323|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 | [[Tel:988.2353|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'' | ''[[Tel:138.4615|138.4615]]'' | ||
|''3\17'' | |''3\17'' | ||
''158.8235'' | ''[[Tel:158.8235|158.8235]]'' | ||
|- | |- | ||
|Reb, Lab | |Reb, Lab | ||
|Βb | |Βb | ||
|''3\19'' | |''3\19'' | ||
''142.1053'' | ''[[Tel:142.1053|142.1053]]'' | ||
|''2\14'' | |''2\14'' | ||
''128.5714'' | ''[[Tel:128.5714|128.5714]]'' | ||
|''3\23'' | |''3\23'' | ||
''117.3913'' | ''[[Tel:117.3913|117.3913]]'' | ||
|''2\22'' | |''2\22'' | ||
''81.{{Overline|81}}'' | ''81.{{Overline|81}}'' | ||
| Line 581: | Line 581: | ||
|Β | |Β | ||
|'''''4\19''''' | |'''''4\19''''' | ||
'''''189.4737''''' | '''''[[Tel:189.4737|189.4737]]''''' | ||
|'''''3\14''''' | |'''''3\14''''' | ||
'''''192.8571''''' | '''''[[Tel:192.8571|192.8571]]''''' | ||
|'''''5\23''''' | |'''''5\23''''' | ||
'''''195.6522''''' | '''''[[Tel:195.6522|195.6522]]''''' | ||
|'''''2\9''''' | |'''''2\9''''' | ||
'''''200''''' | '''''200''''' | ||
| Line 591: | Line 591: | ||
'''''204.{{Overline|54}}''''' | '''''204.{{Overline|54}}''''' | ||
|'''''3\13''''' | |'''''3\13''''' | ||
'''''207.6923''''' | '''''[[Tel:207.6923|207.6923]]''''' | ||
|'''''4\17''''' | |'''''4\17''''' | ||
'''''211.7647''''' | '''''[[Tel:211.7647|211.7647]]''''' | ||
|- | |- | ||
|Re#, La# | |Re#, La# | ||
|Β# | |Β# | ||
|''5\19'' | |''5\19'' | ||
''236.8421'' | ''[[Tel:236.8421|236.8421]]'' | ||
|''4\14'' | |''4\14'' | ||
''257.1429'' | ''[[Tel:257.1429|257.1429]]'' | ||
|''7\23'' | |''7\23'' | ||
''273.913'' | ''273.913'' | ||
| Line 610: | Line 610: | ||
''346.15385'' | ''346.15385'' | ||
|''7\17'' | |''7\17'' | ||
''370.5882'' | ''[[Tel:370.5882|370.5882]]'' | ||
|- | |- | ||
|Mib, Sib | |Mib, Sib | ||
| Line 617: | Line 617: | ||
''331.57895'' | ''331.57895'' | ||
|''5\14'' | |''5\14'' | ||
''321.4286'' | ''[[Tel:321.4286|321.4286]]'' | ||
|''8\23'' | |''8\23'' | ||
''313.0345'' | ''[[Tel:313.0345|313.0345]]'' | ||
|''7\22'' | |''7\22'' | ||
''286.{{Overline|36}}'' | ''286.{{Overline|36}}'' | ||
|''4\13'' | |''4\13'' | ||
''276.9231'' | ''[[Tel:276.9231|276.9231]]'' | ||
|''5\17'' | |''5\17'' | ||
''264.7059'' | ''[[Tel:264.7059|264.7059]]'' | ||
|- | |- | ||
|Mi, Si | |Mi, Si | ||
|Γ | |Γ | ||
|''8\19'' | |''8\19'' | ||
''378.9474'' | ''[[Tel:378.9474|378.9474]]'' | ||
|''6\14'' | |''6\14'' | ||
''385.7143'' | ''[[Tel:385.7143|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'' | ''[[Tel:415.3846|415.3846]]'' | ||
|''8\17'' | |''8\17'' | ||
''423.5294'' | ''[[Tel:423.5294|423.5294]]'' | ||
|- | |- | ||
|Mi#, Si# | |Mi#, Si# | ||
|Γ# | |Γ# | ||
|''9\19'' | |''9\19'' | ||
''426.3158'' | ''[[Tel:426.3158|426.3158]]'' | ||
| rowspan="2" |''7\14'' | | rowspan="2" |''7\14'' | ||
''450'' | ''450'' | ||
|''12\23'' | |''12\23'' | ||
''469.5652'' | ''[[Tel:469.5652|469.5652]]'' | ||
|''5\9'' | |''5\9'' | ||
''500'' | ''500'' | ||
| Line 660: | Line 660: | ||
''553.84615'' | ''553.84615'' | ||
|''11\17'' | |''11\17'' | ||
''582.3529'' | ''[[Tel:582.3529|582.3529]]'' | ||
|- | |- | ||
|Fab, Dob | |Fab, Dob | ||
|Δb | |Δb | ||
|''10\19'' | |''10\19'' | ||
''473.6842'' | ''[[Tel:473.6842|473.6842]]'' | ||
|''11\23'' | |''11\23'' | ||
''430.7692'' | ''[[Tel:430.7692|430.7692]]'' | ||
|''4\9'' | |''4\9'' | ||
''400'' | ''400'' | ||
| Line 675: | Line 675: | ||
''346.15385'' | ''346.15385'' | ||
|''6\17'' | |''6\17'' | ||
''317.6471'' | ''[[Tel:317.6471|317.6471]]'' | ||
|- | |- | ||
|Fa, Do | |Fa, Do | ||
|Δ | |Δ | ||
|''11\19'' | |''11\19'' | ||
''521.0526'' | ''[[Tel:521.0526|521.0526]]'' | ||
|''8\14'' | |''8\14'' | ||
''514.2857'' | ''[[Tel:514.2857|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'' | ''[[Tel:484.6154|484.6154]]'' | ||
|''9\17'' | |''9\17'' | ||
''476.4706'' | ''[[Tel:476.4706|476.4706]]'' | ||
|- | |- | ||
|Fa#, Do# | |Fa#, Do# | ||
| Line 699: | Line 699: | ||
''568.42105'' | ''568.42105'' | ||
|''9\14'' | |''9\14'' | ||
''578.5714'' | ''[[Tel:578.5714|578.5714]]'' | ||
|''15\23'' | |''15\23'' | ||
''587.9655'' | ''[[Tel:587.9655|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'' | ''[[Tel:623.0769|623.0769]]'' | ||
|''12\17'' | |''12\17'' | ||
''635.2931'' | ''[[Tel:635.2931|635.2931]]'' | ||
|- | |- | ||
|Solb, Reb | |Solb, Reb | ||
|Εb | |Εb | ||
|''14\19'' | |''14\19'' | ||
''663.1579'' | ''[[Tel:663.1579|663.1579]]'' | ||
|''10\14'' | |''10\14'' | ||
''642.8571'' | ''[[Tel:642.8571|642.8571]]'' | ||
|''16\23'' | |''16\23'' | ||
''626.087'' | ''626.087'' | ||
| Line 724: | Line 724: | ||
''553.84615'' | ''553.84615'' | ||
|''10\17'' | |''10\17'' | ||
''529.4118'' | ''[[Tel:529.4118|529.4118]]'' | ||
|- | |- | ||
|'''Sol, Re''' | |'''Sol, Re''' | ||
|'''Ε''' | |'''Ε''' | ||
|'''''15\19''''' | |'''''15\19''''' | ||
'''''710.5263''''' | '''''[[Tel:710.5263|710.5263]]''''' | ||
|'''''11\14''''' | |'''''11\14''''' | ||
'''''707.1429''''' | '''''[[Tel:707.1429|707.1429]]''''' | ||
|'''''18\23''''' | |'''''18\23''''' | ||
'''''704.3478''''' | '''''[[Tel:704.3478|704.3478]]''''' | ||
|'''''7\8''''' | |'''''7\8''''' | ||
'''''700''''' | '''''700''''' | ||
| Line 739: | Line 739: | ||
'''''695.{{Overline|45}}''''' | '''''695.{{Overline|45}}''''' | ||
|'''''10\13''''' | |'''''10\13''''' | ||
'''''692.3077''''' | '''''[[Tel:692.3077|692.3077]]''''' | ||
|'''''13\17''''' | |'''''13\17''''' | ||
'''''688.2353''''' | '''''[[Tel:688.2353|688.2353]]''''' | ||
|- | |- | ||
|Sol#, Re# | |Sol#, Re# | ||
|Ε# | |Ε# | ||
|''16\19'' | |''16\19'' | ||
''757.8947'' | ''[[Tel:757.8947|757.8947]]'' | ||
|''12\14'' | |''12\14'' | ||
''771.4286'' | ''[[Tel:771.4286|771.4286]]'' | ||
|''20\23'' | |''20\23'' | ||
''782.6087'' | ''[[Tel:782.6087|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'' | ''[[Tel:830.7692|830.7692]]'' | ||
|''16\14'' | |''16\14'' | ||
''847.0588'' | ''[[Tel:847.0588|847.0588]]'' | ||
|- | |- | ||
|Dob, Solb | |Dob, Solb | ||
|Ϛb/Ϝb | |Ϛb/Ϝb | ||
|''18\19'' | |''18\19'' | ||
''852.6316'' | ''[[Tel:852.6316|852.6316]]'' | ||
|''13\14'' | |''13\14'' | ||
''835.7143'' | ''[[Tel:835.7143|835.7143]]'' | ||
|''21\23'' | |''21\23'' | ||
''821.7391'' | ''[[Tel:821.7391|821.7391]]'' | ||
|''19\22'' | |''19\22'' | ||
''777.{{Overline|27}}'' | ''777.{{Overline|27}}'' | ||
|''11\13'' | |''11\13'' | ||
''761.5385'' | ''[[Tel:761.5385|761.5385]]'' | ||
|''14\17'' | |''14\17'' | ||
''741.1765'' | ''[[Tel:741.1765|741.1765]]'' | ||
|- | |- | ||
!Do, Sol | !Do, Sol | ||
| Line 782: | Line 782: | ||
|Ϛ#/Ϝ# | |Ϛ#/Ϝ# | ||
|''20\19'' | |''20\19'' | ||
''947.3684'' | ''[[Tel:947.3684|947.3684]]'' | ||
|''15\14'' | |''15\14'' | ||
''964.2857'' | ''[[Tel:964.2857|964.2857]]'' | ||
|''25\23'' | |''25\23'' | ||
''978.2609'' | ''[[Tel:978.2609|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'' | ''[[Tel:969.2308|969.2308]]'' | ||
|''18\17'' | |''18\17'' | ||
''952.9412'' | ''[[Tel:952.9412|952.9412]]'' | ||
|- | |- | ||
|'''Re, La''' | |'''Re, La''' | ||
| Line 1,209: | Line 1,209: | ||
[[Comma]] list: [[81/80]] | [[Comma]] list: [[81/80]] | ||
[[POL2]] generator: ~9/8 = 193.8419 | [[POL2]] generator: ~9/8 = [[Tel:193.8419|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 = 216.5781 | [[POL2]] generator: ~9/8 = [[Tel:216.5781|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'' | |''[[Tel:201.1765|201.1765]]'' | ||
|''698.8235'' | |''[[Tel:698.8235|698.8235]]'' | ||
|19 | |19 | ||
|9 | |9 | ||
| Line 1,606: | Line 1,606: | ||
|202.247 | |202.247 | ||
|701.123 | |701.123 | ||
|''201.4925'' | |''[[Tel:201.4925|201.4925]]'' | ||
|''698.5075'' | |''[[Tel:698.5075|698.5075]]'' | ||
|15 | |15 | ||
|7 | |7 | ||
| Line 1,762: | Line 1,762: | ||
|213.084 | |213.084 | ||
|706.542 | |706.542 | ||
|''208.5365'' | |''[[Tel:208.5365|208.5365]]'' | ||
|''691.4635'' | |''[[Tel:691.4635|691.4635]]'' | ||
|19 | |19 | ||
|6 | |6 | ||
| Line 1,834: | Line 1,834: | ||
|216.867 | |216.867 | ||
|708.434 | |708.434 | ||
|''210.9375'' | |''[[Tel:210.9375|210.9375]]'' | ||
|''689.0625'' | |''[[Tel:689.0625|689.0625]]'' | ||
|15 | |15 | ||
|4 | |4 | ||
Revision as of 23:10, 19 August 2022
Lua error in Module:MOS at line 28: attempt to index local 'equave' (a nil value).
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).
Because this diatonic is a major sixth-repeating scale, each tone has a 5/3 major sixth above it. The scale has one augmented chord, two major chords and 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.
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 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[6L 4s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
| Notation | Supersoft | Soft | Semisoft | Basic | Semihard | Hard | Superhard | |
|---|---|---|---|---|---|---|---|---|
| Diatonic | Scala Francisci | 19eds | 14eds | 23eds | 9eds | 22eds | 13eds | 17eds |
| Do#, Sol# | Α# | 1\19
46.15385 |
1\14
63.1579 |
2\23
77.41935 |
1\9
100 |
3\22
[[1]] |
2\13
[[2]] |
3\17
163.63 |
| Reb, Lab | Βb | 3\19
[[3]] |
2\14
[[4]] |
3\23
116.129 |
2\22
82.7586 |
1\13
70.5882 |
1\17
54.54 | |
| Re, La | Β | 4\19
[[5]] |
3\14
[[6]] |
5\23
[[7]] |
2\9
200 |
5\22
206.89655 |
3\13
[[8]] |
4\17
218.18 |
| Re#, La# | Β# | 5\19
[[9]] |
4\14
[[10]] |
7\23
[[11]] |
3\9
300 |
8\22
[[12]] |
5\13
[[13]] |
7\17
381.81 |
| Mib, Sib | Γb | 7\19
[[14]] |
5\14
[[15]] |
8\23
[[16]] |
7\22
[[17]] |
4\13
[[18]] |
5\17
272.72 | |
| Mi, Si | Γ | 8\19
[[19]] |
6\14
[[20]] |
10\23
[[21]] |
4\9
400 |
10\22
[[22]] |
6\13
[[23]] |
8\17
436.36 |
| Mi#, Si# | Γ# | 9\19
[[24]] |
7\14
[[25]] |
12\23
[[26]] |
5\9
500 |
13\22
537.931 |
8\13
[[27]] |
11\17
600 |
| Fab, Dob | Δb | 10\19
[[28]] |
11\23
425.80645 |
4\9
400 |
9\22
[[29]] |
5\13
[[30]] |
6\17
327.27 | |
| Fa, Do | Δ | 11\19
[[31]] |
8\14
[[32]] |
13\23
[[33]] |
5\9
500 |
12\22
[[34]] |
7\13
494.11765 |
9\17
490.90 |
| Fa#, Do# | Δ# | 12\19
553.84615 |
9\14
568.42105 |
15\23
[[35]] |
6\9
600 |
15\22
[[36]] |
9\13
[[37]] |
12\17
654.54 |
| Solb, Reb | Εb | 14\19
646.15385 |
10\14
631.57895 |
16\23
[[38]] |
14\22
[[39]] |
8\13
[[40]] |
10\17
545.45 | |
| Sol, Re | Ε | 15\19
[[41]] |
11\14
[[42]] |
18\23
[[43]] |
7\8
700 |
17\22
[[44]] |
10\13
705.88235 |
13\17
709.09 |
| Sol#, Re# | Ε# | 16\19
[[45]] |
12\14
[[46]] |
20\23
774.19355 |
8\8
800 |
20\22
[[47]] |
12\13
[[48]] |
16\14
872.72 |
| Dob, Solb | Ϛb/Ϝb | 18\19
[[49]] |
13\14
[[50]] |
21\23
[[51]] |
19\22
[[52]] |
11\13
[[53]] |
14\17
763.63 | |
| Do, Sol | Ϛ/Ϝ | 19\19
[[54]] |
14\14
[[55]] |
23\23
[[56]] |
9\9
900 |
22\22
[[57]] |
13\13
[[58]] |
17\17
927.27 |
| Do#, Sol# | Ϛ#/Ϝ# | 20\19
[[59]] |
15\14
[[60]] |
24\23
[[61]] |
10\9
1000 |
25\22
1034.4829 |
15\13
1052.8235 |
20\17
1090.90 |
| Reb, Lab | Ζb | 22\19
1015.3847 |
16\14
1010.5263 |
26\23
1006.4516 |
24\22
993.10345 |
14\13
[[62]] |
18\17
981.81 | |
| Re, La | Ζ | 23\19
1061.5385 |
17\14
1071.6842 |
28\23
1083.871 |
11\9
1100 |
27\22
1117.2414 |
16\13
1129.4118 |
21\17
1145.45 |
| Re#, La# | Ζ# | 24\19
1107.6923 |
18\14
1136.8421 |
30\23
1161.7097 |
12\9
1200 |
30\22
1241.3793 |
18\13
1270.5882 |
24\14
1309.09 |
| Mib, Sib | Ηb | 26\19
1200 |
19\14
1200 |
31\23
1200 |
29\22
1200 |
17\13
1200 |
22\17
1200 | |
| Mi, Si | Η | 27\19
1246.15385 |
20\14
1263.1579 |
33\23
1277.41935 |
13\9
1300 |
32\22
1324.1379 |
19\13
1341.1765 |
25\17
1363.63 |
| Mi#, Si# | Η# | 28\19
1292.3077 |
21\14
1326.3158 |
35\23
1354.8387 |
14\9
1400 |
35\22
1448.2759 |
21\13
1482.3529 |
28\17
1527.27 |
| Fab, Dob | Θb | 29\19
1338.4615 |
34\23
1316.129 |
13\9
1300 |
31\22
1282.7586 |
18\13
1270.5882 |
23\17
1254.54 | |
| Fa, Do | Θ | 30\19
1384.6154 |
22\14
1389.4737 |
36\23
1393.5484 |
14\9
1400 |
34\22
1406.89655 |
20\13
1411.7647 |
26\17
1418.18 |
| Fa#, Do# | Θ# | 31\19
1430.7692 |
23\14
1452.6316 |
38\23
1470.9677 |
15\9
1500 |
37\22
1531.0345 |
22\13
1552.9412 |
29\17
1581.81 |
| Solb, Reb | Ιb | 33\19
1523.0769 |
24\14
1515.7895 |
39\23
1509.6774 |
36\22
1489.6551 |
21\13
1482.3529 |
27\17
1472.72 | |
| Sol, Re | Ι | 34\19
1569.2308 |
25\14
1578.9474 |
41\23
1587.0968 |
16\9
1600 |
39\22
1613.7931 |
23\13
1623.5294 |
30\17
1636.36 |
| Sol#, Re# | Ι# | 35\19
1615.3846 |
26\14
1642.1053 |
43\23
1664.5161 |
17\9
1700 |
42\22
1737.931 |
25\13
1764.7059 |
33\17
1800 |
| Dob, Solb | Αb | 37\19
1707.6923 |
27\14
1705.2632 |
44\23
1703.2258 |
41\22
1696.5517 |
20\13
1694.11765 |
31\17
1490.90 | |
| Do, Sol | Α | 38\19
1753.84615 |
28\14
1768.42105 |
46\23
1780.6452 |
18\9
1800 |
44\22
1820.6897 |
26\13
1835.2941 |
34\17
1854.54 |
| Notation | Supersoft | Soft | Semisoft | Basic | Semihard | Hard | Superhard | |
|---|---|---|---|---|---|---|---|---|
| Diatonic | Scala Francisci | 19eds | 14eds | 23eds | 9eds | 22eds | 13eds | 17eds |
| Do#, Sol# | Α# | 1\19
47.3684 |
1\14
64.2857 |
2\23
78.2609 |
1\9
100 |
3\22
122.72 |
2\13
[[63]] |
3\17
[[64]] |
| Reb, Lab | Βb | 3\19
[[65]] |
2\14
[[66]] |
3\23
[[67]] |
2\22
81.81 |
1\13
69.2308 |
1\17
52.9412 | |
| Re, La | Β | 4\19
[[68]] |
3\14
[[69]] |
5\23
[[70]] |
2\9
200 |
5\22
204.54 |
3\13
[[71]] |
4\17
[[72]] |
| Re#, La# | Β# | 5\19
[[73]] |
4\14
[[74]] |
7\23
273.913 |
3\9
300 |
8\22
327.27 |
5\13
346.15385 |
7\17
[[75]] |
| Mib, Sib | Γb | 7\19
331.57895 |
5\14
[[76]] |
8\23
[[77]] |
7\22
286.36 |
4\13
[[78]] |
5\17
[[79]] | |
| Mi, Si | Γ | 8\19
[[80]] |
6\14
[[81]] |
10\23
391.304 |
4\9
400 |
10\22
409.09 |
6\13
[[82]] |
8\17
[[83]] |
| Mi#, Si# | Γ# | 9\19
[[84]] |
7\14
450 |
12\23
[[85]] |
5\9
500 |
13\22
531.81 |
8\13
553.84615 |
11\17
[[86]] |
| Fab, Dob | Δb | 10\19
[[87]] |
11\23
[[88]] |
4\9
400 |
9\22
368.18 |
5\13
346.15385 |
6\17
[[89]] | |
| Fa, Do | Δ | 11\19
[[90]] |
8\14
[[91]] |
13\23
508.696 |
5\9
500 |
12\22
490.90 |
7\13
[[92]] |
9\17
[[93]] |
| Fa#, Do# | Δ# | 12\19
568.42105 |
9\14
[[94]] |
15\23
[[95]] |
6\9
600 |
15\22
613.63 |
9\13
[[96]] |
12\17
[[97]] |
| Solb, Reb | Εb | 14\19
[[98]] |
10\14
[[99]] |
16\23
626.087 |
14\22
572.72 |
8\13
553.84615 |
10\17
[[100]] | |
| Sol, Re | Ε | 15\19
[[101]] |
11\14
[[102]] |
18\23
[[103]] |
7\8
700 |
17\22
695.45 |
10\13
[[104]] |
13\17
[[105]] |
| Sol#, Re# | Ε# | 16\19
[[106]] |
12\14
[[107]] |
20\23
[[108]] |
8\8
800 |
20\22
818.18 |
12\13
[[109]] |
16\14
[[110]] |
| Dob, Solb | Ϛb/Ϝb | 18\19
[[111]] |
13\14
[[112]] |
21\23
[[113]] |
19\22
777.27 |
11\13
[[114]] |
14\17
[[115]] | |
| Do, Sol | Ϛ/Ϝ | 900 | ||||||
| Do#, Sol# | Ϛ#/Ϝ# | 20\19
[[116]] |
15\14
[[117]] |
25\23
[[118]] |
10\9
1000 |
25\22
1022.72 |
15\13
1038.4615 |
20\17
1058.8235 |
| Reb, Lab | Ζb | 22\19
1042.1053 |
16\14
1028.5714 |
26\23
1017.3913 |
24\22
981.81 |
14\13
[[119]] |
18\17
[[120]] | |
| Re, La | Ζ | 23\19
1089.4737 |
17\14
1092.8571 |
28\23
1095.6522 |
11\9
1100 |
27\22
1104.54 |
16\13
1107.6923 |
21\17
1111.7647 |
| Re#, La# | Ζ# | 24\19
1136.8421 |
18\14
1157.1429 |
30\23
1173.913 |
12\9
1200 |
30\22
1227.27 |
18\13
1246.15385 |
24\14
1270.5882 |
| Mib, Sib | Ηb | 26\19
1231.57895 |
19\14
1221.4286 |
31\23
1213.0345 |
29\22
1186.36 |
17\13
1176.9231 |
22\17
1164.7059 | |
| Mi, Si | Η | 27\19
1278.9474 |
20\14
1285.7143 |
33\23
1291.304 |
13\9
1300 |
32\22
1309.09 |
19\13
1315.3846 |
25\17
1323.5294 |
| Mi#, Si# | Η# | 28\19
1326.3158 |
21\14
1350 |
35\23
1369.5652 |
14\9
1400 |
35\22
1431.81 |
21\13
1453.15385 |
28\17
1482.3529 |
| Fab, Dob | Θb | 29\19
1373.6842 |
34\23
1330.7692 |
13\9
1300 |
31\22
1368.18 |
18\13
1346.84615 |
23\17
1317.6471 | |
| Fa, Do | Θ | 30\19
1421.0526 |
22\14
1414.2857 |
36\23
1408.696 |
14\9
1400 |
34\22
1390.90 |
20\13
1384.6154 |
26\17
1376.4706 |
| Fa#, Do# | Θ# | 31\19
1468.42105 |
23\14
1478.7143 |
38\23
1487.9655 |
15\9
1500 |
37\22
1513.63 |
22\13
1523.0769 |
29\17
1581.81 |
| Solb, Reb | Ιb | 33\19
1563.1579 |
24\14
1542.8571 |
39\23
1526.087 |
36\22
1472.72 |
21\13
1453.15385 |
27\17
1429.4118 | |
| Sol, Re | Ι | 34\19
1610.5263 |
25\14
1607.1429 |
41\23
1604.3478 |
16\9
1600 |
39\22
1595.45 |
23\13
1592.3077 |
30\17
1588.2353 |
| Sol#, Re# | Ι# | 35\19
1657.8947 |
26\14
1671.4286 |
43\23
1682.6087 |
17\9
1700 |
42\22
1718.18 |
25\13
1730.7692 |
33\17
1747.0588 |
| Dob, Solb | Αb | 37\19
1752.6316 |
27\14
1735.7143 |
44\23
1721.7391 |
41\22
1677.27 |
20\13
1661.5385 |
31\17
1641.1761 | |
| Do, Sol | Α | 1800 | ||||||
Intervals
| Generators | Sextave notation | Interval category name | Generators | Notation of sixth inverse | Interval category name |
|---|---|---|---|---|---|
| The 5-note MOS has the following intervals (from some root): | |||||
| 0 | Do, Sol | sextave (major sixth) | 0 | Do, Sol | perfect unison |
| 1 | Sol, Re | perfect fifth | -1 | Re, La | major second |
| 2 | Fa, Do | perfect fourth | -2 | Mi, Si | major third |
| 3 | Mib, Sib | minor third | -3 | Fa#, Do# | augmented fourth |
| 4 | Reb, Lab | minor second | -4 | Sol#, Re# | augmented fifth |
| The chromatic 9-note MOS also has the following intervals (from some root): | |||||
| 5 | Dob, Solb | diminished sextave | -5 | Do#, Sol# | augmented unison (chroma) |
| 6 | Solb, Reb | diminished fifth | -6 | Re#, La# | augmented second |
| 7 | Fab, Dob | diminished fourth | -7 | Mi#, Si# | augmented third |
| 8 | Mibb, Sibb | diminished third | -8 | Fax, Dox | doubly augmented fourth |
Genchain
The generator chain for this scale is as follows:
| Mibb
Sibb |
Fab
Dob |
Solb
Reb |
Dob
Solb |
Reb
Lab |
Mib
Sib |
Fa
Do |
Sol
Re |
Do
Sol |
Re
La |
Mi
Si |
Fa#
Do# |
Sol#
Re# |
Do#
Sol# |
Re#
La# |
Mi#
Si# |
Fax
Dox |
| d3 | d4 | d5 | d6 | m2 | m3 | P4 | P5 | P1 | M2 | M3 | A4 | A5 | A1 | A2 | A3 | AA4 |
Modes
The mode names are based on the major satellites of Uranus, in order of size:
| Mode | Scale | UDP | Interval type | |||
|---|---|---|---|---|---|---|
| name | pattern | notation | 2nd | 3rd | 4th | 5th |
| Lydian Augmented | LLLLs | 4|0 | M | M | A | A |
| Lydian | LLLsL | 3|1 | M | M | A | P |
| Major | LLsLL | 2|2 | M | M | P | P |
| Dorian | LsLLL | 1|3 | M | m | P | P |
| Neapolitan | sLLLL | 0|4 | m | m | P | P |
Temperaments
The most basic rank-2 temperament interpretation of this diatonic is Dorianic, which has pental 4:5:6 or septimal 14:18:21 chords spelled root-(2g)-(p-1g) (p = the major sixth, g = the whole tone). The name "Dorianic" comes from the Dorian major mode having the minor sixth as its characteristic interval.
Dorianic-Meantone
Subgroup: 5/3.4/3.3/2
POL2 generator: ~9/8 = [[121]]
Mapping: [⟨1 1 1], ⟨0 -2 -1]]
Dorianic-Superpyth
Subgroup: 12/7.4/3.3/2
POL2 generator: ~9/8 = [[122]]
Mapping: [⟨1 1 1], ⟨0 -2 -1]]
Scale tree
The spectrum looks like this:
| Generator
(bright) |
Normalised | ed3\4 | L | s | L/s | Comments | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| Chroma-positive | Chroma-negative | Chroma-positive | Chroma-negative | |||||||
| 1\5 | 171.429 | 685.714 | 180 | 720 | 1 | 1 | 1.000 | Equalised | ||
| 6\29 | 180 | 690 | 186.207 | 713.793 | 6 | 5 | 1.200 | |||
| 5\24 | 181.81 | 490.90 | 187.5 | 712.5 | 5 | 4 | 1.250 | |||
| 14\67 | 182.609 | 691.304 | 188.06 | 711.94 | 14 | 11 | 1.273 | |||
| 9\43 | 183.051 | 691.525 | 188.372 | 711.628 | 9 | 7 | 1.286 | |||
| 4\19 | 184.615 | 692.308 | 189.474 | 710.526 | 4 | 3 | 1.333 | |||
| 11\52 | 185.915 | 692.958 | 190.385 | 709.615 | 11 | 8 | 1.375 | |||
| 7\33 | 186.6 | 693.3 | 190.90 | 709.09 | 7 | 5 | 1.400 | |||
| 10\47 | 187.5 | 693.75 | 191.498 | 708.519 | 10 | 7 | 1.429 | |||
| 3\14 | 189.474 | 694.737 | 192.857 | 707.143 | 3 | 2 | 1.500 | Dorianic-Meantone starts here | ||
| 14\65 | 190.90 | 695.45 | 193.846 | 706.154 | 14 | 9 | 1.556 | |||
| 11\51 | 191.304 | 695.652 | 194.118 | 705.882 | 11 | 7 | 1.571 | |||
| 8\37 | 192 | 696 | 194.594 | 705.495 | 8 | 5 | 1.600 | |||
| 13\60 | 192.692 | 696.296 | 195 | 705 | 13 | 8 | 1.625 | |||
| 5\23 | 193.548 | 696.774 | 195.652 | 704.348 | 5 | 3 | 1.667 | |||
| 12\55 | 194.594 | 697.297 | 196.36 | 703.63 | 12 | 7 | 1.714 | |||
| 7\32 | 195.349 | 697.674 | 196.875 | 703.125 | 7 | 4 | 1.750 | |||
| 9\41 | 196.36 | 698.18 | 197.561 | 702.439 | 9 | 5 | 1.800 | |||
| 11\50 | 197.015 | 698.507 | 198 | 702 | 11 | 6 | 1.833 | |||
| 13\59 | 197.468 | 698.734 | 198.305 | 701.695 | 13 | 7 | 1.857 | |||
| 15\68 | 197.802 | 698.901 | 198.529 | 701.471 | 15 | 8 | 1.875 | |||
| 17\77 | 198.058 | 699.029 | 198.701 | 701.299 | 17 | 9 | 1.889 | |||
| 19\86 | 198.261 | 699.13 | 198.837 | 701.163 | 19 | 10 | 1.900 | |||
| 21\95 | 198.425 | 699.213 | 198.947 | 701.053 | 21 | 11 | 1.909 | |||
| 23\104 | 198.561 | 699.281 | 199.039 | 700.961 | 23 | 12 | 1.917 | |||
| 2\9 | 200 | 700 | 200 | 700 | 2 | 1 | 2.000 | Dorianic-Meantone ends, Dorianic-Pythagorean begins | ||
| 23\103 | 201.46 | 700.73 | 200.971 | 699.029 | 23 | 11 | 2.091 | |||
| 21\94 | 201.6 | 700.8 | 201.064 | 698.936 | 21 | 10 | 2.100 | |||
| 19\85 | 201.77 | 700.885 | [[123]] | [[124]] | 19 | 9 | 2.111 | |||
| 17\76 | 201.98 | 700.99 | 201.316 | 698.684 | 17 | 8 | 2.125 | |||
| 15\67 | 202.247 | 701.123 | [[125]] | [[126]] | 15 | 7 | 2.143 | |||
| 13\58 | 202.597 | 701.299 | 201.724 | 698.276 | 13 | 6 | 2.167 | |||
| 11\49 | 203.076 | 701.538 | 202.041 | 697.959 | 11 | 5 | 2.200 | |||
| 9\40 | 203.774 | 701.887 | 202.5 | 697.5 | 9 | 4 | 2.250 | |||
| 7\31 | 204.838 | 702.439 | 203.226 | 696.774 | 7 | 3 | 2.333 | |||
| 12\53 | 205.714 | 702.858 | 203.774 | 696.226 | 12 | 5 | 2.400 | |||
| 5\22 | 206.897 | 703.448 | 204.54 | 695.45 | 5 | 2 | 2.500 | |||
| 18\79 | 207.692 | 703.847 | 205.063 | 694.937 | 18 | 7 | 2.571 | |||
| 8\35 | 208.696 | 704.348 | 205.714 | 694.286 | 8 | 3 | 2.667 | |||
| 11\48 | 209.524 | 704.762 | 206.25 | 693.75 | 11 | 4 | 2.750 | |||
| 14\61 | 210 | 705 | 206.557 | 693.443 | 14 | 5 | 2.800 | |||
| 3\13 | 211.765 | 705.882 | 207.692 | 692.308 | 3 | 1 | 3.000 | Dorianic-Pythagorean ends, Dorianic-Superpyth begins | ||
| 22\95 | 212.903 | 706.452 | 208.421 | 691.579 | 22 | 7 | 3.143 | |||
| 19\82 | 213.084 | 706.542 | [[127]] | [[128]] | 19 | 6 | 3.167 | |||
| 16\69 | 213.3 | 706.6 | 208.696 | 691.304 | 16 | 5 | 3.200 | |||
| 13\56 | 213.699 | 706.849 | 208.929 | 691.071 | 13 | 4 | 3.250 | |||
| 10\43 | 214.286 | 707.143 | 209.322 | 690.678 | 10 | 3 | 3.333 | |||
| 7\30 | 215.385 | 707.692 | 210 | 690 | 7 | 2 | 3.500 | |||
| 11\47 | 216.393 | 708.192 | 210.638 | 689.362 | 11 | 3 | 3.667 | |||
| 15\64 | 216.867 | 708.434 | [[129]] | [[130]] | 15 | 4 | 3.750 | |||
| 19\81 | 217.143 | 708.571 | 211.1 | 688.8 | 19 | 5 | 3.800 | |||
| 4\17 | 218.18 | 709.09 | 211.765 | 688.235 | 4 | 1 | 4.000 | |||
| 21\89 | 219.13 | 709.565 | 212.36 | 687.64 | 21 | 5 | R.200 | |||
| 17\72 | 219.355 | 709.677 | 212.5 | 687.5 | 17 | 4 | 4.250 | |||
| 13\55 | 219.718 | 709.859 | 212.72 | 687.27 | 13 | 3 | 4.333 | |||
| 9\38 | 220.408 | 710.204 | 213.158 | 686.842 | 9 | 2 | 4.500 | |||
| 14\59 | 221.053 | 710.526 | 213.559 | 686.441 | 14 | 3 | 4.667 | |||
| 5\21 | 222.2 | 711.1 | 214.286 | 685.714 | 5 | 1 | 5.000 | Dorianic-Superpyth ends | ||
| 16\67 | 223.256 | 711.628 | 214.925 | 685.075 | 16 | 3 | 5.333 | |||
| 11\46 | 223.729 | 711.864 | 215.217 | 684.783 | 11 | 2 | 5.500 | |||
| 17\71 | 224.176 | 712.088 | 215.492 | 215.508 | 17 | 3 | 5.667 | |||
| 6\25 | 225 | 712.5 | 216 | 684 | 6 | 1 | 6.000 | |||
| 1\4 | 240 | 720 | 225 | 675 | 1 | 0 | → inf | Paucitonic | ||