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'''4L 1s<5/3>''' (sometimes called '''diatonic'''), is a major 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 major 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 176.9 to 221.1 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 5/3 complement (663.7 to 707.5 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, two minor chords. This diatonic also has two dominant 7th chords, making it a warped Neapolitan minor scale.
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, two minor chords. This diatonic also has two dominant 7th chords, making it a warped Neapolitan minor scale.
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!Diatonic
!Diatonic
!Scala Francisci
!Scala Francisci
!19ed'''5/3'''
![[19ed5/3|19ed'''5/3''']]
!14ed'''5/3'''
![[14ed5/3|14ed'''5/3''']]
!23ed'''5/3'''
![[23ed5/3|23ed'''5/3''']]
!9ed'''5/3'''
![[9ed5/3|9ed'''5/3''']]
!22ed'''5/3'''
![[22ed5/3|22ed'''5/3''']]
!13ed'''5/3'''
![[13ed5/3|13ed'''5/3''']]
!17ed'''5/3'''
![[17ed5/3|17ed'''5/3''']]
|-
|-
|Do#, Sol#
|Do#, Sol#
|Α#
|Α#
|1\19, 46.545
|1\19, 46.545
|1\14, 63.1685
|1\14, 63.168
|2\23, 76.901
|2\23, 76.901
| rowspan="2" |1\9, 98.262
| rowspan="2" |1\9, 98.262
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|7\22, 281.387
|7\22, 281.387
|4\13, 272.110
|4\13, 272.110
|5\17, 260.1055
|5\17, 260.106
|-
|-
|Mi, Si
|Mi, Si
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|9\19, 418.906
|9\19, 418.906
| rowspan="2" |7\14, 442.179
| rowspan="2" |7\14, 442.179
|12\23, 461.4045
|12\23, 461.405
|5\9, 491.310
|5\9, 491.310
|13\22, 522.576
|13\22, 522.576
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|13\23, 499.855
|13\23, 499.855
|5\9, 491.310
|5\9, 491.310
|12\22, 482.3775
|12\22, 482.377
|7\13, 476.193
|7\13, 476.193
|9\17, 468.190
|9\17, 468.190
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|9\14, 568.516
|9\14, 568.516
|15\23, 576.756
|15\23, 576.756
| rowspan="2" |6\9, 589.5725
| rowspan="2" |6\9, 589.572
|15\22, 602.972
|15\22, 602.972
|9\13, 612.248
|9\13, 612.248
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|20\23, 769.008
|20\23, 769.008
| rowspan="2" |8\9, 786.096
| rowspan="2" |8\9, 786.096
|20\22, 803.9625
|20\22, 803.962
|12\13, 816.331
|12\13, 816.331
|16\14, 832.338
|16\14, 832.338
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|Dob, Solb
|Dob, Solb
|Ϛb/Ϝb
|Ϛb/Ϝb
|18\19, 837.8135
|18\19, 837.814
|13\14, 821.190
|13\14, 821.190
|21\23, 809.458
|21\23, 809.458
|19\22, 763.764
|19\22, 763.764
|11\13, 748.3035
|11\13, 748.304
|14\17, 728.295
|14\17, 728.295
|-
|-
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|'''Re, La'''
|'''Re, La'''
|'''Ζ'''
|'''Ζ'''
|'''23\19,''' '''1070.5395'''
|'''23\19,''' '''1070.539'''
|'''17\14,''' '''1073.864'''
|'''17\14,''' '''1073.864'''
|'''28\23,''' '''1076.611'''
|'''28\23,''' '''1076.611'''
|'''11\9,''' '''1080.882'''
|'''11\9,''' '''1080.882'''
|'''27\22,''' '''1085.349'''
|'''27\22,''' '''1085.349'''
|'''16\13,''' '''1088.4415'''
|'''16\13,''' '''1088.441'''
|'''21\17,''' '''1092.442'''
|'''21\17,''' '''1092.442'''
|-
|-
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|27\19, 1256.720
|27\19, 1256.720
|20\14, 1263.370
|20\14, 1263.370
|33\23, 1268.8625
|33\23, 1268.863
|13\9, 1277.407
|13\9, 1277.407
|32\22, 1286.340
|32\22, 1286.340
|19\13, 1292.524
|19\13, 1292.524
|25\17, 1300.5275
|25\17, 1300.528
|-
|-
|Mi#, Si#
|Mi#, Si#
|Η#
|Η#
|28\19, 1303.2655
|28\19, 1303.265
| rowspan="2" |21\14, 1326.538
| rowspan="2" |21\14, 1326.538
|35\23, 1345.763
|35\23, 1345.763
|14\9, 1375.669
|14\9, 1375.669
|35\22, 1406.934
|35\22, 1406.934
|21\13, 1428.5795
|21\13, 1428.579
|28\17, 1456.591
|28\17, 1456.591
|-
|-
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|39\23, 1499.565
|39\23, 1499.565
|36\22, 1447.132
|36\22, 1447.132
|21\13, 1428.5795
|21\13, 1428.579
|27\17, 1404.570
|27\17, 1404.570
|-
|-
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|}
|}
==Modes==
==Modes==
The mode names are based on the major satellites of Uranus, in order of size:
The mode names are based on the classical modes:
{| class="wikitable"
{| class="wikitable"
!Mode
!Mode
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|}
|}
==Temperaments==
==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 <code>root-(2g)-(p-1g)</code> (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.
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 <code>root-(2g)-(p-1g)</code> (p = the major sixth, g = the whole tone). The name "Dorianic" comes from the Dorian mode having the major sixth as its characteristic interval.
==='''Dorianic-Meantone'''===
==='''Dorianic-Meantone'''===
[[Subgroup]]: 5/3.4/3.3/2
[[Subgroup]]: 5/3.4/3.3/2
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[[Comma]] list: [[81/80]]
[[Comma]] list: [[81/80]]


[[POL2]] generator: ~9/8 = 193.8419
[[POL2]] generator: ~9/8 = 193.8419¢


[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]
[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]


[[Optimal ET sequence]]: 5ed5/3, 9ed5/3, 14ed5/3
[[Optimal ET sequence]]: [[5ed5/3]], [[9ed5/3]], [[14ed5/3]]
===='''Dorianic-Superpyth'''====
====Scale tree====
[[Subgroup]]: 12/7.4/3.3/2
 
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~9/8 = 216.5781
 
[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]
 
[[Optimal ET sequence]]: 4ed14/9, 13ed14/9, 17ed14/9
==Scale tree==
The spectrum looks like this:
The spectrum looks like this:
{{Scale tree | 4L 1s<5/3>}}
{{Scale tree | 4L 1s<5/3>}}
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/4L_1s_(5/3-equivalent)"