User:Moremajorthanmajor/4L 1s (5/3-equivalent): Difference between revisions
No edit summary |
|||
| Line 1: | Line 1: | ||
{{Infobox MOS| | {{Infobox MOS|Tuning=4L 1s<5/3>}} | ||
'''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]]). | ||
| Line 9: | Line 9: | ||
[[Basic]] diatonic is in [[9ed5/3]], which is a very good major sixth-based equal tuning similar to [[12edo]]. | [[Basic]] diatonic is in [[9ed5/3]], which is a very good major 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 (major 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. | There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (major 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. | ||
| Line 26: | Line 25: | ||
!Diatonic | !Diatonic | ||
!Scala Francisci | !Scala Francisci | ||
! | !19ed'''5/3''' | ||
! | !14ed'''5/3''' | ||
! | !23ed'''5/3''' | ||
! | !9ed'''5/3''' | ||
! | !22ed'''5/3''' | ||
! | !13ed'''5/3''' | ||
! | !17ed'''5/3''' | ||
|- | |- | ||
|Do#, Sol# | |Do#, Sol# | ||
|Α# | |Α# | ||
|1\19 | |1\19, 46.545 | ||
46. | |1\14, 63.1685 | ||
|1\14 | |2\23, 76.901 | ||
63. | | rowspan="2" |1\9, 98.262 | ||
|2\23 | |3\22, 120.594 | ||
|2\13, 136.055 | |||
| rowspan="2" |1\9 | |3\17, 156.063 | ||
|3\22 | |||
|2\13 | |||
|3\17 | |||
|- | |- | ||
|Reb, Lab | |Reb, Lab | ||
|Βb | |Βb | ||
|3\19 | |3\19, 139.636 | ||
|2\14, 126.337 | |||
|2\14 | |3\23, 115.351 | ||
126. | |2\22, 80.396 | ||
|3\23 | |1\13, 68.028 | ||
|1\17, 52.021 | |||
|2\22 | |||
|1\13 | |||
|1\17 | |||
|- | |- | ||
|'''Re, La''' | |'''Re, La''' | ||
|'''Β''' | |'''Β''' | ||
|'''4\19''' | |'''4\19,''' '''186.181''' | ||
''' | |'''3\14,''' '''189.505''' | ||
|'''3\14''' | |'''5\23,''' '''192.252''' | ||
'''189. | |'''2\9, 196.524''' | ||
|'''5\23''' | |'''5\22,''' '''200.991''' | ||
''' | |'''3\13,''' '''204.083''' | ||
|'''2\9 | |'''4\17, 208.084''' | ||
|'''5\22''' | |||
''' | |||
|'''3\13''' | |||
''' | |||
|'''4\17 | |||
|- | |- | ||
|Re#, La# | |Re#, La# | ||
|Β# | |Β# | ||
|5\19 | |5\19, 232.726 | ||
|4\14, 252.673 | |||
|4\14 | |7\23, 269.153 | ||
252. | | rowspan="2" |3\9, 294.786 | ||
|7\23 | |8\22, 321.585 | ||
|5\13, 340.138 | |||
| rowspan="2" |3\9 | |7\17, 364.148 | ||
|8\22 | |||
|5\13 | |||
|7\17 | |||
|- | |- | ||
|Mib, Sib | |Mib, Sib | ||
|Γb | |Γb | ||
|7\19 | |7\19, 325.816 | ||
|5\14, 315.842 | |||
|5\14 | |8\23, 307.603 | ||
315. | |7\22, 281.387 | ||
|8\23 | |4\13, 272.110 | ||
|5\17, 260.1055 | |||
|7\22 | |||
|4\13 | |||
|5\17 | |||
|- | |- | ||
|Mi, Si | |Mi, Si | ||
|Γ | |Γ | ||
|8\19 | |8\19, 372.362 | ||
|6\14, 379.011 | |||
|6\14 | |10\23, 384.504 | ||
|4\9, 393.048 | |||
|10\23 | |10\22, 401.981 | ||
|6\13, 408.166 | |||
|4\9 | |8\17, 416.169 | ||
|10\22 | |||
|6\13 | |||
|8\17 | |||
|- | |- | ||
|Mi#, Si# | |Mi#, Si# | ||
|Γ# | |Γ# | ||
|9\19 | |9\19, 418.906 | ||
| rowspan="2" |7\14, 442.179 | |||
| rowspan="2" |7\14 | |12\23, 461.4045 | ||
442. | |5\9, 491.310 | ||
|12\23 | |13\22, 522.576 | ||
|8\13, 544.221 | |||
|5\9 | |11\17, 572.232 | ||
|13\22 | |||
|8\13 | |||
|11\17 | |||
|- | |- | ||
|Fab, Dob | |Fab, Dob | ||
|Δb | |Δb | ||
|10\19 | |10\19, 465.452 | ||
|11\23, 422.954 | |||
|11\23 | |4\9, 393.048 | ||
|9\22, 361.783 | |||
|4\9 | |5\13, 340.138 | ||
|6\17, 312.127 | |||
|9\22 | |||
|5\13 | |||
|6\17 | |||
|- | |- | ||
|Fa, Do | |Fa, Do | ||
|Δ | |Δ | ||
|11\19 | |11\19, 511.997 | ||
|8\14, 505.348 | |||
|8\14 | |13\23, 499.855 | ||
505. | |5\9, 491.310 | ||
|13\23 | |12\22, 482.3775 | ||
|7\13, 476.193 | |||
|5\9 | |9\17, 468.190 | ||
|12\22 | |||
|7\13 | |||
|9\17 | |||
|- | |- | ||
|Fa#, Do# | |Fa#, Do# | ||
|Δ# | |Δ# | ||
|12\19 | |12\19, 558.542 | ||
|9\14, 568.516 | |||
|9\14 | |15\23, 576.756 | ||
568. | | rowspan="2" |6\9, 589.5725 | ||
|15\23 | |15\22, 602.972 | ||
|9\13, 612.248 | |||
| rowspan="2" |6\9 | |12\17, 624.253 | ||
|15\22 | |||
|9\13 | |||
|12\17 | |||
|- | |- | ||
|Solb, Reb | |Solb, Reb | ||
|Εb | |Εb | ||
|14\19 | |14\19, 651.632 | ||
|10\14, 631.685 | |||
|10\14 | |16\23, 615.206 | ||
631. | |14\22, 562.773 | ||
|16\23 | |8\13, 544.221 | ||
|10\17, 520.211 | |||
|14\22 | |||
|8\13 | |||
|10\17 | |||
|- | |- | ||
|'''Sol, Re''' | |'''Sol, Re''' | ||
|'''Ε''' | |'''Ε''' | ||
|'''15\19''' | |'''15\19,''' '''698.178''' | ||
''' | |'''11\14,''' '''694.853''' | ||
|'''11\14''' | |'''18\23,''' '''692.107''' | ||
'''694. | |'''7\9, 687.835''' | ||
|'''18\23''' | |'''17\22, 683.368''' | ||
''' | |'''10\13, 680.276''' | ||
|'''7\9 | |'''13\17, 676.274''' | ||
|'''17\22 | |||
|'''10\13 | |||
|'''13\17 | |||
|- | |- | ||
|Sol#, Re# | |Sol#, Re# | ||
|Ε# | |Ε# | ||
|16\19 | |16\19, 744.723 | ||
|12\14, 758.022 | |||
|12\14 | |20\23, 769.008 | ||
| rowspan="2" |8\9, 786.096 | |||
|20\23 | |20\22, 803.9625 | ||
|12\13, 816.331 | |||
| rowspan="2" |8\9 | |16\14, 832.338 | ||
|20\22 | |||
|12\13 | |||
|16\14 | |||
|- | |- | ||
|Dob, Solb | |Dob, Solb | ||
|Ϛb/Ϝb | |Ϛb/Ϝb | ||
|18\19 | |18\19, 837.8135 | ||
|13\14, 821.190 | |||
|13\14 | |21\23, 809.458 | ||
821. | |19\22, 763.764 | ||
|21\23 | |11\13, 748.3035 | ||
|14\17, 728.295 | |||
|19\22 | |||
|11\13 | |||
|14\17 | |||
|- | |- | ||
!Do, Sol | !Do, Sol | ||
!Ϛ/Ϝ | !Ϛ/Ϝ | ||
!19\19 | !19\19, 884.359 | ||
!14\14, 884.359 | |||
!14\14 | !23\23, 884.359 | ||
884. | !9\9, 884.359 | ||
!23\23 | !22\22, 884.359 | ||
!13\13, 884.359 | |||
!9\9 | !17\17, 884.359 | ||
!22\22 | |||
!13\13 | |||
!17\17 | |||
|- | |- | ||
|Do#, Sol# | |Do#, Sol# | ||
|Ϛ#/Ϝ# | |Ϛ#/Ϝ# | ||
|20\19 | |20\19, 930.903 | ||
|15\14, 947.527 | |||
|15\14 | |24\23, 922.806 | ||
947. | | rowspan="2" |10\9, 982.621 | ||
|24\23 | |25\22, 1004.953 | ||
|15\13, 1020.413 | |||
| rowspan="2" |10\9 | |20\17, 1040.422 | ||
|25\22 | |||
|15\13 | |||
|20\17 | |||
|- | |- | ||
|Reb, Lab | |Reb, Lab | ||
|Ζb | |Ζb | ||
|22\19 | |22\19, 1023.994 | ||
|16\14, 1010.696 | |||
|16\14 | |26\23, 999.710 | ||
1010. | |24\22, 964.755 | ||
|26\23 | |14\13, 952.386 | ||
|18\17, 936.380 | |||
|24\22 | |||
|14\13 | |||
|18\17 | |||
|- | |- | ||
|'''Re, La''' | |'''Re, La''' | ||
|'''Ζ''' | |'''Ζ''' | ||
|'''23\19''' | |'''23\19,''' '''1070.5395''' | ||
''' | |'''17\14,''' '''1073.864''' | ||
|'''17\14''' | |'''28\23,''' '''1076.611''' | ||
''' | |'''11\9,''' '''1080.882''' | ||
|'''28\23''' | |'''27\22,''' '''1085.349''' | ||
''' | |'''16\13,''' '''1088.4415''' | ||
|'''11\9''' | |'''21\17,''' '''1092.442''' | ||
''' | |||
|'''27\22''' | |||
''' | |||
|'''16\13''' | |||
''' | |||
|'''21\17''' | |||
''' | |||
|- | |- | ||
|Re#, La# | |Re#, La# | ||
|Ζ# | |Ζ# | ||
|24\19 | |24\19, 1117.085 | ||
|18\14, 1137.033 | |||
|18\14 | |30\23, 1153.511 | ||
| rowspan="2" |12\9, 1179.145 | |||
|30\23 | |30\22, 1205.944 | ||
|18\13, 1224.497 | |||
| rowspan="2" |12\9 | |24\14, 1248.506 | ||
|30\22 | |||
|18\13 | |||
|24\14 | |||
|- | |- | ||
|Mib, Sib | |Mib, Sib | ||
|Ηb | |Ηb | ||
|26\19 | |26\19, 1210.175 | ||
|19\14, 1200.201 | |||
|19\14 | |31\23, 1191.952 | ||
1200 | |29\22, 1165.745 | ||
|31\23 | |17\13, 1156.469 | ||
|22\17, 1144.464 | |||
|29\22 | |||
|17\13 | |||
|22\17 | |||
|- | |- | ||
|Mi, Si | |Mi, Si | ||
|Η | |Η | ||
|27\19 | |27\19, 1256.720 | ||
|20\14, 1263.370 | |||
|20\14 | |33\23, 1268.8625 | ||
1263. | |13\9, 1277.407 | ||
|33\23 | |32\22, 1286.340 | ||
|19\13, 1292.524 | |||
|13\9 | |25\17, 1300.5275 | ||
|32\22 | |||
|19\13 | |||
|25\17 | |||
|- | |- | ||
|Mi#, Si# | |Mi#, Si# | ||
|Η# | |Η# | ||
|28\19 | |28\19, 1303.2655 | ||
| rowspan="2" |21\14, 1326.538 | |||
| rowspan="2" |21\14 | |35\23, 1345.763 | ||
1326. | |14\9, 1375.669 | ||
|35\23 | |35\22, 1406.934 | ||
|21\13, 1428.5795 | |||
|14\9 | |28\17, 1456.591 | ||
|35\22 | |||
|21\13 | |||
|28\17 | |||
|- | |- | ||
|Fab, Dob | |Fab, Dob | ||
|Θb | |Θb | ||
|29\19 | |29\19, 1349.811 | ||
|34\23, 1307.313 | |||
|34\23 | |13\9, 1277.407 | ||
|13\9 | |||
|31\22 | |31\22 | ||
1246.142 | |||
|18\13, 1224.497 | |||
|23\17, 1196.485 | |||
| | |||
| | |||
|- | |- | ||
|Fa, Do | |Fa, Do | ||
|Θ | |Θ | ||
| | |30\19, 1396.356 | ||
|22\14, 1389.707 | |||
| | |36\23, 1384.214 | ||
|14\9, 1375.669 | |||
| | |34\22, 1366.736 | ||
|20\13, 1360.552 | |||
| | |26\17, 1352.549 | ||
| | |||
| | |||
| | |||
|- | |- | ||
|Fa#, Do# | |Fa#, Do# | ||
|Θ# | |Θ# | ||
| | |31\19, 1442.901 | ||
|23\14, 1452.875 | |||
| | |38\23, 1461.114 | ||
| rowspan="2" |15\9, 1473.931 | |||
| | |37\22, 1487.331 | ||
|22\13, 1496.606 | |||
| rowspan="2" | | |29\17, 1508.612 | ||
| | |||
| | |||
| | |||
|- | |- | ||
|Solb, Reb | |Solb, Reb | ||
|Ιb | |Ιb | ||
| | |33\19, 1535.991 | ||
|24\14, 1516.0435 | |||
| | |39\23, 1499.565 | ||
|36\22, 1447.132 | |||
| | |21\13, 1428.5795 | ||
|27\17, 1404.570 | |||
| | |||
| | |||
| | |||
|- | |- | ||
|'''Sol, Re''' | |'''Sol, Re''' | ||
|'''Ι''' | |'''Ι''' | ||
| | |'''34\19,''' '''1582.537''' | ||
' | |'''25\14,''' '''1579.212''' | ||
| | |'''41\23,''' '''1576.4655''' | ||
' | |'''16\9, 1572.193''' | ||
| | |'''39\22,''' '''1567.723''' | ||
' | |'''23\13,''' '''1564.635''' | ||
| | |'''30\17,''' '''1560.633''' | ||
| | |||
'' | |||
| | |||
' | |||
| | |||
''''' | |||
|- | |- | ||
|Sol#, Re# | |Sol#, Re# | ||
|Ι# | |Ι# | ||
| | |35\19, 1629.081 | ||
|26\14, 1642.3805 | |||
| | |43\23, 1653.366 | ||
| rowspan="2" |17\9, 1670.455 | |||
| | |42\22, 1688.321 | ||
|25\13, 1700.690 | |||
| rowspan="2" | | |33\17, 1664.675 | ||
| | |||
| | |||
| | |||
|- | |- | ||
|Dob, Solb | |Dob, Solb | ||
|Αb | |Αb | ||
| | |37\19, 1722.172 | ||
|27\14, 1705.549 | |||
| | |44\23, 1691.817 | ||
|41\22, 1648.123 | |||
| | |24\13, 1632.662 | ||
|31\17, 1612.654 | |||
| | |||
| | |||
| | |||
|- | |- | ||
!Do, Sol | !Do, Sol | ||
!Α | !Α | ||
! | !38\19, 1768.717 | ||
!28\14, 1768.717 | |||
!46\23, 1768.717 | |||
!18\9, 1768.717 | |||
!44\22, 1768.717 | |||
!26\13, 1768.717 | |||
!34\17, 1768.717 | |||
|} | |} | ||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable" | ||