|
|
| (19 intermediate revisions by 4 users not shown) |
| Line 1: |
Line 1: |
| {{Infobox MOS|Equalized=1|Equave=5/3|Name=|Collapsed=1|Pattern=LLLLs|nLargeSteps=4|nSmallSteps=1}} | | {{Infobox MOS|Tuning=4L 1s<5/3>}} |
|
| |
|
| '''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]]).
| | {{MOS intro|Scale Signature=4L 1s<5/3>|Other names=diatonic}}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, two minor chords. This diatonic also has two dominant 7th chords, making it a warped Neapolitan minor scale. |
|
| |
|
| 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 major sixth-based equal tuning similar to [[12edo]]. |
| | ==Notation== |
|
| |
|
| [[Basic]] diatonic is in [[9ed5/3]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
| | 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. |
| ==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 sextave notation, Greek numerals 1-10 may be used. | |
| {| class="wikitable" | | {| class="wikitable" |
| |+ | | |+ |
| Normalized | | Normalized |
| ! colspan="2" |Notation | | !Notation |
| !Supersoft | | !Supersoft |
| !Soft | | !Soft |
| Line 23: |
Line 22: |
| |- | | |- |
| !Diatonic | | !Diatonic |
| !Scala Francisci | | ![[19ed5/3|19ed'''5/3''']] |
| !19eds
| | ![[14ed5/3|14ed'''5/3''']] |
| !14eds
| | ![[23ed5/3|23ed'''5/3''']] |
| !23eds
| | ![[9ed5/3|9ed'''5/3''']] |
| !9eds
| | ![[22ed5/3|22ed'''5/3''']] |
| !22eds
| | ![[13ed5/3|13ed'''5/3''']] |
| !13eds
| | ![[17ed5/3|17ed'''5/3''']] |
| !17eds
| |
| |-
| |
| |Do#, Sol#
| |
| |Α#
| |
| |1\19
| |
| 46.15385
| |
| |1\14
| |
| 63.1579
| |
| |2\23
| |
| 77.41935
| |
| | rowspan="2" |1\9
| |
| 100
| |
| |3\22
| |
| 124.1379
| |
| |2\13
| |
| 141.1765
| |
| |3\17
| |
| 163.{{Overline|63}}
| |
| |-
| |
| |Reb, Lab
| |
| |Βb
| |
| |3\19
| |
| 138.4615
| |
| |2\14
| |
| 126.3158
| |
| |3\23
| |
| 116.129
| |
| |2\22
| |
| 82.7586
| |
| |1\13
| |
| 70.5882
| |
| |1\17
| |
| 54.{{Overline|54}}
| |
| |-
| |
| |'''Re, La''' | |
| |'''Β''' | |
| |'''4\19''' | |
| '''184.6154'''
| |
| |'''3\14''' | |
| '''189.4736'''
| |
| |'''5\23''' | |
| '''193.5484'''
| |
| |'''2\9'''
| |
| '''200'''
| |
| |'''5\22''' | |
| '''206.89655'''
| |
| |'''3\13'''
| |
| '''211.7647'''
| |
| |'''4\17'''
| |
| '''218.{{Overline|18}}'''
| |
| |-
| |
| |Re#, La#
| |
| |Β#
| |
| |5\19
| |
| 230.7692
| |
| |4\14
| |
| 252.6316
| |
| |7\23
| |
| 270.9677
| |
| | rowspan="2" |3\9
| |
| 300
| |
| |8\22
| |
| 331.0345
| |
| |5\13
| |
| 352.9412
| |
| |7\17
| |
| 381.{{Overline|81}}
| |
| |-
| |
| |Mib, Sib
| |
| |Γb
| |
| |7\19
| |
| 323.0769
| |
| |5\14
| |
| 315.7895
| |
| |8\23
| |
| 309.6774
| |
| |7\22
| |
| 289.6552
| |
| |4\13
| |
| 282.3529
| |
| |5\17
| |
| 272.{{Overline|72}}
| |
| |-
| |
| |Mi, Si
| |
| |Γ
| |
| |8\19
| |
| 369.2308
| |
| |6\14
| |
| 378.9474
| |
| |10\23
| |
| 387.0968
| |
| |4\9
| |
| | |
| 400
| |
| |10\22
| |
| 413.7931
| |
| |6\13
| |
| 423.5294
| |
| |8\17
| |
| 436.{{Overline|36}}
| |
| |-
| |
| |Mi#, Si#
| |
| |Γ#
| |
| |9\19
| |
| 415.3846
| |
| | rowspan="2" |7\14
| |
| 442.1053
| |
| |12\23
| |
| 464.5161
| |
| |5\9
| |
| 500
| |
| |13\22
| |
| 537.931
| |
| |8\13
| |
| 564.7059
| |
| |11\17
| |
| 600
| |
| |-
| |
| |Fab, Dob
| |
| |Δb
| |
| |10\19
| |
| 461.5385
| |
| |11\23
| |
| 425.80645
| |
| |4\9
| |
| 400
| |
| |9\22
| |
| 372.4138
| |
| |5\13
| |
| 352.9412
| |
| |6\17
| |
| 327.{{Overline|27}}
| |
| |-
| |
| |Fa, Do
| |
| |Δ
| |
| |11\19
| |
| 507.6923
| |
| |8\14
| |
| 505.2632
| |
| |13\23
| |
| 503.2259
| |
| |5\9
| |
| 500
| |
| |12\22
| |
| 496.5517
| |
| |7\13
| |
| 494.11765
| |
| |9\17
| |
| 490.{{Overline|90}}
| |
| |-
| |
| |Fa#, Do#
| |
| |Δ#
| |
| |12\19
| |
| 553.84615
| |
| |9\14
| |
| 568.42105
| |
| |15\23
| |
| 580.6452
| |
| | rowspan="2" |6\9
| |
| 600
| |
| |15\22
| |
| 620.6897
| |
| |9\13
| |
| 635.2941
| |
| |12\17
| |
| 654.{{Overline|54}}
| |
| |-
| |
| |Solb, Reb
| |
| |Εb
| |
| |14\19
| |
| 646.15385
| |
| |10\14
| |
| 631.57895
| |
| |16\23
| |
| 619.3548
| |
| |14\22
| |
| 579.3103
| |
| |8\13
| |
| 564.7059
| |
| |10\17
| |
| 545.{{Overline|45}}
| |
| |-
| |
| |'''Sol, Re'''
| |
| |'''Ε'''
| |
| |'''15\19'''
| |
| '''692.3077'''
| |
| |'''11\14'''
| |
| '''694.7368''' | |
| |'''18\23'''
| |
| '''696.7742'''
| |
| |'''7\8'''
| |
| '''700'''
| |
| |'''17\22'''
| |
| '''703.4483'''
| |
| |'''10\13'''
| |
| '''705.88235'''
| |
| |'''13\17'''
| |
| '''709.{{Overline|09}}'''
| |
| |-
| |
| |Sol#, Re#
| |
| |Ε#
| |
| |16\19
| |
| 738.4615
| |
| |12\14
| |
| 757.8947
| |
| |20\23
| |
| 774.19355
| |
| | rowspan="2" |8\8
| |
| 800
| |
| |20\22
| |
| 827.5862
| |
| |12\13
| |
| 847.0588
| |
| |16\14
| |
| 872.{{Overline|72}}
| |
| |-
| |
| |Dob, Solb
| |
| |Ϛb/Ϝb
| |
| |18\19
| |
| 830.7692
| |
| |13\14
| |
| 821.0526
| |
| |21\23
| |
| 812.9032
| |
| |19\22
| |
| 786.2069
| |
| |11\13
| |
| 776.6471
| |
| |14\17
| |
| 763.{{Overline|63}}
| |
| |-
| |
| !Do, Sol
| |
| !Ϛ/Ϝ
| |
| !19\19
| |
| 876.9231
| |
| !14\14
| |
| 884.2105
| |
| !23\23
| |
| 890.3226
| |
| !9\9
| |
| 900
| |
| !22\22
| |
| 910.3448
| |
| !13\13
| |
| 917.6471
| |
| !17\17
| |
| 927.{{Overline|27}}
| |
| |- | | |- |
| |Do#, Sol# | | |Do#, Sol# |
| |Ϛ#/Ϝ# | | |1\19, 46.545 |
| |20\19
| | |1\14, 63.168 |
| 923.0769
| | |2\23, 76.901 |
| |15\14 | | | rowspan="2" |1\9, 98.262 |
| 947.3684
| | |3\22, 120.594 |
| |24\23 | | |2\13, 136.055 |
| 929.0323
| | |3\17, 156.063 |
| | rowspan="2" |10\9 | |
| 1000
| |
| |25\22 | |
| 1034.4829
| |
| |15\13 | |
| 1052.8235
| |
| |20\17 | |
| 1090.{{Overline|90}}
| |
| |- | | |- |
| |Reb, Lab | | |Reb, Lab |
| |Ζb | | |3\19, 139.636 |
| |22\19
| | |2\14, 126.337 |
| 1015.3847
| | |3\23, 115.351 |
| |16\14 | | |2\22, 80.396 |
| 1010.5263
| | |1\13, 68.028 |
| |26\23 | | |1\17, 52.021 |
| 1006.4516
| |
| |24\22 | |
| 993.10345
| |
| |14\13 | |
| 988.2353
| |
| |18\17 | |
| 981.{{Overline|81}}
| |
| |- | | |- |
| |'''Re, La''' | | |'''Re, La''' |
| |'''Ζ''' | | |'''4\19,''' '''186.181''' |
| |'''23\19'''
| | |'''3\14,''' '''189.505''' |
| '''1061.5385''' | | |'''5\23,''' '''192.252''' |
| |'''17\14''' | | |'''2\9, 196.524''' |
| '''1071.6842''' | | |'''5\22,''' '''200.991''' |
| |'''28\23''' | | |'''3\13,''' '''204.083''' |
| '''1083.871''' | | |'''4\17, 208.084''' |
| |'''11\9''' | |
| '''1100'''
| |
| |'''27\22''' | |
| '''1117.2414''' | |
| |'''16\13''' | |
| '''1129.4118''' | |
| |'''21\17''' | |
| '''1145.{{Overline|45}}'''
| |
| |- | | |- |
| |Re#, La# | | |Re#, La# |
| |Ζ# | | |5\19, 232.726 |
| |24\19
| | |4\14, 252.673 |
| 1107.6923
| | |7\23, 269.153 |
| |18\14 | | | rowspan="2" |3\9, 294.786 |
| 1136.8421
| | |8\22, 321.585 |
| |30\23 | | |5\13, 340.138 |
| 1161.7097
| | |7\17, 364.148 |
| | rowspan="2" |12\9 | |
| | |
| 1200
| |
| |30\22 | |
| 1241.3793
| |
| |18\13 | |
| 1270.5882
| |
| |24\14 | |
| 1309.{{Overline|09}}
| |
| |- | | |- |
| |Mib, Sib | | |Mib, Sib |
| |Ηb | | |7\19, 325.816 |
| |26\19
| | |5\14, 315.842 |
| 1200
| | |8\23, 307.603 |
| |19\14 | | |7\22, 281.387 |
| 1200
| | |4\13, 272.110 |
| |31\23 | | |5\17, 260.106 |
| 1200
| |
| |29\22 | |
| 1200
| |
| |17\13 | |
| 1200
| |
| |22\17 | |
| 1200
| |
| |- | | |- |
| |Mi, Si | | |Mi, Si |
| |Η | | |8\19, 372.362 |
| |27\19
| | |6\14, 379.011 |
| 1246.15385
| | |10\23, 384.504 |
| |20\14 | | |4\9, 393.048 |
| 1263.1579
| | |10\22, 401.981 |
| |33\23 | | |6\13, 408.166 |
| 1277.41935
| | |8\17, 416.169 |
| |13\9 | |
| 1300
| |
| |32\22 | |
| 1324.1379
| |
| |19\13 | |
| 1341.1765
| |
| |25\17 | |
| 1363.{{Overline|63}}
| |
| |- | | |- |
| |Mi#, Si# | | |Mi#, Si# |
| |Η# | | |9\19, 418.906 |
| |28\19
| | | rowspan="2" |7\14, 442.179 |
| 1292.3077
| | |12\23, 461.405 |
| | rowspan="2" |21\14 | | |5\9, 491.310 |
| 1326.3158
| | |13\22, 522.576 |
| |35\23 | | |8\13, 544.221 |
| 1354.8387
| | |11\17, 572.232 |
| |14\9 | |
| 1400
| |
| |35\22 | |
| 1448.2759
| |
| |21\13 | |
| 1482.3529
| |
| |28\17 | |
| 1527.{{Overline|27}}
| |
| |- | | |- |
| |Fab, Dob | | |Fab, Dob |
| |Θb | | |10\19, 465.452 |
| |29\19
| | |11\23, 422.954 |
| 1338.4615
| | |4\9, 393.048 |
| |34\23 | | |9\22, 361.783 |
| 1316.129
| | |5\13, 340.138 |
| |13\9 | | |6\17, 312.127 |
| 1300
| |
| |31\22 | |
| 1282.7586
| |
| |18\13 | |
| 1270.5882
| |
| |23\17 | |
| 1254.{{Overline|54}}
| |
| |- | | |- |
| |Fa, Do | | |Fa, Do |
| |Θ | | |11\19, 511.997 |
| |30\19
| | |8\14, 505.348 |
| 1384.6154
| | |13\23, 499.855 |
| |22\14 | | |5\9, 491.310 |
| 1389.4737
| | |12\22, 482.377 |
| |36\23 | | |7\13, 476.193 |
| 1393.5484
| | |9\17, 468.190 |
| |14\9 | |
| 1400
| |
| |34\22 | |
| 1406.89655
| |
| |20\13 | |
| 1411.7647
| |
| |26\17 | |
| 1418.{{Overline|18}}
| |
| |- | | |- |
| |Fa#, Do# | | |Fa#, Do# |
| |Θ# | | |12\19, 558.542 |
| |31\19
| | |9\14, 568.516 |
| 1430.7692
| | |15\23, 576.756 |
| |23\14 | | | rowspan="2" |6\9, 589.572 |
| 1452.6316
| | |15\22, 602.972 |
| |38\23 | | |9\13, 612.248 |
| 1470.9677
| | |12\17, 624.253 |
| | rowspan="2" |15\9 | |
| 1500
| |
| |37\22 | |
| 1531.0345
| |
| |22\13 | |
| 1552.9412
| |
| |29\17 | |
| 1581.{{Overline|81}}
| |
| |- | | |- |
| |Solb, Reb | | |Solb, Reb |
| |Ιb | | |14\19, 651.632 |
| |33\19
| | |10\14, 631.685 |
| 1523.0769
| | |16\23, 615.206 |
| |24\14 | | |14\22, 562.773 |
| 1515.7895
| | |8\13, 544.221 |
| |39\23 | | |10\17, 520.211 |
| 1509.6774
| |
| |36\22 | |
| 1489.6551
| |
| |21\13 | |
| 1482.3529
| |
| |27\17 | |
| 1472.{{Overline|72}}
| |
| |- | | |- |
| |'''Sol, Re''' | | |'''Sol, Re''' |
| |'''Ι''' | | |'''15\19,''' '''698.178''' |
| |'''34\19'''
| | |'''11\14,''' '''694.853''' |
| '''1569.2308''' | | |'''18\23,''' '''692.107''' |
| |'''25\14''' | | |'''7\9, 687.835''' |
| '''1578.9474''' | | |'''17\22, 683.368''' |
| |'''41\23''' | | |'''10\13, 680.276''' |
| '''1587.0968''' | | |'''13\17, 676.274''' |
| |'''16\9''' | |
| '''1600'''
| |
| |'''39\22''' | |
| '''1613.7931'''
| |
| |'''23\13''' | |
| '''1623.5294'''
| |
| |'''30\17''' | |
| '''1636.{{Overline|36}}'''
| |
| |- | | |- |
| |Sol#, Re# | | |Sol#, Re# |
| |Ι# | | |16\19, 744.723 |
| |35\19
| | |12\14, 758.022 |
| 1615.3846
| | |20\23, 769.008 |
| |26\14 | | | rowspan="2" |8\9, 786.096 |
| 1642.1053
| | |20\22, 803.962 |
| |43\23 | | |12\13, 816.331 |
| 1664.5161
| | |16\14, 832.338 |
| | rowspan="2" |17\9 | |
| 1700
| |
| |42\22 | |
| 1737.931
| |
| |25\13 | |
| 1764.7059
| |
| |33\17 | |
| 1800
| |
| |- | | |- |
| |Dob, Solb | | |Dob, Solb |
| |Αb | | |18\19, 837.814 |
| |37\19
| | |13\14, 821.190 |
| 1707.6923
| | |21\23, 809.458 |
| |27\14 | | |19\22, 763.764 |
| 1705.2632
| | |11\13, 748.304 |
| |44\23 | | |14\17, 728.295 |
| 1703.2258
| |
| |41\22 | |
| 1696.5517
| |
| |20\13 | |
| 1694.11765
| |
| |31\17 | |
| 1490.{{Overline|90}}
| |
| |- | | |- |
| !Do, Sol | | !Do, Sol |
| !Α | | !19\19, 884.359 |
| !38\19
| | !14\14, 884.359 |
| 1753.84615
| | !23\23, 884.359 |
| !28\14 | | !9\9, 884.359 |
| 1768.42105
| | !22\22, 884.359 |
| !46\23 | | !13\13, 884.359 |
| 1780.6452
| | !17\17, 884.359 |
| !18\9 | |
| | |
| 1800
| |
| !44\22 | |
| 1820.6897
| |
| !26\13 | |
| 1835.2941
| |
| !34\17 | |
| 1854.{{Overline|54}}
| |
| |} | | |} |
| {| class="wikitable" | | {| class="wikitable" |
| |+''ed3\4'' | | |+ |
| ! colspan="2" |Notation | | Normalized |
| | !Notation |
| !Supersoft | | !Supersoft |
| !Soft | | !Soft |
| Line 534: |
Line 170: |
| !Semihard | | !Semihard |
| !Hard | | !Hard |
| !Superhard | | ! Superhard |
| |- | | |- |
| !Diatonic
| |
| !Scala Francisci | | !Scala Francisci |
| !19eds | | ![[19ed5/3|19ed'''5/3''']] |
| !14eds | | ![[14ed5/3|14ed'''5/3''']] |
| !23eds | | ![[23ed5/3|23ed'''5/3''']] |
| !9eds | | ![[9ed5/3|9ed'''5/3''']] |
| !22eds | | ![[22ed5/3|22ed'''5/3''']] |
| !13eds | | ![[13ed5/3|13ed'''5/3''']] |
| !17eds | | ![[17ed5/3|17ed'''5/3''']] |
| |- | | |- |
| |Do#, Sol#
| |
| |Α# | | |Α# |
| |''1\19'' | | |1\19, 46.545 |
| ''47.3684''
| | |1\14, 63.168 |
| |''1\14'' | | | 2\23, 76.901 |
| ''64.2857''
| | | rowspan="2" |1\9, 98.262 |
| |''2\23'' | | |3\22, 120.594 |
| ''78.2609''
| | |2\13, 136.055 |
| | rowspan="2" |''1\9'' | | |3\17, 156.063 |
| ''100''
| |
| |''3\22'' | |
| ''122.{{Overline|72}}''
| |
| |''2\13'' | |
| ''138.4615''
| |
| |''3\17'' | |
| ''158.8235''
| |
| |- | | |- |
| |Reb, Lab
| |
| |Βb | | |Βb |
| |''3\19'' | | |3\19, 139.636 |
| ''142.1053''
| | |2\14, 126.337 |
| |''2\14'' | | |3\23, 115.351 |
| ''128.5714''
| | |2\22, 80.396 |
| |''3\23'' | | |1\13, 68.028 |
| ''117.3913''
| | |1\17, 52.021 |
| |''2\22'' | |
| ''81.{{Overline|81}}''
| |
| |''1\13'' | |
| ''69.2308''
| |
| |''1\17'' | |
| ''52.9412''
| |
| |- | | |- |
| |'''Re, La''' | | |'''Β''' |
| |Β
| | |'''4\19,''' '''186.181''' |
| |'''''4\19''''' | | |'''3\14,''' '''189.505''' |
| '''''189.4737''''' | | |'''5\23,''' '''192.252''' |
| |'''''3\14''''' | | |'''2\9, 196.524''' |
| '''''192.8571''''' | | |'''5\22,''' '''200.991''' |
| |'''''5\23''''' | | |'''3\13,''' '''204.083''' |
| '''''195.6522''''' | | |'''4\17, 208.084''' |
| |'''''2\9''''' | |
| '''''200'''''
| |
| |'''''5\22''''' | |
| '''''204.{{Overline|54}}''''' | |
| |'''''3\13''''' | |
| '''''207.6923''''' | |
| |'''''4\17''''' | |
| '''''211.7647'''''
| |
| |- | | |- |
| |Re#, La#
| | | Β# |
| |Β# | | |5\19, 232.726 |
| |''5\19'' | | |4\14, 252.673 |
| ''236.8421''
| | |7\23, 269.153 |
| |''4\14'' | | | rowspan="2" |3\9, 294.786 |
| ''257.1429''
| | |8\22, 321.585 |
| |''7\23'' | | |5\13, 340.138 |
| ''273.913''
| | |7\17, 364.148 |
| | rowspan="2" |''3\9'' | |
| ''300''
| |
| |''8\22'' | |
| ''327.{{Overline|27}}''
| |
| |''5\13'' | |
| ''346.15385''
| |
| |''7\17'' | |
| ''370.5882''
| |
| |- | | |- |
| |Mib, Sib
| |
| |Γb | | |Γb |
| |''7\19'' | | |7\19, 325.816 |
| ''331.57895''
| | |5\14, 315.842 |
| |''5\14'' | | |8\23, 307.603 |
| ''321.4286''
| | | 7\22, 281.387 |
| |''8\23'' | | | 4\13, 272.110 |
| ''313.0345''
| | |5\17, 260.106 |
| |''7\22'' | |
| ''286.{{Overline|36}}''
| |
| |''4\13'' | |
| ''276.9231''
| |
| |''5\17'' | |
| ''264.7059''
| |
| |- | | |- |
| |Mi, Si
| |
| |Γ | | |Γ |
| |''8\19'' | | |8\19, 372.362 |
| ''378.9474''
| | |6\14, 379.011 |
| |''6\14'' | | |10\23, 384.504 |
| ''385.7143''
| | |4\9, 393.048 |
| |''10\23'' | | |10\22, 401.981 |
| ''391.304''
| | |6\13, 408.166 |
| |''4\9'' | | |8\17, 416.169 |
| | |
| ''400''
| |
| |''10\22'' | |
| ''409.{{Overline|09}}''
| |
| |''6\13'' | |
| ''415.3846''
| |
| |''8\17'' | |
| ''423.5294''
| |
| |- | | |- |
| |Mi#, Si#
| |
| |Γ# | | |Γ# |
| |''9\19'' | | |9\19, 418.906 |
| ''426.3158''
| | | rowspan="2" |7\14, 442.179 |
| | rowspan="2" |''7\14'' | | |12\23, 461.405 |
| ''450''
| | |5\9, 491.310 |
| |''12\23'' | | |13\22, 522.576 |
| ''469.5652''
| | | 8\13, 544.221 |
| |''5\9'' | | | 11\17, 572.232 |
| ''500''
| |
| |''13\22'' | |
| ''531.{{Overline|81}}''
| |
| |''8\13'' | |
| ''553.84615''
| |
| |''11\17'' | |
| ''582.3529''
| |
| |- | | |- |
| |Fab, Dob
| |
| |Δb | | |Δb |
| |''10\19'' | | |10\19, 465.452 |
| ''473.6842''
| | |11\23, 422.954 |
| |''11\23'' | | |4\9, 393.048 |
| ''430.7692''
| | |9\22, 361.783 |
| |''4\9'' | | |5\13, 340.138 |
| ''400''
| | |6\17, 312.127 |
| |''9\22'' | |
| ''368.''{{Overline|18}}
| |
| |''5\13'' | |
| ''346.15385''
| |
| |''6\17'' | |
| ''317.6471''
| |
| |- | | |- |
| |Fa, Do
| |
| |Δ | | |Δ |
| |''11\19'' | | |11\19, 511.997 |
| ''521.0526''
| | |8\14, 505.348 |
| |''8\14'' | | |13\23, 499.855 |
| ''514.2857''
| | |5\9, 491.310 |
| |''13\23'' | | |12\22, 482.377 |
| ''508.696''
| | |7\13, 476.193 |
| |''5\9'' | | |9\17, 468.190 |
| ''500''
| |
| |''12\22'' | |
| ''490.{{Overline|90}}''
| |
| |''7\13'' | |
| ''484.6154''
| |
| |''9\17'' | |
| ''476.4706''
| |
| |- | | |- |
| |Fa#, Do#
| |
| |Δ# | | |Δ# |
| |''12\19'' | | |12\19, 558.542 |
| ''568.42105''
| | |9\14, 568.516 |
| |''9\14'' | | |15\23, 576.756 |
| ''578.5714''
| | | rowspan="2" |6\9, 589.572 |
| |''15\23'' | | |15\22, 602.972 |
| ''587.9655''
| | |9\13, 612.248 |
| | rowspan="2" |''6\9'' | | |12\17, 624.253 |
| ''600''
| |
| |''15\22'' | |
| ''613.{{Overline|63}}''
| |
| |''9\13'' | |
| ''623.0769''
| |
| |''12\17'' | |
| ''635.2931''
| |
| |- | | |- |
| |Solb, Reb
| |
| |Εb | | |Εb |
| |''14\19'' | | |14\19, 651.632 |
| ''663.1579''
| | |10\14, 631.685 |
| |''10\14'' | | |16\23, 615.206 |
| ''642.8571''
| | |14\22, 562.773 |
| |''16\23'' | | |8\13, 544.221 |
| ''626.087''
| | |10\17, 520.211 |
| |''14\22'' | |
| ''572.''{{Overline|72}}
| |
| |''8\13'' | |
| ''553.84615''
| |
| |''10\17'' | |
| ''529.4118''
| |
| |- | | |- |
| |'''Sol, Re'''
| |
| |'''Ε''' | | |'''Ε''' |
| |'''''15\19''''' | | |'''15\19,''' '''698.178''' |
| '''''710.5263''''' | | |'''11\14,''' '''694.853''' |
| |'''''11\14''''' | | |'''18\23,''' '''692.107''' |
| '''''707.1429''''' | | |'''7\9, 687.835''' |
| |'''''18\23''''' | | |'''17\22, 683.368''' |
| '''''704.3478''''' | | |'''10\13, 680.276''' |
| |'''''7\8''''' | | |'''13\17, 676.274''' |
| '''''700'''''
| |
| |'''''17\22''''' | |
| '''''695.{{Overline|45}}'''''
| |
| |'''''10\13''''' | |
| '''''692.3077'''''
| |
| |'''''13\17''''' | |
| '''''688.2353'''''
| |
| |- | | |- |
| |Sol#, Re#
| |
| |Ε# | | |Ε# |
| |''16\19'' | | |16\19, 744.723 |
| ''757.8947''
| | |12\14, 758.022 |
| |''12\14'' | | |20\23, 769.008 |
| ''771.4286''
| | | rowspan="2" |8\9, 786.096 |
| |''20\23'' | | |20\22, 803.962 |
| ''782.6087''
| | |12\13, 816.331 |
| | rowspan="2" |''8\8'' | | |16\14, 832.338 |
| ''800''
| |
| |''20\22'' | |
| ''818.{{Overline|18}}''
| |
| |''12\13'' | |
| ''830.7692''
| |
| |''16\14'' | |
| ''847.0588''
| |
| |- | | |- |
| |Dob, Solb
| |
| |Ϛb/Ϝb | | |Ϛb/Ϝb |
| |''18\19'' | | |18\19, 837.814 |
| ''852.6316''
| | |13\14, 821.190 |
| |''13\14'' | | |21\23, 809.458 |
| ''835.7143''
| | |19\22, 763.764 |
| |''21\23'' | | |11\13, 748.304 |
| ''821.7391''
| | |14\17, 728.295 |
| |''19\22'' | |
| ''777.{{Overline|27}}''
| |
| |''11\13'' | |
| ''761.5385''
| |
| |''14\17'' | |
| ''741.1765''
| |
| |- | | |- |
| !Do, Sol
| |
| !Ϛ/Ϝ | | !Ϛ/Ϝ |
| ! colspan="7" |''900'' | | !19\19, 884.359 |
| | !14\14, 884.359 |
| | !23\23, 884.359 |
| | !9\9, 884.359 |
| | !22\22, 884.359 |
| | !13\13, 884.359 |
| | !17\17, 884.359 |
| |- | | |- |
| |Do#, Sol#
| |
| |Ϛ#/Ϝ# | | |Ϛ#/Ϝ# |
| |''20\19'' | | |20\19, 930.903 |
| ''947.3684''
| | |15\14, 947.527 |
| |''15\14'' | | |24\23, 922.806 |
| ''964.2857''
| | | rowspan="2" |10\9, 982.621 |
| |''25\23'' | | |25\22, 1004.953 |
| ''978.2609''
| | |15\13, 1020.413 |
| | rowspan="2" |''10\9'' | | |20\17, 1040.422 |
| ''1000''
| |
| |''25\22'' | |
| ''1022.{{Overline|72}}''
| |
| |''15\13'' | |
| ''1038.4615''
| |
| |''20\17'' | |
| ''1058.8235''
| |
| |- | | |- |
| |Reb, Lab
| |
| |Ζb | | |Ζb |
| |''22\19'' | | |22\19, 1023.994 |
| ''1042.1053''
| | |16\14, 1010.696 |
| |''16\14'' | | |26\23, 999.710 |
| ''1028.5714''
| | |24\22, 964.755 |
| |''26\23'' | | |14\13, 952.386 |
| ''1017.3913''
| | |18\17, 936.380 |
| |''24\22'' | |
| ''981.{{Overline|81}}''
| |
| |''14\13'' | |
| ''969.2308''
| |
| |''18\17'' | |
| ''952.9412''
| |
| |- | | |- |
| |'''Re, La'''
| |
| |'''Ζ''' | | |'''Ζ''' |
| |'''''23\19''''' | | |'''23\19,''' '''1070.539''' |
| '''''1089.4737''''' | | |'''17\14,''' '''1073.864''' |
| |'''''17\14''''' | | |'''28\23,''' '''1076.611''' |
| '''''1092.8571''''' | | |'''11\9,''' '''1080.882''' |
| |'''''28\23''''' | | |'''27\22,''' '''1085.349''' |
| '''''1095.6522''''' | | |'''16\13,''' '''1088.441''' |
| |'''''11\9''''' | | |'''21\17,''' '''1092.442''' |
| '''''1100'''''
| |
| |'''''27\22''''' | |
| '''''1104.{{Overline|54}}''''' | |
| |'''''16\13''''' | |
| '''''1107.6923''''' | |
| |'''''21\17''''' | |
| '''''1111.7647''''' | |
| |- | | |- |
| |Re#, La#
| |
| |Ζ# | | |Ζ# |
| |''24\19'' | | |24\19, 1117.085 |
| ''1136.8421''
| | |18\14, 1137.033 |
| |''18\14'' | | |30\23, 1153.511 |
| ''1157.1429''
| | | rowspan="2" |12\9, 1179.145 |
| |''30\23'' | | |30\22, 1205.944 |
| ''1173.913''
| | |18\13, 1224.497 |
| | rowspan="2" |''12\9'' | | |24\14, 1248.506 |
| | |
| ''1200''
| |
| |''30\22'' | |
| ''1227.{{Overline|27}}''
| |
| |''18\13'' | |
| ''1246.15385''
| |
| |''24\14'' | |
| ''1270.5882''
| |
| |- | | |- |
| |Mib, Sib
| |
| |Ηb | | |Ηb |
| |''26\19'' | | |26\19, 1210.175 |
| ''1231.57895''
| | |19\14, 1200.201 |
| |''19\14'' | | |31\23, 1191.952 |
| ''1221.4286''
| | |29\22, 1165.745 |
| |''31\23'' | | |17\13, 1156.469 |
| ''1213.0345''
| | |22\17, 1144.464 |
| |''29\22'' | |
| ''1186.{{Overline|36}}''
| |
| |''17\13'' | |
| ''1176.9231''
| |
| |''22\17'' | |
| ''1164.7059''
| |
| |- | | |- |
| |Mi, Si
| |
| |Η | | |Η |
| |''27\19'' | | |27\19, 1256.720 |
| ''1278.9474''
| | |20\14, 1263.370 |
| |''20\14'' | | |33\23, 1268.863 |
| ''1285.7143''
| | |13\9, 1277.407 |
| |''33\23'' | | |32\22, 1286.340 |
| ''1291.304''
| | |19\13, 1292.524 |
| |''13\9'' | | |25\17, 1300.528 |
| ''1300''
| |
| |''32\22'' | |
| ''1309.{{Overline|09}}''
| |
| |''19\13'' | |
| ''1315.3846''
| |
| |''25\17'' | |
| ''1323.5294''
| |
| |- | | |- |
| |Mi#, Si#
| |
| |Η# | | |Η# |
| |''28\19'' | | |28\19, 1303.265 |
| ''1326.3158''
| | | rowspan="2" |21\14, 1326.538 |
| | rowspan="2" |''21\14'' | | |35\23, 1345.763 |
| ''1350''
| | |14\9, 1375.669 |
| |''35\23'' | | |35\22, 1406.934 |
| ''1369.5652''
| | |21\13, 1428.579 |
| |''14\9'' | | |28\17, 1456.591 |
| ''1400''
| |
| |''35\22'' | |
| ''1431.{{Overline|81}}''
| |
| |''21\13'' | |
| ''1453.15385''
| |
| |''28\17'' | |
| ''1482.3529''
| |
| |- | | |- |
| |Fab, Dob
| |
| |Θb | | |Θb |
| |''29\19'' | | |29\19, 1349.811 |
| ''1373.6842''
| | |34\23, 1307.313 |
| |''34\23'' | | |13\9, 1277.407 |
| ''1330.7692''
| | |31\22, 1246.142 |
| |''13\9'' | | |18\13, 1224.497 |
| ''1300''
| | |23\17, 1196.485 |
| |''31\22'' | |
| ''1368.{{Overline|18}}''
| |
| |''18\13'' | |
| ''1346.84615''
| |
| |''23\17'' | |
| ''1317.6471''
| |
| |- | | |- |
| |Fa, Do
| |
| |Θ | | |Θ |
| |''30\19'' | | |30\19, 1396.356 |
| ''1421.0526''
| | |22\14, 1389.707 |
| |''22\14'' | | |36\23, 1384.214 |
| ''1414.2857''
| | |14\9, 1375.669 |
| |''36\23'' | | |34\22, 1366.736 |
| ''1408.696''
| | |20\13, 1360.552 |
| |''14\9'' | | |26\17, 1352.549 |
| ''1400''
| |
| |''34\22'' | |
| ''1390.{{Overline|90}}''
| |
| |''20\13'' | |
| ''1384.6154''
| |
| |''26\17'' | |
| ''1376.4706''
| |
| |- | | |- |
| |Fa#, Do#
| |
| |Θ# | | |Θ# |
| |''31\19'' | | |31\19, 1442.901 |
| ''1468.42105''
| | |23\14, 1452.875 |
| |''23\14'' | | |38\23, 1461.114 |
| ''1478.7143''
| | | rowspan="2" |15\9, 1473.931 |
| |''38\23'' | | |37\22, 1487.331 |
| ''1487.9655''
| | |22\13, 1496.606 |
| | rowspan="2" |''15\9'' | | |29\17, 1508.612 |
| ''1500''
| |
| |''37\22'' | |
| ''1513.{{Overline|63}}''
| |
| |''22\13'' | |
| ''1523.0769''
| |
| |''29\17'' | |
| ''1581.{{Overline|81}}''
| |
| |- | | |- |
| |Solb, Reb
| |
| |Ιb | | |Ιb |
| |''33\19'' | | |33\19, 1535.991 |
| ''1563.1579''
| | |24\14, 1516.044 |
| |''24\14'' | | |39\23, 1499.565 |
| ''1542.8571''
| | |36\22, 1447.132 |
| |''39\23'' | | |21\13, 1428.579 |
| ''1526.087''
| | |27\17, 1404.570 |
| |''36\22'' | |
| ''1472.{{Overline|72}}''
| |
| |''21\13'' | |
| ''1453.15385''
| |
| |''27\17'' | |
| ''1429.4118''
| |
| |- | | |- |
| |'''Sol, Re'''
| |
| |'''Ι''' | | |'''Ι''' |
| |'''''34\19''''' | | |'''34\19,''' '''1582.537''' |
| '''''1610.5263''''' | | |'''25\14,''' '''1579.212''' |
| |'''''25\14''''' | | |'''41\23,''' '''1576.466''' |
| '''''1607.1429''''' | | |'''16\9, 1572.193''' |
| |'''''41\23''''' | | |'''39\22,''' '''1567.723''' |
| '''''1604.3478''''' | | |'''23\13,''' '''1564.635''' |
| |'''''16\9''''' | | |'''30\17,''' '''1560.633''' |
| '''''1600'''''
| |
| |'''''39\22''''' | |
| '''''1595.{{Overline|45}}''''' | |
| |'''''23\13''''' | |
| '''''1592.3077''''' | |
| |'''''30\17''''' | |
| '''''1588.2353''''' | |
| |- | | |- |
| |Sol#, Re#
| |
| |Ι# | | |Ι# |
| |''35\19'' | | |35\19, 1629.081 |
| ''1657.8947''
| | |26\14, 1642.380 |
| |''26\14'' | | |43\23, 1653.366 |
| ''1671.4286''
| | | rowspan="2" |17\9, 1670.455 |
| |''43\23'' | | |42\22, 1688.321 |
| ''1682.6087''
| | |25\13, 1700.690 |
| | rowspan="2" |''17\9'' | | |33\17, 1664.675 |
| ''1700''
| |
| |''42\22'' | |
| ''1718.''{{Overline|18}}
| |
| |''25\13'' | |
| ''1730.7692''
| |
| |''33\17'' | |
| ''1747.0588''
| |
| |- | | |- |
| |Dob, Solb
| |
| |Αb | | |Αb |
| |''37\19'' | | |37\19, 1722.172 |
| ''1752.6316''
| | |27\14, 1705.549 |
| |''27\14'' | | |44\23, 1691.817 |
| ''1735.7143''
| | |41\22, 1648.123 |
| |''44\23'' | | |24\13, 1632.662 |
| ''1721.7391''
| | |31\17, 1612.654 |
| |''41\22'' | |
| ''1677.{{Overline|27}}''
| |
| |''20\13'' | |
| ''1661.5385''
| |
| |''31\17'' | |
| ''1641.1761''
| |
| |- | | |- |
| !Do, Sol
| |
| !Α | | !Α |
| ! colspan="7" |''1800'' | | !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" |
| !Generators | | !Generators |
| Line 1,043: |
Line 472: |
| | -2 | | | -2 |
| |Mi, Si | | |Mi, Si |
| |major third | | |major third |
| |- | | |- |
| |3 | | |3 |
| |Mib, Sib | | |Mib, Sib |
| |minor third | | |minor third |
| | -3 | | | -3 |
| |Fa#, Do# | | |Fa#, Do# |
| Line 1,066: |
Line 495: |
| | -5 | | | -5 |
| |Do#, Sol# | | |Do#, Sol# |
| |augmented unison (chroma) | | |augmented unison (chroma) |
| |- | | |- |
| |6 | | |6 |
| Line 1,073: |
Line 502: |
| | -6 | | | -6 |
| |Re#, La# | | |Re#, La# |
| |augmented second | | |augmented second |
| |- | | |- |
| |7 | | |7 |
| Line 1,080: |
Line 509: |
| | -7 | | | -7 |
| |Mi#, Si# | | |Mi#, Si# |
| |augmented third | | |augmented third |
| |- | | |- |
| |8 | | |8 |
| Line 1,147: |
Line 576: |
| |} | | |} |
| ==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 |
| Line 1,203: |
Line 632: |
| |} | | |} |
| ==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 |
| Line 1,209: |
Line 638: |
| [[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}}]
| |
| | |
| [[Vals]]: {{val list|5ed5/3, 9ed5/3, 14ed5/3}}
| |
| ===='''Dorianic-Superpyth'''====
| |
| [[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}}] | | [[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}] |
|
| |
|
| [[Vals]]: {{val list|4ed14/9, 13ed14/9, 17ed14/9}} | | [[Optimal ET sequence]]: [[5ed5/3]], [[9ed5/3]], [[14ed5/3]] |
| ==Scale tree== | | ==Scale tree== |
| The spectrum looks like this: | | The spectrum looks like this: |
| {| class="wikitable" | | {{MOS tuning spectrum|Scale Signature=4L 1s<5/3>}} |
| ! colspan="3" rowspan="2" |Generator
| | |
| (bright)
| | == See also == |
| ! colspan="2" |Normalised
| | [[8L 2s (72/25-equivalent)]] - 8/1 complement of Scala Francisci |
| ! colspan="2" |''ed3\4''
| |
| ! rowspan="2" |L
| |
| ! rowspan="2" |s
| |
| ! rowspan="2" |L/s
| |
| ! rowspan="2" |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.{{Overline|81}}
| |
| |490.{{Overline|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.{{Overline|6}}
| |
| |693.{{Overline|3}}
| |
| |''190.{{Overline|90}}''
| |
| |''709.{{Overline|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.{{Overline|90}}
| |
| |695.{{Overline|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.{{Overline|594}}''
| |
| |''705.{{Overline|495}}''
| |
| |8
| |
| |5
| |
| |1.600
| |
| |
| |
| |-
| |
| |
| |
| |
| |
| |13\60
| |
| |192.{{Overline|692}}
| |
| |696.{{Overline|296}}
| |
| |''195''
| |
| |''705''
| |
| |13
| |
| |8
| |
| |1.625
| |
| |
| |
| |-
| |
| |
| |
| |5\23
| |
| |
| |
| |193.548
| |
| |696.774
| |
| |''195.652''
| |
| |''704.348''
| |
| |5
| |
| |3
| |
| |1.667
| |
| |
| |
| |-
| |
| |
| |
| |
| |
| |12\55
| |
| |194.{{Overline|594}}
| |
| |697.{{Overline|297}}
| |
| |''196.{{Overline|36}}''
| |
| |''703.{{Overline|63}}''
| |
| |12
| |
| |7
| |
| |1.714
| |
| |
| |
| |-
| |
| |
| |
| |7\32
| |
| |
| |
| |195.349
| |
| |697.674
| |
| |''196.875''
| |
| |''703.125''
| |
| |7
| |
| |4
| |
| |1.750
| |
| |
| |
| |-
| |
| |
| |
| |9\41
| |
| |
| |
| |196.{{Overline|36}}
| |
| |698.{{Overline|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
| |
| |''201.1765''
| |
| |''698.8235''
| |
| |19
| |
| |9
| |
| |2.111
| |
| |
| |
| |-
| |
| |
| |
| |17\76
| |
| |
| |
| |201.98
| |
| |700.99
| |
| |''201.316''
| |
| |''698.684''
| |
| |17
| |
| |8
| |
| |2.125
| |
| |
| |
| |-
| |
| |
| |
| |15\67
| |
| |
| |
| |202.247
| |
| |701.123
| |
| |''201.4925''
| |
| |''698.5075''
| |
| |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.{{Overline|54}}''
| |
| |''695.{{Overline|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
| |
| |''208.5365''
| |
| |''691.4635''
| |
| |19
| |
| |6
| |
| |3.167
| |
| |
| |
| |-
| |
| |
| |
| |16\69
| |
| |
| |
| |213.{{Overline|3}}
| |
| |706.{{Overline|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
| |
| |''210.9375''
| |
| |''689.0625''
| |
| |15
| |
| |4
| |
| |3.750
| |
| |
| |
| |-
| |
| |
| |
| |19\81
| |
| |
| |
| |217.143
| |
| |708.571
| |
| |''211.{{Overline|1}}''
| |
| |''688.{{Overline|8}}''
| |
| |19
| |
| |5
| |
| |3.800
| |
| |
| |
| |-
| |
| |4\17
| |
| |
| |
| |
| |
| |218.{{Overline|18}}
| |
| |709.{{Overline|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.{{Overline|72}}''
| |
| |''687.{{Overline|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.{{Overline|2}}
| |
| |711.{{Overline|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
| |
| |}
| |