|
|
(15 intermediate revisions by 6 users not shown) |
Line 1: |
Line 1: |
| This is the scale which occurs as the dominant reformed Mixolydian mode.
| | '''16edX''' is the scale which occurs as the dominant reformed Mixolydian mode. It also gives the period of the 16th-decade Roccocavallo branch of the Carrera temperament family. |
| ==Intervals== | | == Intervals== |
| {| class="wikitable" style="text-align: center" | | {| class="wikitable" |
| ! rowspan="3" |Degrees
| | |+ |
| ! colspan="3" rowspan="3" |Enneatonic | | !Decade |
| ! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian | | ! Period |
| ! colspan="9" |Dorian | | !Notes |
| |- | | |- |
| ! colspan="3" |Subpental
| | | 6\5 |
| ! colspan="3" |Pental
| | |90.000 |
| ! colspan="3" |Superpental
| | |Intense Aeolian-Subpental Dorian mode begins |
| |- | | |- |
| !Min-comma
| | |17\14 |
| !Med
| | | 91.071 |
| !Max+comma
| | | |
| !Min-comma
| |
| !Med
| |
| !Max+comma
| |
| !Min-comma
| |
| !Med
| |
| !Max+comma
| |
| !Min-comma
| |
| !Med
| |
| !Max+comma
| |
| |- | | |- |
| |1 | | |11\9 |
| |1#/2b
| | |91.667 |
| |G#/Jb
| | | Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins |
| |''G#/Ab''
| |
| |88.125-90
| |
| |91.071 | |
| | colspan="2" |89.792-93.542 | |
| |92.308
| |
| | colspan="2" |91.875-95.625
| |
| |95
| |
| | colspan="2" |93.5795-97.3295
| |
| |95.833
| |
| |96.429-98.304
| |
| |- | | |- |
| |2 | | |16\13 |
| |2 | | | 92.308 |
| |J
| | | |
| |''A''
| |
| |176.25-180
| |
| |182.143
| |
| | colspan="2" |179.583-187.083
| |
| |184.615
| |
| | colspan="2" |183.75-191.25 | |
| |190
| |
| | colspan="2" |187.159-194.659
| |
| |191.667
| |
| |192.857-196.607
| |
| |- | | |- |
| |3 | | |5\4 |
| |2#/3b
| | |93.750 |
| |J#/Ab
| | |Subpental Dorian mode ends, Pental Dorian mode begins |
| |''A#/Bb''
| |
| |264.375-270
| |
| |273.214
| |
| | colspan="2" |269.375-280.625
| |
| |276.923
| |
| | colspan="2" |275.625-286.875
| |
| |285
| |
| | colspan="2" |280.739-291.989 | |
| |287.5 | |
| |289.286-294.911
| |
| |- | | |- |
| |4 | | |24\19 |
| |3 | | |94.737 |
| |J
| | | |
| |''B''
| |
| |352.5-360
| |
| |364.286
| |
| | colspan="2" |358.167-373.167
| |
| |369.231
| |
| | colspan="2" |367.5-382.5 | |
| |380
| |
| | colspan="2" |374.318-389.318
| |
| |383.333
| |
| |385.714-393.214
| |
| |- | | |- |
| |5 | | |19\15 |
| |3#/4b | | |95.000 |
| |J#/Ab
| | | |
| |B#/Cb
| |
| |440.625-450
| |
| |455.357
| |
| | colspan="2" |448.958-467.708
| |
| |461.5385
| |
| | colspan="2" |459.375-476.125 | |
| |475
| |
| | colspan="2" |467.898-486.648
| |
| |479.167
| |
| |482.143-491.518
| |
| |- | | |- |
| |6 | | |14\11 |
| |4 | | |95.455 |
| |A
| | |Pental Dorian mode ends, Superpental Dorian mode begins |
| |''C''
| |
| |528.75-540
| |
| |546-429
| |
| | colspan="2" |538.75-561.25
| |
| |553.846
| |
| | colspan="2" |551.25-573.75
| |
| |570
| |
| | colspan="2" |561.477-583.977
| |
| |575
| |
| |578.571-589.821 | |
| |- | | |- |
| |7 | | |23\18 |
| |5 | | |95.833 |
| |A#/Bb
| | | |
| |''C#/Qb''
| |
| |616.875-630
| |
| |637.5
| |
| | colspan="2" |628.542-654.792
| |
| |646.154
| |
| | colspan="2" |643.125-669.375
| |
| |665
| |
| | colspan="2" |655.057-681.307
| |
| |670.833
| |
| |675-688.125 | |
| |- | | |- |
| |8
| | |9\7 |
| |5#/6b
| | |96.429 |
| |B
| | |Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins |
| |''Q''
| |
| |705-720
| |
| |728.571
| |
| | colspan="2" |718.333-748.333
| |
| |738.4615
| |
| | colspan="2" |735-765
| |
| |760
| |
| | colspan="2" |748.636-778.636
| |
| |766.667
| |
| |771.429-786.429
| |
| |-
| |
| |9 | |
| |6
| |
| |C
| |
| |''D''
| |
| |793.125-810
| |
| |819.642
| |
| | colspan="2" |808.125-841.875
| |
| |830.769
| |
| | colspan="2" |826.875-860.625
| |
| |855
| |
| | colspan="2" |842.216-875.966
| |
| |862.5
| |
| |867.857-884.732
| |
| |-
| |
| |10
| |
| |6#/7b
| |
| |C#/Db
| |
| |D#/Sb
| |
| |881.25-900
| |
| |910.714
| |
| | colspan="2" |897.917-935.417
| |
| |923.071
| |
| | colspan="2" |918.75-956.25
| |
| |950
| |
| | colspan="2" |935.7975-973.2975
| |
| |958.333
| |
| |964.286-983.036
| |
| |-
| |
| |11
| |
| |7
| |
| |D | |
| |''S''
| |
| |969.375-990
| |
| |1001.786
| |
| | colspan="2" |987.708-1028.958
| |
| |1015.385
| |
| | colspan="2" |1010.625-1051.875
| |
| |1045
| |
| | colspan="2" |1029.375-1070.605
| |
| |1054.167
| |
| |1060.714-1081.239
| |
| |-
| |
| |12
| |
| |7#/8b
| |
| |D#/Eb
| |
| |''S#/Eb''
| |
| |1057.5-1080
| |
| |1092.857
| |
| | colspan="2" |1077.5-1122.5
| |
| |1107.692
| |
| | colspan="2" |1102.5-1147.5
| |
| |1140
| |
| | colspan="2" |1122.9545-1167.9545
| |
| |1150
| |
| |1157.143-1179.643
| |
| |-
| |
| |13
| |
| |8
| |
| | colspan="2" |E
| |
| |1145.625-1170
| |
| |1183.929
| |
| | colspan="2" |1167.292-1216.042
| |
| |1200 | |
| | colspan="2" |1194.375-1241.125
| |
| |1235
| |
| | colspan="2" |1216.534-1265.284
| |
| |1245.833
| |
| |1253.571-1277.946
| |
| |- | | |- |
| |14 | | |31\24 |
| |8#/9b | | |96.875 |
| | colspan="2" |E#/Fb
| | | |
| |1233.75-1260
| |
| |1275
| |
| | colspan="2" |1257.083-1309.583
| |
| |1292.308
| |
| | colspan="2" |1286.25-1338.75 | |
| |1330
| |
| | colspan="2" |1310.114-1362.614
| |
| |1341.667
| |
| |1350-1376.25
| |
| |- | | |- |
| |15 | | |22\17 |
| |9 | | |97.059 |
| | colspan="2" |F
| | |Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins |
| |1321.875-1350
| |
| |1366.071
| |
| | colspan="2" |1346.875-1403.125
| |
| |1384.615
| |
| | colspan="2" |1378.125-1434.375 | |
| |1425
| |
| | colspan="2" |1403.693-1459.943
| |
| |1437.5
| |
| |1446.429-1474.554
| |
| |- | | |- |
| |16 | | |35\27 |
| |1
| |
| | colspan="2" |G
| |
| |1410-1440
| |
| |1457.143
| |
| | colspan="2" |1436.667-1496.667
| |
| |1476.923
| |
| | colspan="2" |1470-1530
| |
| |1520
| |
| | colspan="2" |1497.273-1557.273
| |
| |1533.333
| |
| |1542.857-1572.857
| |
| |}
| |
| {| class="wikitable" style="text-align: center"
| |
| ! rowspan="2" |Degrees
| |
| ! colspan="5" rowspan="2" |Enneatonic
| |
| ! colspan="4" |Mohajira
| |
| ! colspan="3" |Beatles
| |
| |-
| |
| !Min-comma
| |
| !''r¢''
| |
| !Med
| |
| !Max+comma
| |
| !Min-comma
| |
| !Med
| |
| !Max+comma
| |
| |-
| |
| |1
| |
| |1#/2b
| |
| | colspan="2" |F#/Gb
| |
| |G#/Jb
| |
| |''G#/Ab''
| |
| |94.554-96.429
| |
| | colspan="2" |''96.875''
| |
| | colspan="2" |95.184-98.934
| |
| |97.222 | | |97.222 |
| |97.5-99.375 | | | |
| |-
| |
| |2
| |
| |2
| |
| | colspan="2" |G
| |
| |J
| |
| |''A''
| |
| |189.107-192.857
| |
| | colspan="2" |''193.75''
| |
| | colspan="2" |190.368-197.868
| |
| |194.444
| |
| |195-198.75
| |
| |-
| |
| |3
| |
| |2#/3b
| |
| |G#/Jb
| |
| |''G#/Ab''
| |
| |J#/Ab
| |
| |''A#/Bb''
| |
| |283.661-289.286
| |
| | colspan="2" |''290.625''
| |
| | colspan="2" |285.5515-296.8015
| |
| |291.667
| |
| |292.5-298.125
| |
| |- | | |- |
| |4 | | | 13\10 |
| |3 | | |97.500 |
| |J
| | |Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins |
| |''A''
| |
| |J
| |
| |''B''
| |
| |378.214-385.714
| |
| | colspan="2" |''387.5''
| |
| | colspan="2" |380.735-395.735 | |
| |388.889
| |
| |390-397.5
| |
| |- | | |- |
| |5 | | |17\13 |
| |3#/4b | | |98.077 |
| |J#/Ab
| | | |
| |''A#/Bb''
| |
| |J#/Ab
| |
| |B#/Cb
| |
| |472.767-482.143
| |
| | colspan="2" |''484.375''
| |
| | colspan="2" |475.919-494.669
| |
| |486.111
| |
| |487.5-496.875
| |
| |-
| |
| |6
| |
| |4
| |
| |A
| |
| |''B''
| |
| |A
| |
| |''C''
| |
| |567.321-578.571
| |
| | colspan="2" |''581.25''
| |
| | colspan="2" |571.103-593.603
| |
| |583.333 | |
| |585-596.25
| |
| |-
| |
| |7
| |
| |5
| |
| |B
| |
| |''H''
| |
| |A#/Bb
| |
| |''C#/Qb''
| |
| |661.875-675
| |
| | colspan="2" |''678.125''
| |
| | colspan="2" |666.287-692.537
| |
| |680.556
| |
| |682.5-695.625
| |
| |-
| |
| |8
| |
| |5#/6b
| |
| |B#/Hb
| |
| |''H#/Cb''
| |
| |B
| |
| |''Q''
| |
| |756.429-771.429
| |
| | colspan="2" |''775''
| |
| | colspan="2" |761.471-791.471
| |
| |777.778
| |
| |780-795
| |
| |-
| |
| |9
| |
| |6
| |
| |H
| |
| |''C''
| |
| |C
| |
| |''D''
| |
| |850.982-867.857
| |
| | colspan="2" |''871.875''
| |
| | colspan="2" |856.654-890.404
| |
| |875
| |
| |877.5-894.375
| |
| |- | | |- |
| |10 | | |21\16 |
| |6#/7b | | |98.438 |
| |H#/Cb
| | |Subpental Mixolydian mode ends, Pental Mixolydian mode begins |
| |''C#/Db''
| |
| |C#/Db
| |
| |D#/Sb
| |
| |945.536-964.286
| |
| | colspan="2" |''968.75''
| |
| | colspan="2" |951.738-989.238
| |
| |972.222
| |
| |975-993.75 | |
| |- | | |- |
| |11 | | |25\19 |
| |7
| |
| |C
| |
| |''D''
| |
| |D
| |
| |''S''
| |
| |1040.089-1060.714
| |
| | colspan="2" |''1065.625''
| |
| | colspan="2" |1047.022-1088.252
| |
| |1069.444
| |
| |1072.5-1093.125
| |
| |-
| |
| |12
| |
| |7#/8b
| |
| |C#/Db
| |
| |''D#/Sb''
| |
| |D#/Eb
| |
| |''S#/Eb''
| |
| |1134.643-1157.143
| |
| | colspan="2" |''1162.5''
| |
| | colspan="2" |1142.203-1187.206
| |
| |1166.667
| |
| |1170-1192.5
| |
| |-
| |
| |13
| |
| |8
| |
| |D
| |
| |''S''
| |
| | colspan="2" |E
| |
| |1229.196-1253.571
| |
| | colspan="2" |''1259.375''
| |
| | colspan="2" |1237.39-1286.14
| |
| |1263.889
| |
| |1267.5-1291.875
| |
| |-
| |
| |14
| |
| |8#/9b
| |
| |D#/Eb
| |
| |''S#/Eb''
| |
| | colspan="2" |E#/Fb
| |
| |1323.75-1350
| |
| | colspan="2" |''1356.25''
| |
| | colspan="2" |1332.5735-1385.0735
| |
| |1361.111
| |
| |1365-1391.25
| |
| |-
| |
| |15
| |
| |9
| |
| | colspan="2" |E
| |
| | colspan="2" |F
| |
| |1418.304-1446.429
| |
| | colspan="2" |''1453.125''
| |
| | colspan="2" |1427.757-1484.007
| |
| |1458.333
| |
| |1462.5-1490.625
| |
| |-
| |
| |16
| |
| |1
| |
| | colspan="2" |F
| |
| | colspan="2" |G
| |
| |1512.857-1542.857
| |
| | colspan="2" |''1550''
| |
| | colspan="2" |1522.941-1582.941
| |
| |1555.556
| |
| |1560-1590
| |
| |}
| |
| {| class="wikitable" style="text-align: center"
| |
| |-
| |
| ! rowspan="4" |Degrees
| |
| ! colspan="3" rowspan="4" |Enneatonic
| |
| ! colspan="12" |Mixolydian
| |
| ! colspan="3" rowspan="3" |Mixolydian-Ionian
| |
| |-
| |
| ! colspan="3" rowspan="2" |Subpental
| |
| ! colspan="3" rowspan="2" |Pental
| |
| ! colspan="6" |Superpental
| |
| |-
| |
| ! colspan="3" |Soft
| |
| ! colspan="3" |Intense
| |
| |-
| |
| ! width="4%" |Min-comma
| |
| !Med
| |
| ! width="4%" |Max+comma
| |
| ! width="4%" |Min-comma
| |
| !Med
| |
| ! width="4%" |Max+comma
| |
| ! width="4%" |Min-comma
| |
| !Med
| |
| ! width="4%" |Max+comma
| |
| ! width="4%" |Min-comma
| |
| !Med
| |
| ! width="4%" |Max+comma
| |
| !Min-comma
| |
| !Med
| |
| !Max+comma
| |
| |-
| |
| | |1
| |
| |1#/2b
| |
| | colspan="2" |F#/Gb
| |
| |95.625-97.5
| |
| |98.077
| |
| | colspan="2" |96.5625-100.3125
| |
| |98.684 | | |98.684 |
| | colspan="2" |98.125-101.875 | | | |
| |100.781
| |
| | colspan="2" |98.987-102.737
| |
| |102.155
| |
| | colspan="2" |101.573-105.323
| |
| |103.6765
| |
| |105-106.875
| |
| |- | | |- |
| | |2 | | |29\22 |
| |2
| | |98.864 |
| | colspan="2" |G
| | | |
| |191.25-195
| |
| |196.154
| |
| | colspan="2" |193.125-200.625
| |
| |197.368
| |
| | colspan="2" |196.25-203.75
| |
| |201.5625 | |
| | colspan="2" |197.974-205.474 | |
| |204.31
| |
| | colspan="2" |203.147-210.647
| |
| |207.353
| |
| |210-213.75
| |
| |- | | |- |
| | |3 | | |33\25 |
| |2#/3b
| | |99.000 |
| |G#/Jb
| | | |
| |''G#/Ab''
| |
| |286.875-292.5
| |
| |294.231
| |
| | colspan="2" |289.6875-300.9375
| |
| |296.053
| |
| | colspan="2" |294.375-305.625
| |
| |302.344
| |
| | colspan="2" |296.961-308.211
| |
| |306.4655 | |
| | colspan="2" |304.72-315.97 | |
| |311.029
| |
| |315-320.625
| |
| |- | | |- |
| | |4
| | |4\3 |
| |3
| | |100.000 |
| |J | | |Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins |
| |''A''
| |
| |382.5-390
| |
| |392.308
| |
| | colspan="2" |386.25-401.25
| |
| |394.737 | |
| | colspan="2" |392.5-407.5
| |
| |403.125
| |
| | colspan="2" |395.948-410.948
| |
| |408.621
| |
| | colspan="2" |406.293-421.293
| |
| |414.706
| |
| |420-427.5
| |
| |- | | |- |
| | |5 | | |19\14 |
| |3#/4b
| | |101.786 |
| |J#/Ab
| | | |
| |''A#/Bb''
| |
| |478.125-487.5
| |
| |490.385
| |
| | colspan="2" |482.8125-501.5625
| |
| |493.421
| |
| | colspan="2" |490.625-509.375
| |
| |503.906
| |
| | colspan="2" |494.935-513.685
| |
| |510.776
| |
| | colspan="2" |507.866-526.616
| |
| |518.382
| |
| |525-534.375
| |
| |-
| |
| | |6
| |
| |4
| |
| |A
| |
| |''B''
| |
| |573.75-585
| |
| |588.4615
| |
| | colspan="2" |579.375-601.875
| |
| |592.105
| |
| | colspan="2" |588.75-611.25
| |
| |604.6875
| |
| | colspan="2" |593.922-616.422
| |
| |612.931
| |
| | colspan="2" |609.44-631.94
| |
| |622.059 | |
| |630-641.25
| |
| |-
| |
| | |7 | |
| |5
| |
| |B
| |
| |''H''
| |
| |669.375-682.5
| |
| |686.5385
| |
| | colspan="2" |675.9375-702.1875
| |
| |690.7895
| |
| | colspan="2" |687.875-713.125
| |
| |705.469
| |
| | colspan="2" |692.9095-719.1595
| |
| |715.086
| |
| | colspan="2" |711.012-737.262
| |
| |725.735
| |
| |735-748.125
| |
| |-
| |
| |8
| |
| |5#/6b
| |
| |B#/Hb
| |
| |''H#/Cb''
| |
| |765-780
| |
| |784.615
| |
| | colspan="2" |772.5-802.5
| |
| |789.474
| |
| | colspan="2" |785-815
| |
| |806.25
| |
| | colspan="2" |791.897-821.897
| |
| |817.241
| |
| | colspan="2" |812.586-842.586
| |
| |829.412
| |
| |840-855
| |
| |-
| |
| |9
| |
| |6
| |
| |H
| |
| |''C''
| |
| |860.625-877.5
| |
| |882.962
| |
| | colspan="2" |869.0625-903.8125
| |
| |888.158
| |
| | colspan="2" |883.125-916.875
| |
| |907.031
| |
| | colspan="2" |890.884-924.624
| |
| |919.397
| |
| | colspan="2" |914.1595-947.9095
| |
| |933.088
| |
| |945-961.875
| |
| |-
| |
| |10
| |
| |6#/7b
| |
| |H#/Cb
| |
| |''C#/Db''
| |
| |956.25-975
| |
| |980.769
| |
| | colspan="2" |965.625-1003.125
| |
| |986.842
| |
| | colspan="2" |981.25-1018.75
| |
| |1007.8125
| |
| | colspan="2" |989.871-1027.371
| |
| |1021.552
| |
| | colspan="2" |1015.733-1053.233
| |
| |1036.765
| |
| |1050-1068.75
| |
| |- | | |- |
| |11 | | |15\11 |
| |7 | | |102.273 |
| |C
| | |Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins |
| |''D''
| |
| |1051.875-1072.5
| |
| |1078.846
| |
| | colspan="2" |1062.1875-1103.4375
| |
| |1085.526 | |
| | colspan="2" |1079.375-1120.625
| |
| |1108.594
| |
| | colspan="2" |1088.858-1130.108
| |
| |1123.707
| |
| | colspan="2" |117.306-1158.556
| |
| |1140.441
| |
| |1155-1175.625
| |
| |- | | |- |
| |12 | | |26\19 |
| |7#/8b | | |102.632 |
| |C#/Db
| | | |
| |''D#/Sb''
| |
| |1147.5-1170
| |
| |1176.923
| |
| | colspan="2" |1158.75-1203.75
| |
| |1184.2105
| |
| | colspan="2" |1177.5-1222.5
| |
| |1209.375
| |
| | colspan="2" |1187.845-1232.845 | |
| |1225.862
| |
| | colspan="2" |1218.879-1263.879
| |
| |1244.118
| |
| |1260-1282.5
| |
| |- | | |- |
| |13 | | |11\8 |
| |8
| | |103.125 |
| |D | | |Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins |
| |''S''
| |
| |1243.125-1267.5
| |
| |1275
| |
| | colspan="2" |1255.3125-1304.0625
| |
| |1282.895
| |
| | colspan="2" |1275.625-1324.325 | |
| |1310.156
| |
| | colspan="2" |1286.832-1335.585
| |
| |1328.017
| |
| | colspan="2" |1320.453-1369.203
| |
| |1347.794
| |
| |1365-1389.375
| |
| |- | | |- |
| |14 | | |18\13 |
| |8#/9b | | |103.846 |
| |D#/Eb
| | | |
| |''S#/Eb''
| |
| |1338.25-1365
| |
| |1373.077
| |
| | colspan="2" |1351.875-1404.375
| |
| |1381.579
| |
| | colspan="2" |1373.75-1426.25
| |
| |1410.9375
| |
| | colspan="2" |1385.819-1438.319 | |
| |1430.172
| |
| | colspan="2" |1422.026-1474.526
| |
| |1451.471
| |
| |1470-1496.25
| |
| |- | | |- |
| |15 | | |25\18 |
| |9 | | |104.167 |
| | colspan="2" |E
| | | |
| |1434.375-1462.5
| |
| |1471.154
| |
| | colspan="2" |1448.4375-1504.6875
| |
| |1480.263
| |
| | colspan="2" |1471.875-1528.125
| |
| |1511.719
| |
| | colspan="2" |1484.806-1541.056 | |
| |1532.328
| |
| | colspan="2" |1523.599-1579.849
| |
| |1555.147
| |
| |1575-1603.125
| |
| |- | | |- |
| |16 | | |7\5 |
| |1
| | |105.000 |
| | colspan="2" |F
| | |Mixolydian-Ionian mode ends |
| |1530-1560
| |
| |1569.231
| |
| | colspan="2" |1545-1605
| |
| |1578.947
| |
| | colspan="2" |1570-1630
| |
| |1612.5
| |
| | colspan="2" |1583.793-1643.793. | |
| |1634.483
| |
| | colspan="2" |1625.172-1685.172
| |
| |1658.8235
| |
| |1680-1710 | |
| |}Relative cents | | |}Relative cents |
| {| class="wikitable" style="text-align: center" | | {| class="wikitable" style="text-align: center" |
Line 729: |
Line 120: |
| !Intense Aeolian-Subpental Dorian | | !Intense Aeolian-Subpental Dorian |
| !Dorian | | !Dorian |
| | !Dorian-Mixolydian |
| |- | | |- |
| |1 | | |1 |
Line 734: |
Line 126: |
| |G#/Jb | | |G#/Jb |
| |''G#/Ab'' | | |''G#/Ab'' |
| |90.625 | | |''90.625'' |
| |''93.75'' | | |''93.75'' |
| | |''96.875'' |
| |- | | |- |
| |2 | | |2 |
| |2 | | | 2 |
| |J | | |J |
| |''A'' | | |''A'' |
| |181.25 | | |''181.25'' |
| |''187.5'' | | |''187.5'' |
| | |''193.75'' |
| |- | | |- |
| |3 | | |3 |
Line 748: |
Line 142: |
| |J#/Ab | | |J#/Ab |
| |''A#/Bb'' | | |''A#/Bb'' |
| |271.875 | | |''271.875'' |
| |''281.25'' | | |''281.25'' |
| | |''290.625'' |
| |- | | |- |
| |4 | | |4 |
Line 755: |
Line 150: |
| |J | | |J |
| |''B'' | | |''B'' |
| |362.5 | | |''362.5'' |
| |''375'' | | |''375'' |
| | |''387.5'' |
| |- | | |- |
| |5 | | |5 |
Line 762: |
Line 158: |
| |J#/Ab | | |J#/Ab |
| |B#/Cb | | |B#/Cb |
| |453.125 | | |''453.125'' |
| |''468.75'' | | |''468.75'' |
| | |''484.375'' |
| |- | | |- |
| |6 | | |6 |
Line 769: |
Line 166: |
| |A | | |A |
| |''C'' | | |''C'' |
| |543.75 | | |''543.75'' |
| |''562.5'' | | |''562.5'' |
| | |''581.25'' |
| |- | | |- |
| |7 | | |7 |
Line 776: |
Line 174: |
| |A#/Bb | | |A#/Bb |
| |''C#/Qb'' | | |''C#/Qb'' |
| |633.375 | | |''633.375'' |
| |''656.25'' | | |''656.25'' |
| | |''678.125'' |
| |- | | |- |
| |8 | | |8 |
Line 783: |
Line 182: |
| |B | | |B |
| |''Q'' | | |''Q'' |
| |725 | | |''725'' |
| |''750'' | | |''750'' |
| | |''775'' |
| |- | | |- |
| |9 | | |9 |
Line 790: |
Line 190: |
| |C | | |C |
| |''D'' | | |''D'' |
| |815.625 | | |''815.625'' |
| |''843.75'' | | |''843.75'' |
| | |''871.875'' |
| |- | | |- |
| |10 | | |10 |
| |6#/7b | | |6#/7b |
| |C#/Db | | | C#/Db |
| |D#/Sb | | |D#/Sb |
| |906.25 | | |''906.25'' |
| |''937.5'' | | |''937.5'' |
| | |''968.75'' |
| |- | | |- |
| |11 | | |11 |
Line 804: |
Line 206: |
| |D | | |D |
| |''S'' | | |''S'' |
| |996.875 | | |''996.875'' |
| |''1031.25'' | | |''1031.25'' |
| | |''1065.625'' |
| |- | | |- |
| |12 | | |12 |
| |7#/8b | | | 7#/8b |
| |D#/Eb | | |D#/Eb |
| |''S#/Eb'' | | |''S#/Eb'' |
| |1087.5 | | |''1087.5'' |
| |''1125'' | | |''1125'' |
| | |''1162.5'' |
| |- | | |- |
| |13 | | |13 |
| |8 | | |8 |
| | colspan="2" |E | | | colspan="2" | E |
| |1178.125 | | |''1178.125'' |
| |''1218.75'' | | |''1218.75'' |
| | |''1259.375'' |
| |- | | |- |
| |14 | | |14 |
| |8#/9b | | |8#/9b |
| | colspan="2" |E#/Fb | | | colspan="2" |E#/Fb |
| |1268.75 | | |''1268.75'' |
| |''1312.5'' | | |''1312.5'' |
| | |''1356.25'' |
| |- | | |- |
| |15 | | |15 |
| |9 | | |9 |
| | colspan="2" |F | | | colspan="2" |F |
| |1359.375 | | |''1359.375'' |
| |''1406.25'' | | |''1406.25'' |
| | |''1453.125'' |
| |- | | |- |
| |16 | | |16 |
| |1 | | |1 |
| | colspan="2" |G | | | colspan="2" |G |
| |1450 | | |''1450'' |
| |''1500'' | | |''1500'' |
| | |''1550'' |
| |} | | |} |
| {| class="wikitable" style="text-align: center" | | {| class="wikitable" style="text-align: center" |
Line 870: |
Line 278: |
| |''412.5'' | | |''412.5'' |
| |- | | |- |
| | |5 | | | | 5 |
| |3#/4b | | |3#/4b |
| |J#/Ab | | |J#/Ab |
Line 884: |
Line 292: |
| |''618.75'' | | |''618.75'' |
| |- | | |- |
| | |7 | | | | 7 |
| |5 | | |5 |
| |B | | |B |
Line 935: |
Line 343: |
| |14 | | |14 |
| |8#/9b | | |8#/9b |
| |D#/Eb | | | D#/Eb |
| |''S#/Eb'' | | |''S#/Eb'' |
| |''1400'' | | |''1400'' |
| |''1443.75'' | | |''1443.75'' |
| |- | | |- |
| |15 | | | 15 |
| |9 | | |9 |
| | colspan="2" |E | | | colspan="2" |E |
Line 951: |
Line 359: |
| |''1600'' | | |''1600'' |
| |''1650'' | | |''1650'' |
| |}Golden/Pyrite Tunings±13¢
| |
| {| class="wikitable" style="text-align: center"
| |
| ! rowspan="2" |Degrees
| |
| ! colspan="3" rowspan="2" |Enneatonic
| |
| ! rowspan="2" |Intense Aeolian-Subpental Dorian
| |
| ! colspan="3" |Dorian
| |
| |-
| |
| !Subpental
| |
| !Pental
| |
| !Superpental
| |
| |-
| |
| |1
| |
| |1#/2b
| |
| |G#/Jb
| |
| |''G#/Ab''
| |
| |90.428-92.053
| |
| |91.303-92.928
| |
| |94.329-95.943
| |
| |94.917-96.542
| |
| |-
| |
| |2
| |
| |2
| |
| |J
| |
| |''A''
| |
| |180.856-184.106
| |
| |182.606-185.856
| |
| |188.2585-191.9085
| |
| |189.834-193.084
| |
| |-
| |
| |3
| |
| |2#/3b
| |
| |J#/Ab
| |
| |''A#/Bb''
| |
| |271.2845-276.159
| |
| |273.909-278.784
| |
| |282.988-287.863
| |
| |284.751-289.626
| |
| |-
| |
| |4
| |
| |3
| |
| |J
| |
| |''B''
| |
| |361.712-368.213
| |
| |365.212-371.712
| |
| |377.317-383.817
| |
| |379.668-386.168
| |
| |-
| |
| |5
| |
| |3#/4b
| |
| |J#/Ab
| |
| |B#/Cb
| |
| |452.141-460.266
| |
| |456.5155-464.6405
| |
| |471.646-479.771
| |
| |474.585-482.71
| |
| |-
| |
| |6
| |
| |4
| |
| |A
| |
| |''C''
| |
| |542.569-552.319
| |
| |547.819-557.569
| |
| |565.974-575.726
| |
| |569.502-579.252
| |
| |-
| |
| |7
| |
| |5
| |
| |A#/Bb
| |
| |''C#/Qb''
| |
| |632.997-644.372
| |
| |639.122-650.497
| |
| |660.305-671.68
| |
| |664.419-675.794
| |
| |-
| |
| |8
| |
| |5#/6b
| |
| |B
| |
| |''Q''
| |
| |723.425-736.425
| |
| |730.425-743.425
| |
| |754.634-767.634
| |
| |759.336-771.336
| |
| |-
| |
| |9
| |
| |6
| |
| |C
| |
| |''D''
| |
| |813.854-828.479
| |
| |821.728-836.353
| |
| |848.963-863.588
| |
| |854.253-868.878
| |
| |-
| |
| |10
| |
| |6#/7b
| |
| |C#/Db
| |
| |D#/Sb
| |
| |904.282-920.532
| |
| |913.031-920.281
| |
| |943.293-959.543
| |
| |949.17-965.42
| |
| |-
| |
| |11
| |
| |7
| |
| |D
| |
| |''S''
| |
| |994.71-1012.585
| |
| |1004.334-1022.209
| |
| |1037.622-1055.497
| |
| |1044.087-1061.962
| |
| |-
| |
| |12
| |
| |7#/8b
| |
| |D#/Eb
| |
| |''S#/Eb''
| |
| |1085.138-1104.638
| |
| |1095.637-1115.137
| |
| |1131.951-1151.451
| |
| |1139.004-1158.503
| |
| |-
| |
| |13
| |
| |8
| |
| | colspan="2" |E
| |
| |1175.566-1106.691
| |
| |1186.94-1208.065
| |
| |1226.38-1247.405
| |
| |1233.921-1255.046
| |
| |-
| |
| |14
| |
| |8#/9b
| |
| | colspan="2" |E#/Fb
| |
| |1265.9945-1288.7445
| |
| |1278.2435-1300.9935
| |
| |1320.61-1343.36
| |
| |1328.838-1351.588
| |
| |-
| |
| |15
| |
| |9
| |
| | colspan="2" |F
| |
| |1356.423-1380.798
| |
| |1369.547-1393.922
| |
| |1414.939-1439.314
| |
| |1423.755-1448.13
| |
| |-
| |
| |16
| |
| |1
| |
| | colspan="2" |G
| |
| |1446.851-1472.851
| |
| |1460.85-1486.85
| |
| |1509.268-1535.268
| |
| |1518.672-1544.672
| |
| |}
| |
| {| class="wikitable" style="text-align: center"
| |
| !Degrees
| |
| ! colspan="5" |Enneatonic
| |
| !Mohajira
| |
| !Beatles
| |
| |-
| |
| |1
| |
| |1#/2b
| |
| | colspan="2" |F#/Gb
| |
| |G#/Jb
| |
| |''G#/Ab''
| |
| |96.1185-97.7435
| |
| |96.364-97.989
| |
| |-
| |
| |2
| |
| |2
| |
| | colspan="2" |G
| |
| |J
| |
| |''A''
| |
| |192.237-195.487
| |
| |192.728-195.978
| |
| |-
| |
| |3
| |
| |2#/3b
| |
| |G#/Jb
| |
| |''G#/Ab''
| |
| |J#/Ab
| |
| |''A#/Bb''
| |
| |288.355-293.23
| |
| |289.092-293.965
| |
| |-
| |
| |4
| |
| |3
| |
| |J
| |
| |''A''
| |
| |J
| |
| |''B''
| |
| |384.474-390.974
| |
| |385.456-391.956
| |
| |-
| |
| |5
| |
| |3#/4b
| |
| |J#/Ab
| |
| |''A#/Bb''
| |
| |J#/Ab
| |
| |B#/Cb
| |
| |480.592-488.717
| |
| |481.82-489.945
| |
| |-
| |
| |6
| |
| |4
| |
| |A
| |
| |''B''
| |
| |A
| |
| |''C''
| |
| |576.711-585.961
| |
| |578.184-587.934
| |
| |-
| |
| |7
| |
| |5
| |
| |B
| |
| |''H''
| |
| |A#/Bb
| |
| |''C#/Qb''
| |
| |672.829-684.454
| |
| |674.548-685.923
| |
| |-
| |
| |8
| |
| |5#/6b
| |
| |B#/Hb
| |
| |''H#/Cb''
| |
| |B
| |
| |''Q''
| |
| |768.948-781.948
| |
| |770.912-783.912
| |
| |-
| |
| |9
| |
| |6
| |
| |H
| |
| |''C''
| |
| |C
| |
| |''D''
| |
| |865.066-879.691
| |
| |867.276-881.901
| |
| |-
| |
| |10
| |
| |6#/7b
| |
| |H#/Cb
| |
| |''C#/Db''
| |
| |C#/Db
| |
| |D#/Sb
| |
| |961.185-977.435
| |
| |963.6395-979.8895
| |
| |-
| |
| |11
| |
| |7
| |
| |C
| |
| |''D''
| |
| |D
| |
| |''S''
| |
| |1057.303-1075.178
| |
| |1060.0035-1077.8785
| |
| |-
| |
| |12
| |
| |7#/8b
| |
| |C#/Db
| |
| |''D#/Sb''
| |
| |D#/Eb
| |
| |''S#/Eb''
| |
| |1153.422-1172.921
| |
| |1156.367-1175.867
| |
| |-
| |
| |13
| |
| |8
| |
| |D
| |
| |''S''
| |
| | colspan="2" |E
| |
| |1249.54-1270.665
| |
| |1252.731-1273.856
| |
| |-
| |
| |14
| |
| |8#/9b
| |
| |D#/Eb
| |
| |''S#/Eb''
| |
| | colspan="2" |E#/Fb
| |
| |1345.659-1368.409
| |
| |1349.095-1372.345
| |
| |-
| |
| |15
| |
| |9
| |
| | colspan="2" |E
| |
| | colspan="2" |F
| |
| |1441.777-1366.152
| |
| |1445.459-1469.834
| |
| |-
| |
| |16
| |
| |1
| |
| | colspan="2" |F
| |
| | colspan="2" |G
| |
| |1537.8955-1563.8955
| |
| |1541.823-1577.823
| |
| |}
| |
| {| class="wikitable" style="text-align: center"
| |
| |-
| |
| ! rowspan="3" |Degrees
| |
| ! colspan="3" rowspan="3" |Enneatonic
| |
| ! colspan="4" |Mixolydian
| |
| ! rowspan="3" |Mixolydian-Ionian
| |
| |-
| |
| ! rowspan="2" |Subpental
| |
| ! rowspan="2" |Pental
| |
| ! colspan="2" |Superpental
| |
| |-
| |
| !Soft
| |
| !Intense
| |
| |-
| |
| |1
| |
| |1#/2b
| |
| | colspan="2" |F#/Gb
| |
| |97.364-98.989
| |
| |97.787-99.412
| |
| |99.998-101.623
| |
| |101.648-103.273
| |
| |102.785-104.41
| |
| |-
| |
| | |2
| |
| |2
| |
| | colspan="2" |G
| |
| |194.7275-197.9775
| |
| |195.5745-198.8245
| |
| |199.9955-203.2455
| |
| |203.296-206.546
| |
| |205.57-208.82
| |
| |-
| |
| |3
| |
| |2#/3b
| |
| |G#/Jb
| |
| |''G#/Ab''
| |
| |292.091-296.966
| |
| |293.362-298.237
| |
| |299.993-304.868
| |
| |304.944-309.819
| |
| |308.356-313.231
| |
| |-
| |
| | |4
| |
| |3
| |
| |J
| |
| |''A''
| |
| |389.455-395.955
| |
| |391.149-397.649
| |
| |399.991-406.491
| |
| |406.592-413.092
| |
| |411.141-417.641
| |
| |-
| |
| |5
| |
| |3#/4b
| |
| |J#/Ab
| |
| |''A#/Bb''
| |
| |486.819-494.944
| |
| |488.936-497.061
| |
| |499.989-508.114
| |
| |508.24-516.365
| |
| |513.926-522.051
| |
| |-
| |
| | |6
| |
| |4
| |
| |A
| |
| |''B''
| |
| |584.183-593.933
| |
| |586.724-596.474
| |
| |599.987-609.737
| |
| |609.888-619.638
| |
| |616.711-626.461
| |
| |-
| |
| |7
| |
| |5
| |
| |B
| |
| |''H''
| |
| |681.546-692.921
| |
| |684.571-695.886
| |
| |699.984-711.359
| |
| |711.5355-722.9105
| |
| |719.496-730.871
| |
| |-
| |
| |8
| |
| |5#/6b
| |
| |B#/Hb
| |
| |''H#/Cb''
| |
| |778.91-791.91
| |
| |782.298-795.298.
| |
| |799.982-812.982
| |
| |813.1835-826.1835
| |
| |822.282-835.282
| |
| |-
| |
| |9
| |
| |6
| |
| |H
| |
| |''C''
| |
| |876.274-890.899
| |
| |880.085-894.71
| |
| |899.98-914.605
| |
| |914.831-929.456
| |
| |925.067-939.692
| |
| |-
| |
| |10
| |
| |6#/7b
| |
| |H#/Cb
| |
| |''C#/Db''
| |
| |973.638-989.888
| |
| |977.873-994.123
| |
| |999.978-1016.238
| |
| |1016.479-1032.729
| |
| |1027.852-1044.102
| |
| |-
| |
| |11
| |
| |7
| |
| |C
| |
| |''D''
| |
| |1071.0015-1088.8765
| |
| |1075.66-1093.535
| |
| |1099.975-1117.85
| |
| |1118.127-1136.002
| |
| |1130.637-1148.512
| |
| |-
| |
| |12
| |
| |7#/8b
| |
| |C#/Db
| |
| |''D#/Sb''
| |
| |1168.365-1187.865
| |
| |1173.447-1192.947
| |
| |1199.973-1219.473
| |
| |1219.775-1239.275
| |
| |1233.422-1252.922
| |
| |-
| |
| |13
| |
| |8
| |
| |D
| |
| |''S''
| |
| |1265.729-1286.854
| |
| |1271.234-1292.359
| |
| |1299.971-1321.096
| |
| |1321.423-1342.548
| |
| |1336.208-1357.333
| |
| |-
| |
| |14
| |
| |8#/9b
| |
| |D#/Eb
| |
| |''S#/Eb''
| |
| |1363.093-1385.843
| |
| |1369.022-1391.772
| |
| |1399.968-1422.719
| |
| |1423.071-1445.821
| |
| |1438.993-1461.743
| |
| |-
| |
| |15
| |
| |9
| |
| | colspan="2" |E
| |
| |1460.457-1484.832
| |
| |1455.809-1491.184
| |
| |1499.9665-1524.3415
| |
| |1524.719-1549.094
| |
| |1541.778-1566.153
| |
| |-
| |
| |16
| |
| |1
| |
| | colspan="2" |F
| |
| |1557.82-1583.82
| |
| |1564.596-1590.596
| |
| |1599.964-1625.964
| |
| |1626.366-1652.366
| |
| |1644.563-1670.563
| |
| |}By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.686 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of [[110edo]], and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step. | | |}By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.686 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of [[110edo]], and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step. |
| [[Category:16-tone]] | | ==See also== |
| [[Category:ed7/3]] | | *[[16ed5/2]] - equal division of the classic major tenth |
| [[Category:edX]]
| | *[[16ed7/3]] - equal division of the septimal minor tenth |
| [[Category:todo:add_definition]] | | |
| [[Category:todo:unify_precision]] | | [[Category:16-tone scales]] |
| | [[Category:EdX]] |