User:Moremajorthanmajor/9edIX: Difference between revisions

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This Long Common Practice minor mode is the neutral scale of the Fujiyama temperament family.
This Long Common Practice minor mode gives the wide values for the period of the Greater [[Ennealimmal]] and [[Tritrizo clan|Tritrizo temperaments]].
 
== Intervals==
==Intervals==
 
{| class="wikitable"
{| class="wikitable"
|+
!Nonet
!Period
!Notes
|-
|-
! rowspan="3" |Degrees
|1/1
! colspan="5" |Soft Phrygian
|''133.333''
! colspan="11" |Phrygian
|Soft Phrygian mode begins
|-
|25\24
|''138.889''
|
|-
|24/23
|139.130
|
|-
|23/22
| 139.394
|
|-
|22\21
|139.683
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|-
|-
! rowspan="2" |Minimum
|21\20
! rowspan="2" |Min-Med±13¢
|140.000
! rowspan="2" |Median
|
! rowspan="2" |Min-Max/Med-Max±13¢
! rowspan="2" |Maximum
! colspan="5" |Thirdtone
! colspan="6" |Semitone
|-
|-
!Minimum
|20\19
!Min-Med/Min-Max±13¢
|140.351
!Median
|
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!15/7±13¢
!Maximum
|-
|-
|1
|19\18
|''133.333''
| 140.741
|137.784-140.673
|
|139.394
|138.057-140.9455
| colspan="2" |139.6825
|138.6045-142.053
|140.741-140.952
|139.8-142.744
| colspan="2" |142.222-142.857
|142.075-145.468
|144-''144.444''
|143.084-146.444
|145.16-148.049
|146.667
|-
|-
|2
|37\35
|''266.667''
|140.952
|275.568-281.346
|
|278.788
|276.113-281.891
| colspan="2" |279.365
|277.209-284.107
|281.4815-281.905
|279.6-285.549
| colspan="2" |284.444-285.714
|284.149-290.9365
|288-''288.889''
|286.168-293.287
|290.321-296.098
|293.333
|-
|-
|3
|18\17
|''400''
|141.176
|413.352-422.018
|
|418.182
|414.17-422.836
| colspan="2" |419.048
|415.814-426.16
|422.222-422.857
|419.4-428.323
| colspan="2" |426.667-428.429
|426.224-436.405
|432-''433.333''
|429.252-439.933
|435.481-444.148
|440
|-
|-
|4
|17\16
|''533.333''
|141.667
|551.136-562.691
|
|557.576
|552.226-563.782
| colspan="2" |558.73
|554.418-568.213
|562.963-563.8095
|559.2-571.0975
| colspan="2" |568.889-571.429
|568.299-581.873
|576-''577.778''
|572.3365-586.577
|580.641-592.197
|586.667
|-
|-
|5
|16\15
|''666.667''
|142.222
|688.919-703.364
|Thirdtone Phrygian mode ends
|696.97
|690.283-704.727
| colspan="2" |698.413
|693.023-710.267
|703.704-704.762
|699-713.872
| colspan="2" |711.111-714.286
|710.373-727.341
|720-''722.222''
|715.42-733.222
|725.802-740.246
|733.333
|-
|-
|6
|15\14
|''800''
|142.857
|826.70-844.037
|Semitone Phrygian mode begins
|836.364
|828.3395-845.673
| colspan="2" |838.095
|831.627-852.32
|844.444-845.714
|838.7995-856.646
| colspan="2" |853.333-857.142
|853.448-872.81
|864-''866.667''
|858.505-879.866
|870.962-888.295
|880
|-
|-
|7
|14\13
|''933.333''
|143.590
|964.487-984.7095
|
|975.7575
|966.396-986.6148
| colspan="2" |977.778
|970.232-994.373
|985.185-986.666-7
|978.5995-999.421
| colspan="2" |995.556-1000
|994.5225-1018.278
|1008-''1011.111''
|1001.589-1026.51
|1016.122-1036.344
|1026.667
|-
|-
|8
|27\25
|''1066.667''
|144.000
|1102.271-1125.382-
|
|1115.1515
|1104.453-1127.564
| colspan="2" |1116.46
|1108.836-1136.427
|1125.926-1127.619
|1118.399-1142.195
| colspan="2" |1137.778-1142.857
|1136.597-1163.746
|1152-''1155.556''
|1144.673-1173.155
|1161.2825-1184.395
|1177.333
|}
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
|13\12
! colspan="5" |Intense Phrygian
| ''144.444''
! colspan="5" |Intense Phrygian-Soft Aeolian
|
! colspan="6" |Soft Aeolian
|-
|-
!Minimum
|12\11
!Min-Med/Min-Max±13¢
|145.455
!Median
|
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!11/5±13¢
!Maximum
|-
|-
|1
|11\10
|146.667
|146.667
|145.751-148.641
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|-
|21\19
|147.368
|147.368
|146.101-148.99
|
| colspan="2" |148.148
|147.36-150.249
|149.02
|147.796-150.685
| colspan="2" |''150''
|149.391-152.28
|151.111
|149.951-152.84
|150.223-153.112
|152.381
|-
|-
|2
|10\9
|293.333
|148.148
|291.5035-297.282
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|294.737
|292.201-297.979
| colspan="2" |296.296
|294.721-300.498
|288.039
|295.592-301.37
| colspan="2" |''300''
|298.782-304.56
|302.222
|299.902-305.68
|300.445-306.223
|304.762
|-
|-
|3
|19\17
|440
|149.020
|437.255-445.922
|
|442.105
|438.302-446.968
| colspan="2" |444.444
|442.081-450.748
|447.059
|443.388-452.055
| colspan="2" |''450''
|448.174-456.84
|453.333
|449.853-458.519
|450.668459.335
|457.143
|-
|-
|4
|9\8
|586.667
|''150.000''
|583.007-594.5625
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|589.474
|584.402-595.958
| colspan="2" |592.593
|589.441-600.997
|596.078
|591.164-602.74
| colspan="2" |''600''
|597.565-609.12
|604.444
|599.804-611.359
|600.891-612.446
|609.524
|-
|-
|5
|17\15
|733.333
|151.111
|728.759-743.203
|
|736.845
|730.502-744.947
| colspan="2" |740.741
|736.802-751.246
|745.098
|738.98-753.425
| colspan="2" |''750''
|746.956-761.4005
|755.556
|749.755-764.199
|751.1135-765.558
|761.905
|-
|-
|6
|8\7
|880
|152.381
|874.51-891.844
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|884.2015
|876.603-893.937
| colspan="2" |888.889
|884.161-901.495
|894.118
|886.776-904.11
| colspan="2" |''900''
|896.347-913.681
|906.667
|899.7055-917.039
|901.336-918.6695
|914.286
|-
|-
|7
|15\13
|1026.667
|153.846
|1020.262-1040.484
|
|1031.158
|1022.704-1042.926
| colspan="2" |1037.037
|1031.522-1051.7445
|1043.137
|1034.572-1054.795
| colspan="2" |''1050''
|1045.7385-1065.961
|1057.778
|1049.6565-1069.879
|1051.559-1071.781
|1066.667
|-
|-
|8
|22\19
|1177.333
|154.386
|1166.014-1189.125
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|1178.947
|1168.804-1191.9155
| colspan="2" |1185.1858
|1178.883-1201.994
|1192.157
|1182.269-1205.48
| colspan="2" |''1200''
|1195.13-1216.241
|1208.889
|1199.607-1222.7185
|1201.7815-1224.893
|1219.048
|}
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="7" |Aeolian
! colspan="8" |Intense Aeolian
|-
|-
! colspan="4" |Flattone
|29\25
! colspan="3" |Meantone
| 154.667
! colspan="4" |Superpyth
|
! colspan="4" |Ultrapyth
|-
|-
!Minimum
|7\6
!20/9±13¢
|''155.556''
!Median
|Meantone Aeolian mode ends, Superpyth Intense Aeolian begins
!Maximum
!Minimum
!Median
!Maximum
!Minimum
!9/4±13¢
!Median
!Maximum
!Minimum
!Median
!16/7±13¢
!Maximum
|-
|-
|1
|20\17
|152.381
|152.156-155.045
|153.846
| colspan="2" |154.386
|154.667
| colspan="2" |''155.556''
|154.546-157.434
|156.863
|156.863
| colspan="2" |157.576
|
|158.333
|157.575-160.464
|160
|-
|-
|2
|14\11
|304.762
|157.576
|304.312-310.09
| Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|307.692
| colspan="2" |308.772
|309.333
| colspan="2" |''311.111''
|309.091-314.869
|313.7255
| colspan="2" |315.1515
|316.667
|315.15-320.928
|320
|-
|-
|3
|19\16
|457.143
|158.333
|456.468-465.135
|
|461.5385
| colspan="2" |463.159
|464
| colspan="2" |''466.667''
|463.637-473.303
|470.588
| colspan="2" |472.727
|475
|472.725-480.392
|480
|-
|4
|609.524
|608.624-620.18
|615.385
| colspan="2" |617.544
|618.667
| colspan="2" |''622.222''
|618.182-629.738
|627.451
| colspan="2" |630.303
|633.333
|630.3-641.744
|640
|-
|-
|5
|25\21
|761.905
|158.730
|760.78-775.224
|
|769.231
| colspan="2" |771.93
|773.333
| colspan="2" |''777.778''
|772.728-787.172
|784.314
| colspan="2" |787.879
|791.667
|787.8745-802.319
|800
|-
|-
|6
|31\26
|914.286
|158.974
|912.936-930.269
|
|923.077
| colspan="2" |926.316
|928
| colspan="2" |''933.333''
|927.273-944.607
|941.1765
| colspan="2" |945.4545
|950
|945.449-962.782
|960
|-
|-
|7
|37\31
|1066.667
|159.140
|1065.091-1085.313
|
|1076.923
| colspan="2" |1080.702
|1072.667
| colspan="2" |''1088.889''
|1081.819-1102.041
|1098.804
| colspan="2" |1103.03
|1108.333
|1103.024-1123.246
|1120
|-
|-
|8
|6\5
|1219.048
|160.000
|1217.248-1240.359
|Ultrapyth Intense Aeolian mode ends
|1230.769
|}By coincidence, using an equivalence wider than 1305 cents is identical to repeating a Phrygian mode Napoli scale one tone later.
| colspan="2" |1235.088
|1237.333
| colspan="2" |''1244.444''
|1236.364-1259.476
|1254.902
| colspan="2" |1260.606
|1266.667
|1260.6-1283.711
|1280
|}By coincidence, using an equivalence wider than 1350 cents is identical to repeating a Phrygian mode Napoli scale one tone later.
[[Category:9-tone]]
[[Category:ed9/4]]
[[Category:edIX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]

Latest revision as of 18:50, 1 August 2025

This Long Common Practice minor mode gives the wide values for the period of the Greater Ennealimmal and Tritrizo temperaments.

Intervals

Nonet Period Notes
1/1 133.333 Soft Phrygian mode begins
25\24 138.889
24/23 139.130
23/22 139.394
22\21 139.683 Soft Phrygian mode ends, Thirdtone Phrygian mode begins
21\20 140.000
20\19 140.351
19\18 140.741
37\35 140.952
18\17 141.176
17\16 141.667
16\15 142.222 Thirdtone Phrygian mode ends
15\14 142.857 Semitone Phrygian mode begins
14\13 143.590
27\25 144.000
13\12 144.444
12\11 145.455
11\10 146.667 Semitone Phrygian mode ends, Intense Phrygian mode begins
21\19 147.368
10\9 148.148 Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
19\17 149.020
9\8 150.000 Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
17\15 151.111
8\7 152.381 Soft Aeolian mode ends, Flattone Aeolian mode begins
15\13 153.846
22\19 154.386 Flattone Aeolian mode ends, Meantone Aeolian mode begins
29\25 154.667
7\6 155.556 Meantone Aeolian mode ends, Superpyth Intense Aeolian begins
20\17 156.863
14\11 157.576 Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
19\16 158.333
25\21 158.730
31\26 158.974
37\31 159.140
6\5 160.000 Ultrapyth Intense Aeolian mode ends

By coincidence, using an equivalence wider than 1305 cents is identical to repeating a Phrygian mode Napoli scale one tone later.

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