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This Long Common Practice minor mode is the neutral scale of the temperament family formerly named Fujiyama.
This Long Common Practice minor mode gives the wide values for the period of the Greater [[Tritrizo clan|Tritrizo temperaments]] .
 
== Intervals==
==Intervals==
 
{| class="wikitable"
{| class="wikitable"
|+
! colspan="6" |Nonet
!Period
!Notes
|-
|-
! rowspan="3" |Degrees
|1/1
! colspan="3" |Soft Phrygian
|
! colspan="6" |Phrygian
|
|
|
|
|''133.{{Overline|3}}''
|Soft Phrygian mode begins
|-
|-
! rowspan="2" |Minimum-comma
|
! rowspan="2" |Median
|23/22
! rowspan="2" |Maximum+comma
|
! colspan="3" |Thirdtone
|
! colspan="3" |Semitone
|
|
| 139.{{Overline|39}}
|
|-
|-
!Minimum-comma
|22\21
!Median
|
! colspan="2" |Maximum+comma~Minimum-comma
|
!Median
|
!Maximum+comma
|
|
|139.6825
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|-
|-
|1
|21\20
|128.889-''133.333''
|
|139.394
|
| colspan="2" |135.238-144.127
|
|140.741-140.952
|
| colspan="2" |137.778-147.302
|
|144-''144.444''
|140
|146.667-151.111
|
|-
|-
|2
|20\19
|257.778-''266.667''
|
|278.788
|
| colspan="2" |270.476-288.254
|
|281.4815-281.905
|
| colspan="2" |275.556-294.603
|
|288-''288.889''
|140.351
|293.333-302.222
|
|-
|-
|3
|19\18
|386.667-''400''
|
|418.182
|
| colspan="2" |405.714-432.3841
|
|422.222-422.857
|
| colspan="2" |413.333-441.905
|
|432-''433.333''
| 140.741
|440-453.333
|
|-
|-
|4
|
|515.556-''533.333''
|37\35
|557.576
|
| colspan="2" |540.925-576.508
|
|562.963-563.8095
|
| colspan="2" |551.111-589.206
|
|576-''577.778''
|140.952
|586.667-604.444
|
|-
|-
|5
|18\17
|644.444-''666.667''
|
|696.97
|
| colspan="2" |676.1905-720.635
|
|703.704-704.762
|
| colspan="2" |688.889-736.508
|
|720-''722.222''
|141.1765
|733.333-755.556
|
|-
|-
|6
|17\16
|773.333-''800''
|
|836.364
|
| colspan="2" |811.459-865.762
|
|844.444-845.714
|
| colspan="2" |826.667-883.8095
|
|864-''866.667''
|141.{{Overline|6}}
|880-906.667
|
|-
|-
|7
|16\15
|902.222-''933.333''
|
|975.7575
|
| colspan="2" |946.667-1008.889
|
|985.185-986.666
|
| colspan="2" |964.444-1031.111
|
|1008-''1011.111''
|142.{{Overline|2}}
|1026.667-1057.778
|Thirdtone Phrygian mode ends
|-
|-
|8
|15\14
|1031.111-''1066.667''
|
|1115.1515
|
| colspan="2" |1081.905-1153.016
|
|1125.926-1127.619
|
| colspan="2" |1112.222-1178.413
|
|1152-''1155.556''
|142.857
|1177.333-1208.889
|Semitone Phrygian mode begins
|}
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
|14\13
! colspan="3" |Intense Phrygian
|
! colspan="3" |Intense Phrygian-Soft Aeolian
|
! colspan="4" |Soft Aeolian
|
|
|
|143.59
|
|-
|-
!Minimum-comma
|
!Median
|27\25
! colspan="2" |Maximum+comma~Minimum-comma
|
!Median
|
! colspan="2" |Maximum+comma~Minimum-comma
|
!''r¢''
|
!Median
|144
!Maximum+comma
|
|-
|-
|1
|13\12
|142.222-146.667
|
|147.368
|
| colspan="2" |143.704-152.593
|
|149.02
|
| colspan="2" |145.556-154.444
|
|''150''
| ''144.{{Overline|4}}''
|151.111
|
|152.381-156.825
|-
|-
|2
|12\11
|284.444-293.333
|
|294.737
|
| colspan="2" |287.407-305.185
|
|288.039
|
| colspan="2" |291.111-308.889
|
|''300''
|145.{{Overline|45}}
|302.222
|
|304.762-313.651
|-
|-
|3
|11\10
|426.667-440
|
|442.105
|
| colspan="2" |431.111-457.778
|
|447.059
|
| colspan="2" |436.667-463.333
|
|''450''
|146.{{Overline|6}}
|453.333
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|457.143-470.476
|-
|-
|4
|
|568.889-586.667
|21\19
|589.474
|
| colspan="2" |574.815-610.37
|
|596.078
|
| colspan="2" |582.222-617.778
|
|''600''
|147.368
|604.444
|
|609.524-627.302
|-
|-
|5
|10\9
|711.111-733.333
|
|736.845
|
| colspan="2" |718.5185-762.693
|
|745.098
|
| colspan="2" |727.778-772.222
|
|''750''
|148.{{Overline|148}}
|755.556
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|761.905-784.127
|-
|-
|6
|
|853.333-880
|19\17
|884.2015
|
| colspan="2" |862.222-915.556
|
|894.118
|
| colspan="2" |873.333-926.667
|
|''900''
|149.02
|906.667
|
|914.286-940.952
|-
|-
|7
|9\8
|995.556-1026.667
|
|1031.158
|
| colspan="2" |1005.926-1068.148
|
|1043.137
|
| colspan="2" |1018.889-1081.111
|
|''1050''
|''150''
|1057.778
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|1066.667-1097.778
|-
|-
|8
|
|1137.778-1177.333
| 17\15
|1178.947
|
| colspan="2" |1149.63-1220.741
|
|1192.157
|
| colspan="2" |1164.444-1235.556
|
|''1200''
|151.{{Overline|1}}
|1208.889
|
|1219.048-1254.603
|}
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="6" |Aeolian
! colspan="8" |Intense Aeolian
|-
|-
! colspan="3" |Flattone
|8\7
! colspan="3" |Meantone
|
! colspan="5" |Superpyth
|
! colspan="3" |Ultrapyth
|
|
|
|152.381
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|-
|-
!Minimum-comma
|
!Median
|15\13
! colspan="2" |Maximum+comma~Minimum-comma
|
!Median
|
! colspan="2" |Maximum+comma~Minimum-comma
|
! colspan="2" |''r¢''
|
!'''Median'''
! colspan="2" |Maximum+comma~Minimum-comma
!'''Median'''
!Maximum+comma
|-
|1
|147.9365-152.381
|153.846
|153.846
| colspan="2" |149.9065-158.795
|
|154.667
| colspan="2" |151.111-160
| colspan="2" |''155.556''
|156.863
| colspan="2" |153.131-162.02
|158.333
|160-164.444
|-
|-
|2
|
|295.873-304.762
|
|307.692
|22\19
| colspan="2" |299.813-317.591
|
|309.333
|
| colspan="2" |302.222-320
|
| colspan="2" |''311.111''
|154.386
|313.7255
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
| colspan="2" |306.263-324.04
|316.667
|320-328.887
|-
|-
|3
|
|443.8095-457.143
|
|461.5385
|
| colspan="2" |449.715-476.386
|29\25
|464
|
| colspan="2" |453.333-480
|
| colspan="2" |''466.667''
| 154.{{Overline|6}}
|470.588
|
| colspan="2" |459.394-486.061
|475
|480-493.333
|-
|-
|4
|7\6
|591.746-609.524
|
|615.385
|
| colspan="2" |599.626-635.181
|
|618.667
|
| colspan="2" |604.444-640
|
| colspan="2" |''622.222''
|''155.{{Overline|5}}''
|627.451
|Meantone Aeolian mode ends, Superpyth Intense Aeolian begins
| colspan="2" |612.525-648.081
|633.333
|640-657.778
|-
|-
|5
|
|739.6825-761.905
|
|769.231
|20\17
| colspan="2" |749.532-793.977
|
|773.333
|
| colspan="2" |755.556-800
|
| colspan="2" |''777.778''
|156.863
|784.314
|
| colspan="2" |765.657-810.101
|791.667
|800-822.222
|-
|6
|887.916-914.286
|923.077
| colspan="2" |899.439-952.772
|928
| colspan="2" |906.667-960
| colspan="2" |''933.333''
|941.1765
| colspan="2" |918.788-972.121
|950
|960-986.667
|-
|7
|1035.556-1066.667
|1076.923
| colspan="2" |1049.345-1111.567
|1072.667
| colspan="2" |1057.778-1120
| colspan="2" |''1088.889''
|1098.804
| colspan="2" |1071.919-1134.141
|1108.333
|1120-1151.111
|-
|8
|1183.492-1219.048
|1230.769
| colspan="2" |1199.2515-1270.363
|1237.333
| colspan="2" |1208.889-1280
| colspan="2" |''1244.444''
|1254.902
| colspan="2" |1225.0505-1296.162
|1266.667
|1280-1315.556
|}Golden/Pyrite Tunings±13¢
{| class="wikitable"
|-
! rowspan="3" |Degrees
! colspan="2" |Soft Phrygian
! colspan="4" |Phrygian
|-
! rowspan="2" |Min-Med
! rowspan="2" |Min-Max/Med-Max
! colspan="2" |Thirdtone
! colspan="2" |Semitone
|-
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|1
|137.784-140.673
|138.057-140.9455
|138.6045-142.053
|139.8-142.744
|142.075-145.468
|143.084-146.444
|-
|2
|275.568-281.346
|276.113-281.891
|277.209-284.107
|279.6-285.549
|284.149-290.9365
|286.168-293.287
|-
|3
|413.352-422.018
|414.17-422.836
|415.814-426.16
|419.4-428.323
|426.224-436.405
|429.252-439.933
|-
|4
|551.136-562.691
|552.226-563.782
|554.418-568.213
|559.2-571.0975
|568.299-581.873
|572.3365-586.577
|-
|5
|688.919-703.364
|690.283-704.727
|693.023-710.267
|699-713.872
|710.373-727.341
|715.42-733.222
|-
|6
|826.70-844.037
|828.3395-845.673
|831.627-852.32
|838.7995-856.646
|853.448-872.81
|858.505-879.866
|-
|7
|964.487-984.7095
|966.396-986.6148
|970.232-994.373
|978.5995-999.421
|994.5225-1018.278
|1001.589-1026.51
|-
|8
|1102.271-1125.382-
|1104.453-1127.564
|1108.836-1136.427
|1118.399-1142.195
|1136.597-1163.746
|1144.673-1173.155
|}
{| class="wikitable"
|-
! rowspan="2" |Degrees
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|1
|145.751-148.641
|146.101-148.99
|147.36-150.249
|147.796-150.685
|149.391-152.28
|149.951-152.84
|-
|2
|291.5035-297.282
|292.201-297.979
|294.721-300.498
|295.592-301.37
|298.782-304.56
|299.902-305.68
|-
|3
|437.255-445.922
|438.302-446.968
|442.081-450.748
|443.388-452.055
|448.174-456.84
|449.853-458.519
|-
|4
|583.007-594.5625
|584.402-595.958
|589.441-600.997
|591.164-602.74
|597.565-609.12
|599.804-611.359
|-
|5
|728.759-743.203
|730.502-744.947
|736.802-751.246
|738.98-753.425
|746.956-761.4005
|749.755-764.199
|-
|6
|874.51-891.844
|876.603-893.937
|884.161-901.495
|886.776-904.11
|896.347-913.681
|899.7055-917.039
|-
|7
|1020.262-1040.484
|1022.704-1042.926
|1031.522-1051.7445
|1034.572-1054.795
|1045.7385-1065.961
|1049.6565-1069.879
|-
|8
|1166.014-1189.125
|1168.804-1191.9155
|1178.883-1201.994
|1182.269-1205.48
|1195.13-1216.241
|1199.607-1222.7185
|}
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
! colspan="2" |Flattone
! colspan="2" |Meantone
! colspan="2" |Superpyth
! colspan="2" |Ultrapyth
|-
!Min-Med
!Med-Max~Min-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med
!Min-Max/Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|1
|152.036-154.925
| colspan="2" |152.67-156.021
|153.337-156.226
|154.185-157.074
|155.622-158.511
|156.663-159.552
|157.159-160.047
|-
|2
|304.072-309.85
| colspan="2" |305.139-312.043
|306.673-312.451
|310.368-316.146
|311.244-317.022
|313.325-319.103
|314.317-320.095
|-
|-
|3
|
|456.108-464.774
|14\11
| colspan="2" |457.809-468.064
|
|460.011-468.678
|
|465.553-478.22
|
|466.866-475.532
|
|469.989-478.655
|157.{{Overline|57}}
|471.476-480.142
| Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|-
|-
|4
|
|608.144-619.699
|
| colspan="2" |610.278-624.085
| 19\16
|613.348-624.903
|
|620.737-632.293
|
|622.488-634.044
|
|626.652-638.208
|158.{{Overline|3}}
|628.635-640.189
|
|-
|-
|5
|
|760.192-774.623
|
| colspan="2" |762.838-780.107
|
|766.685-781.109
|25\21
|775.921-790.3655
|
|778.11-792.554
|
|783.315-797.759
|158.73
|785.794-800.238
|
|-
|-
|6
|
|912.215-929.549
|
| colspan="2" |915.418-936.128
|
|920.023-937.356
|
|931.105-948.439
|31\26
|934.066-950.732
|
|940.315-956.978
|158.974
|942.952-960.286
|
|-
|-
|7
|
|1064.251-1084.473
|
| colspan="2" |1067.988-1092.15
|
|1073.359-1093.5815
|
|1086.29-1106.512
|
|1089.354-1109.576
| 37\31
|1096.64-1116.862
|159.14
|1100.111-1120.333
|
|-
|-
|8
|6\5
|1216.286-1239.398
|
| colspan="2" |1220.557-1248.172
|
|1226.696-1249.808
|
|1241.473-1264.585
|
|1244.975-1268.087
|
|1253.303-1276.415
|160
|1257.27-1280.381
|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.
|}By coincidence, using an equivalence wider than 1305 cents is identical to repeating a Phrygian mode Napoli scale one tone later.
[[Category:9-tone scales]]
[[Category:9-tone scales]]
[[Category:ed9/4]]
[[Category:ed9/4]]
[[Category:edIX]]
[[Category:edIX]]
[[Category:todo:add_definition]]
[[Category:todo:add definition]]
[[Category:todo:unify_precision]]
[[Category:todo:unify precision]]

Revision as of 05:52, 17 May 2023

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

Intervals

Nonet Period Notes
1/1 133.3 Soft Phrygian mode begins
23/22 139.39
22\21 139.6825 Soft Phrygian mode ends, Thirdtone Phrygian mode begins
21\20 140
20\19 140.351
19\18 140.741
37\35 140.952
18\17 141.1765
17\16 141.6
16\15 142.2 Thirdtone Phrygian mode ends
15\14 142.857 Semitone Phrygian mode begins
14\13 143.59
27\25 144
13\12 144.4
12\11 145.45
11\10 146.6 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\17 149.02
9\8 150 Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
17\15 151.1
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\25 154.6
7\6 155.5 Meantone Aeolian mode ends, Superpyth Intense Aeolian begins
20\17 156.863
14\11 157.57 Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
19\16 158.3
25\21 158.73
31\26 158.974
37\31 159.14
6\5 160 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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