User:Moremajorthanmajor/9edIX: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! colspan="3" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="2" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="2" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
!Absolute Minimum
!Absolute Minimum
! |Minimum
! |Minimum
!Median
! |Maximum
! |Maximum
! |Minimum
! |Minimum
!Median
! |Maximum
! |Maximum
!Minimum
!Minimum
!Median
! |Maximum
! |Maximum
|-
|-
Line 20: Line 23:
|133.333
|133.333
| |138.667
| |138.667
|142.222
| colspan="2" |146.667
| colspan="2" |146.667
|149.02
| colspan="2" |152.381
| colspan="2" |152.381
|155.556
| |160
| |160
|-
|-
Line 27: Line 33:
|266.667
|266.667
|277.333
|277.333
|284.444
| colspan="2" |293.333
| colspan="2" |293.333
|288.039
| colspan="2" |304.762
| colspan="2" |304.762
|311.111
|320
|320
|-
|-
Line 34: Line 43:
|400
|400
|416
|416
|426.667
| colspan="2" |440
| colspan="2" |440
|447.059
| colspan="2" |457.143
| colspan="2" |457.143
|466.667
|480
|480
|-
|-
| |4
| |4
|566.667
|533.333
|554.667
|554.667
|568.889
| colspan="2" |586.667
| colspan="2" |586.667
|596.078
| colspan="2" |609.524
| colspan="2" |609.524
|622.222
|640
|640
|-
|-
| |5
| |5
|633.333
|666.667
|693.333
|693.333
|711.111
| colspan="2" |733.333
| colspan="2" |733.333
|745.098
| colspan="2" |761.905
| colspan="2" |761.905
|777.778
|800
|800
|-
|-
Line 55: Line 73:
|800
|800
|832
|832
|853.333
| colspan="2" |880
| colspan="2" |880
|894.118
| colspan="2" |914.286
| colspan="2" |914.286
|933.333
|960
|960
|-
|-
Line 62: Line 83:
|933.333
|933.333
|970.667
|970.667
|995.556
| colspan="2" |1026.667
| colspan="2" |1026.667
|1043.137
| colspan="2" |1066.667
| colspan="2" |1066.667
|1088.889
|1120
|1120
|-
|-
Line 69: Line 93:
|1066.667
|1066.667
|1109.333
|1109.333
|1137.778
| colspan="2" |1177.333
| colspan="2" |1177.333
|1192.157
| colspan="2" |1219.048
| colspan="2" |1219.048
|1244.444
|1280
|1280
|}Golden Tunings
|}Golden Tunings
{| class="wikitable"
{| class="wikitable"
|-
|-
! |Degrees
! rowspan="2"|Degrees
! |Phrygian Mode (natural minor)
! colspan="3" |Phrygian Mode (natural minor)
! |Phrygian-Aeolian Mode (intermediate minor)
! colspan="2"|Phrygian-Aeolian Mode (intermediate minor)
! |Aeolian Mode (melodic/harmonic minor)
! colspan="3" |Aeolian Mode (melodic/harmonic minor)
|-
!Min-Med
!Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med
!Min-Max
!Med-Max
|-
|-
| |1
| |1
| |145.891
|141.218
| |141.81
|143.519
| |148.392
| |148.392
|149.7015
|153.48
| |154.714
| |154.714
|157.066
|-
|-
| |2
| |2
| |291.781
|282.437
| |283.62
|287.038
| |296.7845
| |296.7845
|299.403
|306.961
| |308.429
| |308.429
|314.133
|-
|-
| |3
| |3
| |437.672
|423.655
| |424.43
|430.557
| |445.177
| |445.177
|449.1045
|460.441
| |464.143
| |464.143
|471.199
|-
|-
| |4
| |4
| |583.562
|564.876
| |593.5659
| |566.24
|574.076
| |593.5695
|598.806
|613.921
| |618.857
| |618.857
|628.266
|-
|-
| |5
| |5
| |729.543
|706.0915
| |709.05
|717.5955
| |741.961
| |741.961
|748.507
|767.4015
| |773.572
| |773.572
|785.332
|-
|-
| |6
| |6
| |875.3435
|847.308
| |850.86
|861.115
| |890.354
| |890.354
|898.209
|920.882
| |928.286
| |928.286
|942.399
|-
|-
| |7
| |7
| |1021.234
|988.528
| |992.67
|1004.634
| |1038.746
| |1038.746
|1047.91
|1074.362
| |1083
| |1083
|1099.465
|-
|-
|8
|8
|1167.125
|1129.746
|1134.48
|1148.153
|1187.138
|1187.138
|1197.612
|1227.842
|1237.715
|1237.715
|1256.531
|}
|}


By coincidence, using an equivalence wider than 1350 cents is identical to repeating a fairly flat Napoli scale one tone later.
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:9-tone]]
[[Category:ed9/4]]
[[Category:ed9/4]]

Revision as of 16:51, 26 October 2018

This Long Common Practice minor mode is the neutral scale of the Fujiyama temperament family.

Intervals

Degrees Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
Absolute Minimum Minimum Median Maximum Minimum Median Maximum Minimum Median Maximum
1 133.333 138.667 142.222 146.667 149.02 152.381 155.556 160
2 266.667 277.333 284.444 293.333 288.039 304.762 311.111 320
3 400 416 426.667 440 447.059 457.143 466.667 480
4 533.333 554.667 568.889 586.667 596.078 609.524 622.222 640
5 666.667 693.333 711.111 733.333 745.098 761.905 777.778 800
6 800 832 853.333 880 894.118 914.286 933.333 960
7 933.333 970.667 995.556 1026.667 1043.137 1066.667 1088.889 1120
8 1066.667 1109.333 1137.778 1177.333 1192.157 1219.048 1244.444 1280

Golden Tunings

Degrees Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
Min-Med Min-Max Med-Max Min-Med/Min-Max Med-Max Min-Med Min-Max Med-Max
1 141.218 141.81 143.519 148.392 149.7015 153.48 154.714 157.066
2 282.437 283.62 287.038 296.7845 299.403 306.961 308.429 314.133
3 423.655 424.43 430.557 445.177 449.1045 460.441 464.143 471.199
4 564.876 566.24 574.076 593.5695 598.806 613.921 618.857 628.266
5 706.0915 709.05 717.5955 741.961 748.507 767.4015 773.572 785.332
6 847.308 850.86 861.115 890.354 898.209 920.882 928.286 942.399
7 988.528 992.67 1004.634 1038.746 1047.91 1074.362 1083 1099.465
8 1129.746 1134.48 1148.153 1187.138 1197.612 1227.842 1237.715 1256.531

By coincidence, using an equivalence wider than 1350 cents is identical to repeating a Phrygian mode Napoli scale one tone later.

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