User:Moremajorthanmajor/13edIX: Difference between revisions

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==Intervals==
==Intervals==


Phrygian Mode (aka Double) Neapolitan Temperament
{| class="wikitable"
{| class="wikitable"
!Degrees
!Octatonic
!Minimum
!Mean
!Median
!Golden
!Maximum
|-
|-
! | Degrees
|1
! | Octatonic
|F#/Gb
! | Minimum
| rowspan="13" |see [[13edo]]
! | Golden
|96.923
! | Median
|100.699
! | Mean
|101.001
! | ed(9/4)
|101.5385
! | Maximum
|-
|-
| | 1
|2
| | A#/Bb
|G
| | 98.4615
|193.846
| | 100.564
|201.399
| | 101.5385
|202.002
| | 104.615
|203.077
| | 107.993
| | 110.769
|-
|-
| | 2
|3
| | B
|A
| | 196.923
|290.769
| | 201.128
|302.098
| | 203.077
|303.0035
| | 209.308
|304.615
| | 215.986
| | 221.5385
|-
|-
| | 3
|4
| | C
|A#/Bb
| | 295.385
|387.692
| | 301.692
|402.797
| | 304.615
|404.005
| | 313.923
|406.154
| | 323.979
| | 332.308
|-
|-
| | 4
|5
| | C#/Db
|B
| | 393.846
|484.615
| | 402.256
|503.4965
| | 406.154
|505.006
| | 418.5385
|507.692
| | 431.972
| | 443.076
|-
|-
| | 5
|6
| | D
|B#/Hb
| | 492.308
|581.5385
| | 502.82
|604.196
| | 507.692
|606.007
| | 523.231
|609.231
| | 539.965
| | 553.846
|-
|-
| | 6
|7
| | D#/Eb
|H
| | 590.769
|678.4615
| | 603.381
|704.895
| | 609.231
|707.008
| | 627.846
|710.769
| | 647.9585
| | 664.615
|-
|-
| | 7
|8
| | E
|C
| | 689.231
|775.385
| | 703.948
|805.594
| | 710.769
|808.009
| | 732.154
|812.308
| | 755.9515
| | 775.385
|-
|-
| | 8
|9
| | F
|C#/Db
| | 787.692
|872.318
| | 804.5115
|906.294
| | 812.308
|909.011
| | 836.769
|913.846
| | 863.945
| | 886.154
|-
|-
| | 9
|10
| | F#/Gb
|D
| | 886.154
|969.231
| | 905.0755
|1006.993
| | 913.846
|1010.012
| | 941.4615
|1015.385
| | 971.938
| | 996.923
|-
|-
| | 10
|11
| | G
|D#/Eb
| | 984.615
|1066.154
| | 1005.639
|1107.692
| | 1015.385
|1111.013
| | 1046.077
|1116.923
| | 1079.931
| | 1107.692
|-
|-
| | 11
|12
| | G#/Hb
|E
| | 1083.077
|1163.077
| | 1106.203
|1208.392
| | 1116.923
|1212.014
| | 1150.692
|1218.4615
| | 1187.924
| | 1218.4615
|-
|-
| | 12
|13
| | H
|F
| | 1181.5385
|1260
| | 1206.767
|1309.091
| | 1218.4615
|1313.015
| | 1255.385
|1320
| | 1295.917
|}
| | 1329.231
Phrygian-Aeolian Mode Neapolitan Temperament
{| class="wikitable"
!Degrees
!Octatonic
!Minimum
!Golden
!Mean
!Median
!Maximum
|-
|1
|F#/Gb
|101.5385
|102.733
|103.5165
|104.615
|105.4945
|-
|2
|G
|203.077
|205.466
|207.033
|209.231
|210.989
|-
|3
|A
|304.615
|308.199
|310.5465
|313.846
|316.4835
|-
|4
|A#/Bb
|406.154
|410.932
|414.066
|418.4615
|421.978
|-
|5
|B
|507.692
|513.6655
|517.582
|523.077
|527.4725
|-
|6
|B#/Hb
|609.231
|616.399
|621.099
|627.692
|632.967
|-
|7
|H
|710.769
|719.132
|724.615
|732.318
|738.4615
|-
|8
|C
|812.308
|821.865
|828.132
|836.923
|843.856
|-
|9
|C#/Db
|913.846
|924.598
|931.648
|941.5385
|949.4505
|-
|10
|D
|1015.385
|1027.331
|1035.165
|1046.154
|1054.945
|-
|11
|D#/Eb
|1116.923
|1130.064
|1138.681
|1150.769
|1160.44
|-
|12
|E
|1218.4615
|1232.797
|1242.198
|1255.385
|1265.9348
|-
|13
|F
|1320
|1335.53
|1345.714
|1360
|1371.429
|}
Aeolian Mode Neapolitan Temperament
{| class="wikitable"
|-
! |Degrees
! |Octatonic
! |Minimum
! |Golden
! |Median
! |ed(9/4)
! |Mean
! |Maximum
|-
| |1
| |F#/Gb
| |105.4945
| |107.11
| |107.692
| |107.993
| |108.132
| |110.769
|-
| |2
| |G
| |210.989
| |214.22
| |214.385
| |215.986
| |216.264
| |221.5385
|-
| |3
| |A
| |316.4835
| |321.33
| |322.077
| |323.979
| |324.396
| |332.308
|-
| |4
| |A#/Bb
| |421.978
| |428.44
| |429.769
| |431.972
| |432.5275
| |443.076
|-
| |5
| |B
| |527.4725
| |535.55
| |583.4615
| |539.965
| |540.659
| |553.846
|-
| |6
| |B#/Hb
| |632.967
| |642.6595
| |646.154
| |647.9585
| |648.791
| |664.615
|-
| |7
| |H
| |738.4615
| |749.769
| |753.846
| |755.9515
| |756.923
| |775.385
|-
| |8
| |C
| |843.856
| |856.879
| |861.5385
| |863.945
| |865.055
| |886.154
|-
| |9
| |C#/Db
| |949.4505
| |963.989
| |969.231
| |971.938
| |973.187
| |996.923
|-
| |10
| |D
| |1054.945
| |1071.099
| |1076.923
| |1079.931
| |1081.319
| |1107.692
|-
| |11
| |D#/Eb
| |1160.44
| |1178.209
| |1184.615
| |1187.924
| |1189.4505
| |1218.4615
|-
| |12
| |E
| |1265.9348
| |1285.319
| |1292.308
| |1295.917
| |1297.582
| |1329.231
|-
|-
| | 13
| |13
| | A
| |F
| | 1280
| |1371.429
| | 1307.331
| |1392.429
| | 1320
| |1400
| | 1360
| |1403.91
| | 1403.91
| |1405.714
| | 1440
| |1440
|}
|}
[[Category:13-tone]]
[[Category:13-tone]]

Revision as of 20:02, 21 September 2018

This scale occurs in 12edo, where it is the equal division of the minor ninth.

Intervals

Phrygian Mode (aka Double) Neapolitan Temperament

Degrees Octatonic Minimum Mean Median Golden Maximum
1 F#/Gb see 13edo 96.923 100.699 101.001 101.5385
2 G 193.846 201.399 202.002 203.077
3 A 290.769 302.098 303.0035 304.615
4 A#/Bb 387.692 402.797 404.005 406.154
5 B 484.615 503.4965 505.006 507.692
6 B#/Hb 581.5385 604.196 606.007 609.231
7 H 678.4615 704.895 707.008 710.769
8 C 775.385 805.594 808.009 812.308
9 C#/Db 872.318 906.294 909.011 913.846
10 D 969.231 1006.993 1010.012 1015.385
11 D#/Eb 1066.154 1107.692 1111.013 1116.923
12 E 1163.077 1208.392 1212.014 1218.4615
13 F 1260 1309.091 1313.015 1320

Phrygian-Aeolian Mode Neapolitan Temperament

Degrees Octatonic Minimum Golden Mean Median Maximum
1 F#/Gb 101.5385 102.733 103.5165 104.615 105.4945
2 G 203.077 205.466 207.033 209.231 210.989
3 A 304.615 308.199 310.5465 313.846 316.4835
4 A#/Bb 406.154 410.932 414.066 418.4615 421.978
5 B 507.692 513.6655 517.582 523.077 527.4725
6 B#/Hb 609.231 616.399 621.099 627.692 632.967
7 H 710.769 719.132 724.615 732.318 738.4615
8 C 812.308 821.865 828.132 836.923 843.856
9 C#/Db 913.846 924.598 931.648 941.5385 949.4505
10 D 1015.385 1027.331 1035.165 1046.154 1054.945
11 D#/Eb 1116.923 1130.064 1138.681 1150.769 1160.44
12 E 1218.4615 1232.797 1242.198 1255.385 1265.9348
13 F 1320 1335.53 1345.714 1360 1371.429

Aeolian Mode Neapolitan Temperament

Degrees Octatonic Minimum Golden Median ed(9/4) Mean Maximum
1 F#/Gb 105.4945 107.11 107.692 107.993 108.132 110.769
2 G 210.989 214.22 214.385 215.986 216.264 221.5385
3 A 316.4835 321.33 322.077 323.979 324.396 332.308
4 A#/Bb 421.978 428.44 429.769 431.972 432.5275 443.076
5 B 527.4725 535.55 583.4615 539.965 540.659 553.846
6 B#/Hb 632.967 642.6595 646.154 647.9585 648.791 664.615
7 H 738.4615 749.769 753.846 755.9515 756.923 775.385
8 C 843.856 856.879 861.5385 863.945 865.055 886.154
9 C#/Db 949.4505 963.989 969.231 971.938 973.187 996.923
10 D 1054.945 1071.099 1076.923 1079.931 1081.319 1107.692
11 D#/Eb 1160.44 1178.209 1184.615 1187.924 1189.4505 1218.4615
12 E 1265.9348 1285.319 1292.308 1295.917 1297.582 1329.231
13 F 1371.429 1392.429 1400 1403.91 1405.714 1440
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