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User:Moremajorthanmajor/13edIX: Difference between revisions

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==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! rowspan="3" |Octatonic
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! rowspan="2" |Absolute Minimum
! rowspan="2" |Degrees
! rowspan="2" |Minimum
! rowspan="2" |Octatonic
! rowspan="2" |Median
! colspan="3" |Soft Phrygian
! rowspan="2" |Maximum
! colspan="4" |Phrygian
|-
!Minimum
!Median
!Maximum
!Minimum
!Median
!15/7±13¢
!Maximum
|-
| |1
| |G#/Ab
|92.308
|96.5035
| colspan="2" |96.703
|98.263
|100.496-102.496
|101.5385
|-
| |2
| |A
|184.615
|193.007
| colspan="2" |193.407
|196.526
|200.991-204.912
|203.077
|-
| |3
| |A#/Bb
|276.923
|289.5105
| colspan="2" |290.11
|294.789
|301.487-307.487
|304.615
|-
| |4
| |B
|369.231
|386.014
| colspan="2" |386.813
|393.052
|401.982-409.982
|406.154
|-
| |5
| |C
|461.5385
|482.5175
| colspan="2" |483.5165
|491.315
|502.478-512.478
|507.692
|-
| |6
| |C#/Qb
|553.846
|579.021
| colspan="2" |580.22
|589.578
|602.974-614.974
|609.231
|-
| |7
| |Q
|646.154
|675.5245
| colspan="2" |676.923
|687.841
|703.469-717.469
|710.769
|-
| |8
| |D
|738.4615
|772.0228
| colspan="2" |773.626
|786.104
|803.965-819.965
|812.308
|-
| |9
| |D#/Eb
|830.769
|868.5315
| colspan="2" |870.33
|884.367
|904.46-922.46
|913.846
|-
| |10
| |E
|923.077
|965.035
| colspan="2" |967.033
|982.63
|1004.956-1024.956
|1015.385
|-
| |11
| |E#/Fb
|1015.385
|1061.5385
| colspan="2" |1063.736
|1080.893
|1105.452-1127.452
|1116.923
|-
| |12
| |F
|1107.692
|1158.042
| colspan="2" |1160.4395
|1179.156
|1205.947-1299.947
|1218.4615
|-
| |13
| |G
|1200
|1254.5455
| colspan="2" |1257.143
|1277.419
|1306.443-1332.443
|1320
|}
 
{| class="wikitable"
|-
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="3" |Intense Phrygian
! colspan="3" |Intense Phrygian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Soft Aeolian
! colspan="4" |Soft Aeolian
! rowspan="2" |Minimum
! rowspan="2" |Median
! rowspan="2" |Maximum
|-
|-
!Minimum
!Minimum
Line 27: Line 150:
!Minimum
!Minimum
!Median
!Median
!11/5±13¢
!Maximum
!Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|92.308
|G#/Ab
|97.582
|101.5385
|98.4615
| colspan="2" |101.5385
|102.024
|102.024
| colspan="2" |102.564
| colspan="2" |102.564
Line 40: Line 162:
| colspan="2" |103.846
| colspan="2" |103.846
|104.615
|104.615
| colspan="2" |105.4945
|104-106
|107.692
|105.4945
|110.769
|-
|-
| |2
| |2
| |G
| |G
|184.615
|A
|195.165
|203.077
|196.923
| colspan="2" |203.077
|204.0485
|204.0485
| colspan="2" |205.128
| colspan="2" |205.128
Line 55: Line 174:
| colspan="2" |207.692
| colspan="2" |207.692
|209.231
|209.231
| colspan="2" |210.989
|208.001-212.001
|215.385
|210.989
|221.5385
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|276.923
|A#/Bb
|292.747
|304.615
|295.385
| colspan="2" |304.615
|306.073
|306.073
| colspan="2" |307.692
| colspan="2" |307.692
Line 70: Line 186:
| colspan="2" |311.5385
| colspan="2" |311.5385
|313.846
|313.846
| colspan="2" |316.4835
|312.001-318.001
|323.077
|316.4835
|332.308
|-
|-
| |4
| |4
| |A
| |A
|369.231
|B
|390.33
|406.154
|393.846
| colspan="2" |406.154
|408.097
|408.097
| colspan="2" |410.256
| colspan="2" |410.256
Line 85: Line 198:
| colspan="2" |415.385
| colspan="2" |415.385
|418.4615
|418.4615
| colspan="2" |421.978
|416.001-424.001
|430.769
|421.978
|443.076
|-
|-
| |5
| |5
| |B
| |B
|461.5385
|C
|487.912
|507.692
|491.308
| colspan="2" |507.692
|510.1215
|510.1215
| colspan="2" |512.8205
| colspan="2" |512.8205
Line 100: Line 210:
| colspan="2" |519.231
| colspan="2" |519.231
|523.077
|523.077
| colspan="2" |527.4725
|520.002-530.002
|538.4615
|527.4725
|553.846
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|553.846
|C#/Qb
|585.4945
|609.231
|589.769
| colspan="2" |609.231
|612.146
|612.146
| colspan="2" |615.384
| colspan="2" |615.384
Line 115: Line 222:
| colspan="2" |623.077
| colspan="2" |623.077
|627.692
|627.692
| colspan="2" |632.967
|624.002-636.002
|646.154
|632.967
|664.615
|-
|-
| |7
| |7
| |H
| |H
|646.154
|Q
|683.077
|710.769
|690.231
| colspan="2" |710.769
|714.17
|714.17
| colspan="2" |717.945
| colspan="2" |717.945
Line 130: Line 234:
| colspan="2" |736.923
| colspan="2" |736.923
|732.308
|732.308
| colspan="2" |738.4615
|728.002-742.0022
|754.846
|738.4615
|775.385
|-
|-
| |8
| |8
| |C
| |C
|738.4615
|D
|780.66
|812.308
|788.692
| colspan="2" |812.308
|816.194
|816.194
| colspan="2" |820.513
| colspan="2" |820.513
Line 145: Line 246:
| colspan="2" |830.769
| colspan="2" |830.769
|836.923
|836.923
| colspan="2" |843.856
|832.003-848.002
|861.5385
|843.856
|886.154
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|830.769
|D#/Eb
|878.242
|913.846
|896.154
| colspan="2" |913.846
|918.219
|918.219
| colspan="2" |923.077
| colspan="2" |923.077
Line 160: Line 258:
| colspan="2" |934.615
| colspan="2" |934.615
|941.5385
|941.5385
| colspan="2" |949.4505
|936.003-924.003
|969.231
|949.4505
|996.923
|-
|-
| |10
| |10
| |D
| |D
|923.077
|E
|975.824
|1015.385
|984.615
| colspan="2" |1015.385
|1020.243
|1020.243
| colspan="2" |1025.641
| colspan="2" |1025.641
Line 175: Line 270:
| colspan="2" |1038.4165
| colspan="2" |1038.4165
|1046.154
|1046.154
| colspan="2" |1054.945
|1040.003-1060.003
|1076.923
|1054.945
|1107.692
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1015.385
|E#/Fb
|1073.407
|1116.923
|1083.077
| colspan="2" |1116.923
|1123.267
|1123.267
| colspan="2" |1128.205
| colspan="2" |1128.205
Line 190: Line 282:
| colspan="2" |1142.308
| colspan="2" |1142.308
|1150.769
|1150.769
| colspan="2" |1160.44
|1144.004-1166.004
|1184.615
|1160.44
|1218.4615
|-
|-
| |12
| |12
| |E
| |E
|1107.692
|F
|1170.99
|1218.4615
|1181.5385
| colspan="2" |1218.4615
|1224.291
|1224.291
| colspan="2" |1230.769
| colspan="2" |1230.769
Line 205: Line 294:
| colspan="2" |1246.154
| colspan="2" |1246.154
|1255.385
|1255.385
| colspan="2" |1265.9348
|1248.004-1272.004
|1292.308
|1265.935
|1329.231
|-
|-
| |13
| |13
| |F
| |F
|1200
|G
|1268.571
|1320
|1280
| colspan="2" |1320
|1326.316
|1326.316
| colspan="2" |1333.333
| colspan="2" |1333.333
Line 220: Line 306:
| colspan="2" |1350
| colspan="2" |1350
|1360
|1360
| colspan="2" |1371.429
|1352.004-1378.004
|1400
|1371.429
|1440
|}
|}
Most harmonic tunings
 
{| class="wikitable"
{| class="wikitable"
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! rowspan="2" |Octatonic
!Phrygian Mode (natural minor)
! colspan="3" |Aeolian  
!Phrygian-Aeolian Mode (intermediate minor)
! colspan="4" |Intense Aeolian  
!Aeolian Mode (melodic/harmonic minor)
|-
|-
!15/7±13¢
!Minimum
!11/5±13¢
!Median
!Maximum
!Minimum
!9/4±13¢
!9/4±13¢
!Median
!Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|100.496-102.496
|105.4945
|104-106
|106.509
| colspan="2" |107.692
|106.993-108.993
|106.993-108.993
|109.091
|110.769
|-
|-
| |2
| |2
| |G
| |G
|200.991-204.912
|210.989
|208.001-212.001
|213.018
| colspan="2" |215.385
|213.986-217.986
|213.986-217.986
|218.182
|221.5385
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|301.487-307.487
|316.4835
|312.001-318.001
|319.527
| colspan="2" |323.077
|320.979-326.979
|320.979-326.979
|327.273
|332.308
|-
|-
| |4
| |4
| |A
| |A
|401.982-409.982
|421.978
|416.001-424.001
|426.036
| colspan="2" |430.769
|427.972-435.972
|427.972-435.972
|436.364
|443.076
|-
|-
| |5
| |5
| |B
| |B
|502.478-512.478
|527.4725
|520.002-530.002
|532.544
| colspan="2" |538.4615
|534.965-544.965
|534.965-544.965
|545.4545
|553.846
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|602.974-614.974
|632.967
|624.002-636.002
|639.053
| colspan="2" |646.154
|641.9585-653.9585
|641.9585-653.9585
|654.5455
|664.615
|-
|-
| |7
| |7
| |H
| |H
|703.469-717.469
|738.4615
|728.002-742.0022
|745.562
| colspan="2" |754.846
|748.9515-762.9515
|748.9515-762.9515
|763.636
|775.385
|-
|-
| |8
| |8
| |C
| |C
|803.965-819.965
|843.856
|832.003-848.002
|853.071
| colspan="2" |861.5385
|855.945-871.945
|855.945-871.945
|872.727
|886.154
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|904.46-922.46
|949.4505
|936.003-924.003
|958.58
| colspan="2" |969.231
|962.938-980.938
|962.938-980.938
|981.818
|996.923
|-
|-
| |10
| |10
| |D
| |D
|1004.956-1024.956
|1054.945
|1040.003-1060.003
|1065.089
| colspan="2" |1076.923
|1069.931-1089.931
|1069.931-1089.931
|1090.909
|1107.692
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1105.452-1127.452
|1160.44
|1144.004-1166.004
|1171.598
| colspan="2" |1184.615
|1177-924-1199.924
|1177-924-1199.924
|1200
|1218.4615
|-
|-
| |12
| |12
| |E
| |E
|1205.947-1299.947
|1265.9344
|1248.004-1272.004
|1278.1065
| colspan="2" |1292.308
|1283.917-1307.917
|1283.917-1307.917
|1309.094
|1329.231
|-
|-
| |13
| |13
| |F
| |F
|1306.443-1332.443
|1371.429
|1352.004-1378.004
|1384.615
| colspan="2" |1400
|1390.91-1416.91
|1390.91-1416.91
|1418.182
|1440
|}
|}
Golden Tunings
Golden Tunings


Phrygian Mode (natural minor)
Phrygian Mode (Neapolitan minor/"major")
{| class="wikitable"
{| class="wikitable"
|-
|-
!Degrees
! rowspan="2" |Degrees
!Octatonic
! rowspan="2" |Octatonic
! colspan="2" |Soft Phrygian
! colspan="3" |Phrygian
|-
!Min-Med±13¢
!Min-Max/Med-Max±13¢
!Min-Med±13¢
!Min-Med±13¢
!Min-Max±13¢
!Min-Max±13¢
Line 327: Line 458:
|-
|-
| |1
| |1
| |F#/Gb
| |G#/Ab
|95.389-97.389
|95.578-97.578
|96.7665-98.7665
|96.7665-98.7665
|97.176-99.176
|97.176-99.176
Line 333: Line 466:
|-
|-
| |2
| |2
| |G
| |A
|190.778-194.778
|191.155-195.155
|193.533-197.533
|193.533-197.533
|194.352-198.352
|194.352-198.352
Line 339: Line 474:
|-
|-
| |3
| |3
| |G#/Ab
| |A#/Bb
|286.1665-292.1665
|286.733-292.733
|290.2995-296.2995
|290.2995-296.2995
|291.528-297.528
|291.528-297.528
Line 345: Line 482:
|-
|-
| |4
| |4
| |A
| |B
|381.555-389.555
|382.3105-390.3105
|387.063-395.063
|387.063-395.063
|388.705-396.705
|388.705-396.705
Line 351: Line 490:
|-
|-
| |5
| |5
| |B
| |C
|476.944-486.944
|477.888-487.888
|483.833-493.833
|483.833-493.833
|485.881-495.881
|485.881-495.881
Line 357: Line 498:
|-
|-
| |6
| |6
| |B#/Hb
| |C#/Qb
|572.333-584.333
|573.466-585.466
|580.299-592.299
|580.299-592.299
|583.057-595.057
|583.057-595.057
Line 363: Line 506:
|-
|-
| |7
| |7
| |H
| |Q
|667.722-681.722
|669.043-683.043
|677.366-691.366
|677.366-691.366
|680.233-694.233
|680.233-694.233
Line 369: Line 514:
|-
|-
| |8
| |8
| |C
| |D
|763.111-781.111
|764.621-780.621
|774.132-790.132
|774.132-790.132
|777.409-793.409
|777.409-793.409
Line 375: Line 522:
|-
|-
| |9
| |9
| |C#/Db
| |D#/Eb
|858.5-876.5
|860.199-878.199
|870.899-888.899
|870.899-888.899
|874.585-892.585
|874.585-892.585
Line 381: Line 530:
|-
|-
| |10
| |10
| |D
| |E
|953.8885-973.8885
|955.776-975.776
|967.665-987.665
|967.665-987.665
|971.761-991.761
|971.761-991.761
Line 387: Line 538:
|-
|-
| |11
| |11
| |D#/Eb
| |E#/Fb
|1049.277-1071.277
|1051.354-1073.354
|1064.432-1086.432
|1064.432-1086.432
|1068.9375-1090.9375
|1068.9375-1090.9375
Line 393: Line 546:
|-
|-
| |12
| |12
| |E
| |F
|1144.666-1168.666
|1146.932-1170.932
|1161.198-1185.198
|1161.198-1185.198
|1166.114-1190.114
|1166.114-1190.114
Line 399: Line 554:
|-
|-
| |13
| |13
| |F
| |G
|1240.055-1266.055
|1242.506-1268.509
|1257.965-1283.965
|1257.965-1283.965
|1263.29-1289.29
|1263.29-1289.29
Line 408: Line 565:
|-
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="2" rowspan="2" |Octatonic
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Intense Phrygian-Soft Aeolian
Line 422: Line 579:
| |1
| |1
| |F#/Gb
| |F#/Gb
|G#/Ab
|100.905-102.905
|100.905-102.905
|101.1465-103.1465
|101.1465-103.1465
Line 431: Line 589:
| |2
| |2
| |G
| |G
|A
|201.81-205.81
|201.81-205.81
|202.293-206.293
|202.293-206.293
Line 440: Line 599:
| |3
| |3
| |G#/Ab
| |G#/Ab
|A#/Bb
|302.715-308.715
|302.715-308.715
|303.44-309.44
|303.44-309.44
Line 449: Line 609:
| |4
| |4
| |A
| |A
|B
|403.62-411.62
|403.62-411.62
|404.586-412.586
|404.586-412.586
Line 458: Line 619:
| |5
| |5
| |B
| |B
|C
|504.525-514.525
|504.525-514.525
|505.733-515.733
|505.733-515.733
Line 467: Line 629:
| |6
| |6
| |B#/Hb
| |B#/Hb
|C#/Qb
|605.43-617.43
|605.43-617.43
|606.879-618.879
|606.879-618.879
Line 476: Line 639:
| |7
| |7
| |H
| |H
|Q
|706.335-720.335
|706.335-720.335
|708.026-722.026
|708.026-722.026
Line 485: Line 649:
| |8
| |8
| |C
| |C
|D
|807.24-823.24
|807.24-823.24
|809.172-825.172
|809.172-825.172
Line 494: Line 659:
| |9
| |9
| |C#/Db
| |C#/Db
|D#/Eb
|908.145-926.145
|908.145-926.145
|910.319-928.319
|910.319-928.319
Line 503: Line 669:
| |10
| |10
| |D
| |D
|E
|1009.0505-1029.0505
|1009.0505-1029.0505
|1011.465-1031.465
|1011.465-1031.465
Line 512: Line 679:
| |11
| |11
| |D#/Eb
| |D#/Eb
|E#/Fb
|1109.9555-1131.9555
|1109.9555-1131.9555
|1112.61-1134.612
|1112.61-1134.612
Line 521: Line 689:
| |12
| |12
| |E
| |E
|F
|1210.861-1234.861
|1210.861-1234.861
|1213.758-1227.758
|1213.758-1227.758
Line 530: Line 699:
| |13
| |13
| |F
| |F
|G
|1311.767-1337.767
|1311.767-1337.767
|1314.905-1340.905
|1314.905-1340.905
Line 537: Line 707:
|1349.558-1375.558
|1349.558-1375.558
|}
|}
Aeolian Mode (melodic/harmonic minor)
Aeolian Mode (natural/harmonic minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="2" |Aeolian
! colspan="2" |Intense Aeolian
|-
|-
!Degrees
!Min-Med/Min-Max±13¢
!Octatonic
!Med-Max-13c
!Min-Med±13¢
!Min-Med/Min-Max±13¢
!Min-Max±13¢
!Med-Max-13c
!Med-Max-13c
|-
|-
Line 549: Line 722:
| |F#/Gb
| |F#/Gb
|105.256-107.256
|105.256-107.256
|106.11-108.11
|105.7715-107.7715
|107.738-109.738
|107.738-109.738
|108.459-110.459
|-
|-
| |2
| |2
| |G
| |G
|210.511-214.511
|210.511-214.511
|212.22-216.22
|211.543-215.543
|215.477-219.477
|215.477-219.477
|216.918-220.918
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|315.767-321.767
|315.767-321.767
|318.33-324.33
|317.315-323.315
|323.215-329.215
|323.215-329.215
|325.377-331.377
|-
|-
| |4
| |4
| |A
| |A
|421.022-429.022
|421.022-429.022
|424.44-432.44
|423.086-431.086
|430.953-438.953
|430.953-438.953
|433.836-437.836
|-
|-
| |5
| |5
| |B
| |B
|526.278-536.278
|526.278-536.278
|530.55-540.55
|528.858-538.858
|538.6915-548.6915
|538.6915-548.6915
|542.295-552.295
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|631.534-643.534
|631.534-643.534
|636.6595-648.6595
|634.629-646.629
|646.43-658.43
|646.43-658.43
|650.754-666.754
|-
|-
| |7
| |7
| |H
| |H
|736.789-750.789
|736.789-750.789
|742.769-756.769
|740.401-754.401
|754.168-768.168
|754.168-768.168
|759.213-773.213
|-
|-
| |8
| |8
| |C
| |C
|842.045-858.045
|842.045-858.045
|848.879-864.879
|846.172-862.172
|861.906-877.906
|861.906-877.906
|867.672-883.672
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|947.3-965.3
|947.3-965.3
|954.989-972.989
|951.944-969.944
|969.645-986.645
|969.645-986.645
|976.131-994.131
|-
|-
| |10
| |10
| |D
| |D
|1052.556-1072.556
|1052.556-1072.556
|1061.099-1081.099
|1057.715-1077.715
|1077.383-1077.383
|1077.383-1077.383
|1084.59-1104.59
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1157.8115-1179.8115
|1157.8115-1179.8115
|1167.209-1189.209
|1163.487-1187.487
|1185.121-1207.121
|1185.121-1207.121
|1193.049-1215.049
|-
|-
| |12
| |12
| |E
| |E
|1264.067-1287.067
|1264.067-1287.067
|1273.319-1297.319
|1269.258-1293.258
|1292.86-1316.86
|1292.86-1316.86
|1301.508-1325.508
|-
|-
| |13
| |13
| |F
| |F
|1368.322-1394.322
|1368.322-1394.322
|1379.429-1405.429
|1375.03-1401.03
|1400.598-1426.598
|1400.598-1426.598
|1409.967-1435.967
|}
|}
[[Category:13-tone]]
[[Category:13-tone]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/13edIX"