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]]

Revision as of 02:31, 12 December 2018

This scale, a Long Common Practice minor mode, occurs in 12edo; where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small.

Intervals

Degrees Octatonic Soft Phrygian Phrygian
Minimum Median Maximum Minimum Median 15/7±13¢ Maximum
1 G#/Ab 92.308 96.5035 96.703 98.263 100.496-102.496 101.5385
2 A 184.615 193.007 193.407 196.526 200.991-204.912 203.077
3 A#/Bb 276.923 289.5105 290.11 294.789 301.487-307.487 304.615
4 B 369.231 386.014 386.813 393.052 401.982-409.982 406.154
5 C 461.5385 482.5175 483.5165 491.315 502.478-512.478 507.692
6 C#/Qb 553.846 579.021 580.22 589.578 602.974-614.974 609.231
7 Q 646.154 675.5245 676.923 687.841 703.469-717.469 710.769
8 D 738.4615 772.0228 773.626 786.104 803.965-819.965 812.308
9 D#/Eb 830.769 868.5315 870.33 884.367 904.46-922.46 913.846
10 E 923.077 965.035 967.033 982.63 1004.956-1024.956 1015.385
11 E#/Fb 1015.385 1061.5385 1063.736 1080.893 1105.452-1127.452 1116.923
12 F 1107.692 1158.042 1160.4395 1179.156 1205.947-1299.947 1218.4615
13 G 1200 1254.5455 1257.143 1277.419 1306.443-1332.443 1320
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum Median Maximum Minimum Median Maximum Minimum Median 11/5±13¢ Maximum
1 F#/Gb G#/Ab 101.5385 102.024 102.564 103.167 103.846 104.615 104-106 105.4945
2 G A 203.077 204.0485 205.128 206.335 207.692 209.231 208.001-212.001 210.989
3 G#/Ab A#/Bb 304.615 306.073 307.692 309.502 311.5385 313.846 312.001-318.001 316.4835
4 A B 406.154 408.097 410.256 412.67 415.385 418.4615 416.001-424.001 421.978
5 B C 507.692 510.1215 512.8205 515.837 519.231 523.077 520.002-530.002 527.4725
6 B#/Hb C#/Qb 609.231 612.146 615.384 619.0045 623.077 627.692 624.002-636.002 632.967
7 H Q 710.769 714.17 717.945 722.172 736.923 732.308 728.002-742.0022 738.4615
8 C D 812.308 816.194 820.513 825.339 830.769 836.923 832.003-848.002 843.856
9 C#/Db D#/Eb 913.846 918.219 923.077 929.507 934.615 941.5385 936.003-924.003 949.4505
10 D E 1015.385 1020.243 1025.641 1031.674 1038.4165 1046.154 1040.003-1060.003 1054.945
11 D#/Eb E#/Fb 1116.923 1123.267 1128.205 1134.842 1142.308 1150.769 1144.004-1166.004 1160.44
12 E F 1218.4615 1224.291 1230.769 1238.009 1246.154 1255.385 1248.004-1272.004 1265.935
13 F G 1320 1326.316 1333.333 1341.1765 1350 1360 1352.004-1378.004 1371.429
Degrees Octatonic Aeolian Intense Aeolian
Minimum Median Maximum Minimum 9/4±13¢ Median Maximum
1 F#/Gb 105.4945 106.509 107.692 106.993-108.993 109.091 110.769
2 G 210.989 213.018 215.385 213.986-217.986 218.182 221.5385
3 G#/Ab 316.4835 319.527 323.077 320.979-326.979 327.273 332.308
4 A 421.978 426.036 430.769 427.972-435.972 436.364 443.076
5 B 527.4725 532.544 538.4615 534.965-544.965 545.4545 553.846
6 B#/Hb 632.967 639.053 646.154 641.9585-653.9585 654.5455 664.615
7 H 738.4615 745.562 754.846 748.9515-762.9515 763.636 775.385
8 C 843.856 853.071 861.5385 855.945-871.945 872.727 886.154
9 C#/Db 949.4505 958.58 969.231 962.938-980.938 981.818 996.923
10 D 1054.945 1065.089 1076.923 1069.931-1089.931 1090.909 1107.692
11 D#/Eb 1160.44 1171.598 1184.615 1177-924-1199.924 1200 1218.4615
12 E 1265.9344 1278.1065 1292.308 1283.917-1307.917 1309.094 1329.231
13 F 1371.429 1384.615 1400 1390.91-1416.91 1418.182 1440

Golden Tunings

Phrygian Mode (Neapolitan minor/"major")

Degrees Octatonic Soft Phrygian Phrygian
Min-Med±13¢ Min-Max/Med-Max±13¢ Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 G#/Ab 95.389-97.389 95.578-97.578 96.7665-98.7665 97.176-99.176 98.359-100.359
2 A 190.778-194.778 191.155-195.155 193.533-197.533 194.352-198.352 196.719-200.719
3 A#/Bb 286.1665-292.1665 286.733-292.733 290.2995-296.2995 291.528-297.528 295.078-301.078
4 B 381.555-389.555 382.3105-390.3105 387.063-395.063 388.705-396.705 393.4375-401.4375
5 C 476.944-486.944 477.888-487.888 483.833-493.833 485.881-495.881 491.797-501.797
6 C#/Qb 572.333-584.333 573.466-585.466 580.299-592.299 583.057-595.057 590.156-602.156
7 Q 667.722-681.722 669.043-683.043 677.366-691.366 680.233-694.233 688.516-702.516
8 D 763.111-781.111 764.621-780.621 774.132-790.132 777.409-793.409 786.875-802.875
9 D#/Eb 858.5-876.5 860.199-878.199 870.899-888.899 874.585-892.585 885.234-903.234
10 E 953.8885-973.8885 955.776-975.776 967.665-987.665 971.761-991.761 983.594-1003.594
11 E#/Fb 1049.277-1071.277 1051.354-1073.354 1064.432-1086.432 1068.9375-1090.9375 1081.953-1103.953
12 F 1144.666-1168.666 1146.932-1170.932 1161.198-1185.198 1166.114-1190.114 1180.312-1204.312
13 G 1240.055-1266.055 1242.506-1268.509 1257.965-1283.965 1263.29-1289.29 1278.672-1304.672

Phrygian-Aeolian Mode (intermediate minor)

Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢
1 F#/Gb G#/Ab 100.905-102.905 101.1465-103.1465 102.019-104.019 102.32-104.32 103.425-105.425 103.812-105.812
2 G A 201.81-205.81 202.293-206.293 204.037-208.037 204.641-208.641 206.849-210.849 207.624-211.624
3 G#/Ab A#/Bb 302.715-308.715 303.44-309.44 306.056-312.056 306.961-312.961 310.274-316.274 311.4365-317.4365
4 A B 403.62-411.62 404.586-412.586 408.075-416.075 409.281-417.281 413.699-421.699 415.249-423.249
5 B C 504.525-514.525 505.733-515.733 510.093-520.093 511.602-521.602 517.123-527.123 519.061-529.061
6 B#/Hb C#/Qb 605.43-617.43 606.879-618.879 612.112-624.112 613.922-625.922 620.548-632.548 622.873-634.873
7 H Q 706.335-720.335 708.026-722.026 714.131-728.131 716.242-730.242 723.973-737.973 726.685-740.685
8 C D 807.24-823.24 809.172-825.172 816.1495-832.1495 818.563-834.563 827.3975-843.3975 830.497-846.497
9 C#/Db D#/Eb 908.145-926.145 910.319-928.319 918.168-936.168 920.883-938.883 930.822-948.822 934.309-952.309
10 D E 1009.0505-1029.0505 1011.465-1031.465 1020.186-1040.186 1023.2035-1043.2035 1034.247-1054.2547 1038.122-1058.122
11 D#/Eb E#/Fb 1109.9555-1131.9555 1112.61-1134.612 1122.2055-1143.2055 1125.524-1147.524 1137.672-1159.672 1141.934-1163.934
12 E F 1210.861-1234.861 1213.758-1227.758 1224.224-1248.224 1225.844-1249.884 1241.096-1265.096 1245.746-1269.746
13 F G 1311.767-1337.767 1314.905-1340.905 1326.243-1352.243 1343.1645-1396.1645 1344.521-1370.521 1349.558-1375.558

Aeolian Mode (natural/harmonic minor)

Degrees Octatonic Aeolian Intense Aeolian
Min-Med/Min-Max±13¢ Med-Max-13c Min-Med/Min-Max±13¢ Med-Max-13c
1 F#/Gb 105.256-107.256 105.7715-107.7715 107.738-109.738 108.459-110.459
2 G 210.511-214.511 211.543-215.543 215.477-219.477 216.918-220.918
3 G#/Ab 315.767-321.767 317.315-323.315 323.215-329.215 325.377-331.377
4 A 421.022-429.022 423.086-431.086 430.953-438.953 433.836-437.836
5 B 526.278-536.278 528.858-538.858 538.6915-548.6915 542.295-552.295
6 B#/Hb 631.534-643.534 634.629-646.629 646.43-658.43 650.754-666.754
7 H 736.789-750.789 740.401-754.401 754.168-768.168 759.213-773.213
8 C 842.045-858.045 846.172-862.172 861.906-877.906 867.672-883.672
9 C#/Db 947.3-965.3 951.944-969.944 969.645-986.645 976.131-994.131
10 D 1052.556-1072.556 1057.715-1077.715 1077.383-1077.383 1084.59-1104.59
11 D#/Eb 1157.8115-1179.8115 1163.487-1187.487 1185.121-1207.121 1193.049-1215.049
12 E 1264.067-1287.067 1269.258-1293.258 1292.86-1316.86 1301.508-1325.508
13 F 1368.322-1394.322 1375.03-1401.03 1400.598-1426.598 1409.967-1435.967
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