Kartvelian scales
Todo: clarify
Explain why edo degrees are implied when the scale is based on an edf segment and an ed4/3 segment.
The Kartvelian scales generalize the traditional scale of Georgian folk music, the Kartvelian scale, to divide the perfect fourth and fifth into arbitrary numbers of equal steps. The fifth, or conversely the fourth, will be an interval of the corresponding edo which may generate 2L 3s or 3L 2s and normally stands within one edo degree of 3/2. The optimal patent tuning of a well tempered nonet targets the nonet of a Kartvelian scale where a 3/2 is available.
Examples
(Intervals given in cents.)
Kartvelian ditonic
An alternating pattern of 1edf and 1ed4/3.
- 701.955
- 1200.000
Kartvelian tritonic
An alternating pattern of 2edf and 1ed4/3.
- 350.978
- 701.955
- 1200.000
Kartvelian tetratonic
An alternating pattern of 2edf and 2ed4/3.
- 350.978
- 701.955
- 950.978
- 1200.000
Kartvelian pentatonic
An alternating pattern of 3edf and 2ed4/3. Approximates the Slendro scale.
- 233.985
- 467.970
- 701.955
- 950.978
- 1200.000
3edf Kartvelian hexatonic
An alternating pattern of 3edf and 3ed4/3.
- 233.985
- 467.970
- 701.955
- 867.970
- 1033.985
- 1200.000
4edf Kartvelian hexatonic
An alternating pattern of 4edf and 2ed4/3.
- 175.489
- 350.978
- 526.466
- 701.955
- 950.979
- 1200.000
Traditional Kartvelian scale
An alternating pattern of 4edf and 3ed4/3. Used in traditional Georgian music from ancient times to the present day.
- 175.489
- 350.978
- 526.466
- 701.955
- 867.970
- 1033.985
- 1200.000
4edf Kartvelian octatonic
An alternating pattern of 4edf and 4ed4/3.
- 175.489
- 350.978
- 526.466
- 701.955
- 826.466
- 950.978
- 1075.489
- 1200.000
5edf Kartvelian octatonic
An alternating pattern of 5edf and 3ed4/3.
- 140.391
- 280.782
- 421.173
- 561.564
- 701.955
- 867.970
- 1033.985
- 1200.000
5edf Kartvelian enneatonic
An alternating pattern of 5edf and 4ed4/3. Approximates the 9-tone Pelog scale.
- 140.391
- 280.872
- 421.173
- 561.564
- 701.955
- 826.466
- 950.978
- 1075.489
- 1200.000
6edf Kartvelian enneatonic
An alternating pattern of 6edf and 3ed4/3.
- 116.993
- 233.985
- 350.978
- 467.970
- 584.963
- 701.955
- 867.970
- 1033.985
- 1200.000
5edf Kartvelian decatonic
An alternating pattern of 5edf and 5ed4/3.
- 140.391
- 280.782
- 421.173
- 561.564
- 701.955
- 801.564
- 901.173
- 1000.782
- 1100.391
- 1200.000
6edf Kartvelian decatonic
An alternating pattern of 6edf and 4ed4/3.
- 116.993
- 233.985
- 350.978
- 467.970
- 584.963
- 701.955
- 826.466
- 950.978
- 1075.489
- 1200.000
6edf Kartvelian hendecatonic
An alternating pattern of 6edf and 5ed4/3.
- 116.993
- 233.985
- 350.978
- 467.970
- 584.963
- 701.955
- 801.564
- 901.173
- 1000.782
- 1100.391
- 1200.000
7edf Kartvelian hendecatonic
An alternating pattern of 7edf and 4ed4/3.
- 100.279
- 200.559
- 300.838
- 401.117
- 501.396
- 601.676
- 701.955
- 826.466
- 950.978
- 1075.489
- 1200.000
7edf Kartvelian dodecatonic
An alternating pattern of 7edf and 5ed4/3. Very close to 12edo.
- 100.279
- 200.559
- 300.838
- 401.117
- 501.396
- 601.676
- 701.955
- 801.564
- 901.173
- 1000.782
- 1100.391
- 1200.000
8edf Kartvelian dodecatonic
An alternating pattern of 8edf and 4ed4/3.
- 87.744
- 175.489
- 263.223
- 350.978
- 438.729
- 526.466
- 614.211
- 701.955
- 826.466
- 950.978
- 1075.489
- 1200.000
7edf Kartvelian triskaidekatonic
An alternating pattern of 7edf and 6ed4/3.
- 100.279
- 200.559
- 300.838
- 401.117
- 501.396
- 601.676
- 701.955
- 784.962
- 867.970
- 950.978
- 1033.985
- 1116.993
- 1200.000
8edf Kartvelian triskaidekatonic
An alternating pattern of 8edf and 5ed4/3.
- 87.744
- 175.489
- 263.223
- 350.978
- 438.729
- 526.466
- 614.211
- 701.955
- 801.564
- 901.173
- 1000.782
- 1100.391
- 1200.000
8edf Kartvelian tetradecatonic
An alternating pattern of 8edf and 6ed4/3. Notably, this scale contains within it the traditional Kartvelian scale, so it is a useful extension of that scale.
- 87.744
- 175.489
- 263.223
- 350.978
- 438.729
- 526.466
- 614.211
- 701.955
- 784.962
- 867.970
- 950.978
- 1033.985
- 1116.993
- 1200.000
Subsets
Fennec scale
- 175.489
- 350.978
- 526.466
- 701.955
- 784.962
- 1116.993
- 1200.000
- 175.489
- 350.978
- 526.466
- 701.955
- 867.970
- 1033.985
- 1200.000
9edf Kartvelian tetradecatonic
An alternating pattern of 9edf and 5ed4/3.
- 87.744
- 175.489
- 263.223
- 350.978
- 438.729
- 526.466
- 614.211
- 701.955
- 801.564
- 901.173
- 1000.782
- 1100.391
- 1200.000
8edf Kartvelian pentadecatonic
An alternating pattern of 8edf and 7ed4/3.
- 87.744
- 175.489
- 263.223
- 350.978
- 438.729
- 526.466
- 614.211
- 701.955
- 773.104
- 842.254
- 914.403
- 986.552
- 1057.701
- 1128.851
- 1200.000
9edf Kartvelian pentadecatonic
An alternating pattern of 9edf and 6ed4/3.
- 77.995
- 155.990
- 233.985
- 311.980
- 379.975
- 467.970
- 545.965
- 623.965
- 701.955
- 784.962
- 867.970
- 950.978
- 1033.985
- 1116.993
- 1200.000
9edf Kartvelian hexadecatonic
An alternating pattern of 9edf and 7ed4/3.
- 77.995
- 155.990
- 233.985
- 311.980
- 379.975
- 467.970
- 545.965
- 623.965
- 701.955
- 773.104
- 842.254
- 914.403
- 986.552
- 1057.701
- 1128.851
- 1200.000
10edf Kartvelian hexadecatonic
An alternating pattern of 10edf and 6ed4/3.
- 70.196
- 140.391
- 210.587
- 280.782
- 350.978
- 421.173
- 491.396
- 561.564
- 631.760
- 701.955
- 784.962
- 867.970
- 950.978
- 1033.985
- 1116.993
- 1200.000
9edf Kartvelian heptadecatonic
An alternating pattern of 9edf and 8ed4/3.
- 77.995
- 155.990
- 233.985
- 311.980
- 379.975
- 467.970
- 545.965
- 623.965
- 701.955
- 764.211
- 826.466
- 888.722
- 950.978
- 1013.233
- 1075.489
- 1137.744
- 1200.000
10edf Kartvelian heptadecatonic
An alternating pattern of 10edf and 7ed4/3. Very close to 17edo.
- 70.196
- 140.391
- 210.587
- 280.782
- 350.978
- 421.173
- 491.396
- 561.564
- 631.760
- 701.955
- 773.104
- 842.254
- 914.403
- 986.552
- 1057.701
- 1128.851
- 1200.000
Subsets
See 17edo#Scales
10edf Kartvelian octadecatonic
An alternating pattern of 10edf and 8ed4/3.
- 70.196
- 140.391
- 210.587
- 280.782
- 350.978
- 421.173
- 491.396
- 561.564
- 631.760
- 701.955
- 764.211
- 826.466
- 888.722
- 950.978
- 1013.233
- 1075.489
- 1137.744
- 1200.000
11edf Kartvelian octadecatonic
An alternating pattern of 11edf and 7ed4/3.
- 63.814
- 127.628
- 191.442
- 255.256
- 319.070
- 382.885
- 446.699
- 510.513
- 574.327
- 638.141
- 701.955
- 773.104
- 842.254
- 914.403
- 986.552
- 1057.701
- 1128.851
- 1200.000
11edf Kartvelian enneadecatonic
An alternating pattern of 11edf and 8ed4/3.
- 63.814
- 127.628
- 191.442
- 255.256
- 319.070
- 382.885
- 446.699
- 510.513
- 574.327
- 638.141
- 701.955
- 764.211
- 826.466
- 888.722
- 950.978
- 1013.233
- 1075.489
- 1137.744
- 1200.000
12edf Kartvelian enneadecatonic
An alternating pattern of 12edf and 7ed4/3.
- 58.496
- 116.993
- 175.489
- 233.985
- 292.481
- 350.978
- 409.474
- 467.970
- 526.466
- 584.963
- 643.459
- 701.955
- 773.104
- 842.254
- 914.403
- 986.552
- 1057.701
- 1128.851
- 1200.000
11edf Kartvelian icositonic
An alternating pattern of 11edf and 9ed4/3.
- 63.814
- 127.628
- 191.442
- 255.256
- 319.070
- 382.885
- 446.699
- 510.513
- 574.327
- 638.141
- 701.955
- 757.293
- 811.632
- 867.970
- 923.308
- 978.946
- 1033.985
- 1089.323
- 1144.668
- 1200.000
12edf Kartvelian icositonic
An alternating pattern of 12edf and 8ed4/3.
- 58.496
- 116.993
- 175.489
- 233.985
- 292.481
- 350.978
- 409.474
- 467.970
- 526.466
- 584.963
- 643.459
- 701.955
- 764.211
- 826.466
- 888.722
- 950.978
- 1013.233
- 1075.489
- 1137.744
- 1200.000
12edf Kartvelian 21-tonic
An alternating pattern of 12edf and 9ed4/3. Notably, this scale contains within it the traditional Kartvelian scale, so it is a useful extension of that scale.
- 58.496
- 116.993
- 175.489
- 233.985
- 292.481
- 350.978
- 409.474
- 467.970
- 526.466
- 584.963
- 643.459
- 701.955
- 757.293
- 811.632
- 867.970
- 923.308
- 978.946
- 1033.985
- 1089.323
- 1144.668
- 1200.000
Subsets
- 175.489
- 350.978
- 526.466
- 701.955
- 867.970
- 1033.985
- 1200.000
13edf Kartvelian 21-tonic
An alternating pattern of 13edf and 8ed4/3.
- 53.997
- 107.993
- 161.990
- 215.986
- 269.983
- 323.979
- 377.979
- 431.972
- 495.969
- 539.996
- 593.962
- 647.958
- 701.955
- 764.211
- 826.466
- 888.722
- 950.978
- 1013.233
- 1075.489
- 1137.744
- 1200.000
12edf Kartvelian 22-tonic
An alternating pattern of 12edf and 10ed4/3.
- 58.496
- 116.993
- 175.489
- 233.985
- 292.481
- 350.978
- 409.474
- 467.970
- 526.466
- 584.963
- 643.459
- 701.955
- 757.293
- 811.632
- 867.970
- 923.308
- 978.946
- 1033.985
- 1089.323
- 1144.668
- 1200.000
13edf Kartvelian 22-tonic
An alternating pattern of 13edf and 9ed4/3.
- 53.997
- 107.993
- 161.990
- 215.986
- 269.983
- 323.979
- 377.979
- 431.972
- 495.969
- 539.996
- 593.962
- 647.958
- 701.955
- 757.293
- 811.632
- 867.970
- 923.308
- 978.946
- 1033.985
- 1089.323
- 1144.668
- 1200.000
13edf Kartvelian 23-tonic
An alternating pattern of 13edf and 10ed4/3.
- 53.997
- 107.993
- 161.990
- 215.986
- 269.983
- 323.979
- 377.979
- 431.972
- 495.969
- 539.996
- 593.962
- 647.958
- 701.955
- 751.760
- 801.564
- 851.370
- 901.173
- 950.978
- 1000.782
- 1050.586
- 1100.391
- 1150.196
- 1200.000
14edf Kartvelian 23-tonic
An alternating pattern of 14edf and 9ed4/3.
- 50.140
- 100.297
- 150.419
- 200.594
- 250.698
- 300.838
- 350.978
- 401.117
- 451.257
- 501.396
- 551.536
- 601.676
- 651.815
- 701.955
- 757.293
- 811.632
- 867.970
- 923.308
- 978.946
- 1033.985
- 1089.323
- 1144.668
- 1200.000
13edf Kartvelian 24-tonic
An alternating pattern of 13edf and 11ed4/3.
- 53.997
- 107.993
- 161.990
- 215.986
- 269.983
- 323.979
- 377.979
- 431.972
- 495.969
- 539.996
- 593.962
- 647.958
- 701.955
- 747.232
- 792.509
- 837.785
- 883.062
- 928.339
- 973.616
- 1018.893
- 1064.170
- 1109.446
- 1154.723
- 1200.000
14edf Kartvelian 24-tonic
An alternating pattern of 14edf and 10ed4/3. Very close to 24edo.
- 50.140
- 100.297
- 150.419
- 200.594
- 250.698
- 300.838
- 350.978
- 401.117
- 451.257
- 501.396
- 551.536
- 601.676
- 651.815
- 701.955
- 751.760
- 801.564
- 851.370
- 901.173
- 950.978
- 1000.782
- 1050.586
- 1100.391
- 1150.196
- 1200.000
Subsets
14edf Kartvelian 25-tonic
An alternating pattern of 14edf and 11ed4/3.
- 50.140
- 100.297
- 150.419
- 200.594
- 250.698
- 300.838
- 350.978
- 401.117
- 451.257
- 501.396
- 551.536
- 601.676
- 651.815
- 701.955
- 747.232
- 792.509
- 837.785
- 883.062
- 928.339
- 973.616
- 1018.893
- 1064.170
- 1109.446
- 1154.723
- 1200.000
15edf Kartvelian 25-tonic
An alternating pattern of 15edf and 10ed4/3.
- 46.797
- 93.594
- 140.391
- 187.188
- 233.985
- 280.782
- 327.579
- 374.376
- 421.173
- 467.970
- 514.767
- 561.564
- 608.361
- 655.158
- 701.955
- 751.760
- 801.564
- 851.370
- 901.173
- 950.978
- 1000.782
- 1050.586
- 1100.391
- 1150.196
- 1200.000
15edf Kartvelian 26-tonic
An alternating pattern of 15edf and 11ed4/3.
- 46.797
- 93.594
- 140.391
- 187.188
- 233.985
- 280.782
- 327.579
- 374.376
- 421.173
- 467.970
- 514.767
- 561.564
- 608.361
- 655.158
- 701.955
- 747.232
- 792.509
- 837.785
- 883.062
- 928.339
- 973.616
- 1018.893
- 1064.170
- 1109.446
- 1154.723
- 1200.000
16edf Kartvelian 26-tonic
An alternating pattern of 16edf and 10ed4/3.
- 43.872
- 87.744
- 131.617
- 175.489
- 219.360
- 263.233
- 307.105
- 350.978
- 394.850
- 438.722
- 482.594
- 526.466
- 570.338
- 614.211
- 658.083
- 701.955
- 751.760
- 801.564
- 851.370
- 901.173
- 950.978
- 1000.782
- 1050.586
- 1100.391
- 1150.196
- 1200.000
15edf Kartvelian 27-tonic
An alternating pattern of 15edf and 12ed4/3.
- 46.797
- 93.594
- 140.391
- 187.188
- 233.985
- 280.782
- 327.579
- 374.376
- 421.173
- 467.970
- 514.767
- 561.564
- 608.361
- 655.158
- 701.955
- 743.459
- 784.962
- 826.466
- 867.970
- 909.474
- 950.978
- 992.481
- 1033.985
- 1075.489
- 1116.983
- 1158.496
- 1200.000
16edf Kartvelian 27-tonic
An alternating pattern of 16edf and 11ed4/3.
- 43.872
- 87.744
- 131.617
- 175.489
- 219.360
- 263.233
- 307.105
- 350.978
- 394.850
- 438.722
- 482.594
- 526.466
- 570.338
- 614.211
- 658.083
- 701.955
- 747.232
- 792.509
- 837.785
- 883.062
- 928.339
- 973.616
- 1018.893
- 1064.170
- 1109.446
- 1154.723
- 1200.000
16edf Kartvelian 28-tonic
An alternating pattern of 16edf and 12ed4/3. Notably, this scale contains within it the traditional Kartvelian scale, so it is a useful extension of that scale.
- 43.872
- 87.744
- 131.617
- 175.489
- 219.360
- 263.233
- 307.105
- 350.978
- 394.850
- 438.722
- 482.594
- 526.466
- 570.338
- 614.211
- 658.083
- 701.955
- 743.459
- 784.962
- 826.466
- 867.970
- 909.474
- 950.978
- 992.481
- 1033.985
- 1075.489
- 1116.983
- 1158.496
- 1200.000
Subsets
Fennec scale
- 175.489
- 350.978
- 526.466
- 701.955
- 784.962
- 1116.993
- 1200.000
- 175.489
- 350.978
- 526.466
- 701.955
- 867.970
- 1033.985
- 1200.000
17edf Kartvelian 28-tonic
An alternating pattern of 17edf and 11ed4/3.
- 41.291
- 82.583
- 123.874
- 165.166
- 206.457
- 247.749
- 289.040
- 330.332
- 371.623
- 412.915
- 454.206
- 495.498
- 536.789
- 578.081
- 619.372
- 660.664
- 701.955
- 747.232
- 792.509
- 837.785
- 883.062
- 928.339
- 973.616
- 1018.893
- 1064.170
- 1109.446
- 1154.723
- 1200.000
16edf Kartvelian 29-tonic
An alternating pattern of 16edf and 13ed4/3.
- 43.872
- 87.744
- 131.617
- 175.489
- 219.360
- 263.233
- 307.105
- 350.978
- 394.850
- 438.722
- 482.594
- 526.466
- 570.338
- 614.211
- 658.083
- 701.955
- 740.266
- 778.577
- 816.888
- 855.200
- 893.511
- 931.822
- 970.135
- 1008.444
- 1046.755
- 1085.067
- 1123.378
- 1161.689
- 1200.000
17edf Kartvelian 29-tonic
An alternating pattern of 17edf and 12ed4/3. Very close to 29edo.
- 41.291
- 82.583
- 123.874
- 165.166
- 206.457
- 247.749
- 289.040
- 330.332
- 371.623
- 412.915
- 454.206
- 495.498
- 536.789
- 578.081
- 619.372
- 660.664
- 701.955
- 743.459
- 784.962
- 826.466
- 867.970
- 909.474
- 950.978
- 992.481
- 1033.985
- 1075.489
- 1116.983
- 1158.496
- 1200.000
Subsets
See 29edo#Scales
17edf Kartvelian triacontatonic
An alternating pattern of 17edf and 13ed4/3.
- 41.291
- 82.583
- 123.874
- 165.166
- 206.457
- 247.749
- 289.040
- 330.332
- 371.623
- 412.915
- 454.206
- 495.498
- 536.789
- 578.081
- 619.372
- 660.664
- 701.955
- 740.266
- 778.577
- 816.888
- 855.200
- 893.511
- 931.822
- 970.135
- 1008.444
- 1046.755
- 1085.067
- 1123.378
- 1161.689
- 1200.000
18edf Kartvelian triacontatonic
An alternating pattern of 18edf and 12ed4/3.
- 38.998
- 77.995
- 116.993
- 155.990
- 194.988
- 233.985
- 272.983
- 311.980
- 350.978
- 389.975
- 428.973
- 467.970
- 506.068
- 545.965
- 584.963
- 622.980
- 661.978
- 701.955
- 743.459
- 784.962
- 826.466
- 867.970
- 909.474
- 950.978
- 992.481
- 1033.985
- 1075.489
- 1116.983
- 1158.496
- 1200.000