# 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

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

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

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

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

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

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

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

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

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

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

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

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

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

• 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

### 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

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

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