The Kartvelian scales generalize the traditional scale of Georgian folk music to divide the perfect fourth and fifth into arbitrary numbers of equal steps. This scale, called “untempered” on Wikipedia, is more properly described as the first known well temperament in music history. 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.

Examples

(Intervals given in cents.)

Kartvelian ditonic

An alternating pattern of 1edf and 1ed4/3.

701.978
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.

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.

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.

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

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.

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

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.

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 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.

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.

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

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.

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

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

Kartvelian scales