Kartvelian scales: Difference between revisions

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The Kartvelian scales generalize the [[wikipedia:Music_of_Georgia_(country)#Scales_and_tuning_system|traditional scale of Georgian folk music]], the [[Kartvelian scale]], to divide the perfect [[Ed4/3|fourth]] and [[EDF|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.
{{todo|clarify|inline=1|comment=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 [[Music of Georgia|Georgian folk music]], the [[Kartvelian scale]], to divide the perfect [[Ed4/3|fourth]] and [[EDF|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 =
= Examples =
Line 6: Line 7:
=== Kartvelian ditonic ===
=== Kartvelian ditonic ===
An alternating pattern of [[1edf]] and [[1ed4/3]].
An alternating pattern of [[1edf]] and [[1ed4/3]].
*701.978
*701.955
*1200.000
*1200.000
=== Kartvelian tritonic ===
=== Kartvelian tritonic ===
Line 47: Line 48:


=== Traditional [[Kartvelian scale]]===
=== Traditional [[Kartvelian scale]]===
An alternating pattern of [[4edf]] and [[3ed4/3]].
An alternating pattern of [[4edf]] and [[3ed4/3]]. Inspired by scales used in [[Music of Georgia|Georgian folk music]].
*175.489
*175.489
*350.978
*350.978
Line 53: Line 54:
*701.955
*701.955
*867.970
*867.970
 
*1033.985
* 1033.985
*1200.000
*1200.000


Line 158: Line 158:


=== 7edf Kartvelian dodecatonic ===
=== 7edf Kartvelian dodecatonic ===
An alternating pattern of [[7edf]] and [[5ed4/3]].
An alternating pattern of [[7edf]] and [[5ed4/3]]. Very close to [[12edo]].
*100.279
*100.279
*200.559
*200.559
Line 235: Line 235:
*1116.993
*1116.993
*1200.000
*1200.000
==== Subsets ====
Fennec scale
* 175.489
* 350.978
* 526.466
* 701.955
* 784.962
* 1116.993
* 1200.000
[[Kartvelian scale]]
* 175.489
* 350.978
* 526.466
* 701.955
* 867.970
* 1033.985
* 1200.000
==== Music ====
* [https://m.youtube.com/watch?v=rzcuLiE3HhE Funny Snakecharmer] - [[Sven Karma]] (Dec 2023)


=== 9edf Kartvelian tetradecatonic ===
=== 9edf Kartvelian tetradecatonic ===
Line 347: Line 370:


=== 10edf Kartvelian heptadecatonic ===
=== 10edf Kartvelian heptadecatonic ===
An alternating pattern of [[10edf]] and [[7ed4/3]].
An alternating pattern of [[10edf]] and [[7ed4/3]]. Very close to [[17edo]].
*70.196
*70.196
*140.391
*140.391
Line 365: Line 388:
*1128.851
*1128.851
*1200.000
*1200.000
==== Subsets ====
''See [[17edo#Scales]]''


=== 10edf Kartvelian octadecatonic ===
=== 10edf Kartvelian octadecatonic ===
Line 499: Line 525:


=== 12edf Kartvelian 21-tonic ===
=== 12edf Kartvelian 21-tonic ===
An alternating pattern of [[12edf]] and [[9ed4/3]].
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
*58.496
*116.993
*116.993
Line 521: Line 547:
*1144.668
*1144.668
*1200.000
*1200.000
==== Subsets ====
[[Kartvelian scale]]
* 175.489
* 350.978
* 526.466
* 701.955
* 867.970
* 1033.985
* 1200.000


=== 13edf Kartvelian 21-tonic ===
=== 13edf Kartvelian 21-tonic ===
Line 675: Line 711:


=== 14edf Kartvelian 24-tonic ===
=== 14edf Kartvelian 24-tonic ===
An alternating pattern of [[14edf]] and [[10ed4/3]].
An alternating pattern of [[14edf]] and [[10ed4/3]]. Very close to [[24edo]].
*50.140
*50.140
*100.297
*100.297
Line 700: Line 736:
*1150.196
*1150.196
*1200.000
*1200.000
==== Subsets ====
''See [[24edo#Scales_.2F_modes]]''


=== 14edf Kartvelian 25-tonic ===
=== 14edf Kartvelian 25-tonic ===
Line 876: Line 915:


=== 16edf Kartvelian 28-tonic ===
=== 16edf Kartvelian 28-tonic ===
An alternating pattern of [[16edf]] and [[12ed4/3]].
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
*43.872
*87.744
*87.744
Line 905: Line 944:
*1158.496
*1158.496
*1200.000
*1200.000
==== Subsets ====
Fennec scale
* 175.489
* 350.978
* 526.466
* 701.955
* 784.962
* 1116.993
* 1200.000
[[Kartvelian scale]]
* 175.489
* 350.978
* 526.466
* 701.955
* 867.970
* 1033.985
* 1200.000


=== 17edf Kartvelian 28-tonic ===
=== 17edf Kartvelian 28-tonic ===
Line 970: Line 1,030:


=== 17edf Kartvelian 29-tonic ===
=== 17edf Kartvelian 29-tonic ===
An alternating pattern of [[17edf]] and [[12ed4/3]].
An alternating pattern of [[17edf]] and [[12ed4/3]]. Very close to [[29edo]].
*41.291
*41.291
*82.583
*82.583
Line 1,000: Line 1,060:
*1158.496
*1158.496
*1200.000
*1200.000
==== Subsets ====
''See [[29edo#Scales]]''


=== 17edf Kartvelian triacontatonic ===
=== 17edf Kartvelian triacontatonic ===
Line 1,066: Line 1,129:
*1158.496
*1158.496
*1200.000
*1200.000
 
[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[Category:Scales by family]]
[[Category:EDF]]
[[Category:EDF]]
[[Category:ED4/3]]
[[Category:ED4/3]]
[[Category:Gamelan]]
[[Category:Tempered scales]]
[[Category:Pages with mostly numerical content]]
[[Category:Well tempered nonet]]

Latest revision as of 03:06, 24 June 2025

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. Inspired by scales used in Georgian folk music.

  • 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

Kartvelian scale

  • 175.489
  • 350.978
  • 526.466
  • 701.955
  • 867.970
  • 1033.985
  • 1200.000

Music

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

Kartvelian scale

  • 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

See 24edo#Scales_.2F_modes

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

Kartvelian scale

  • 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
Retrieved from "https://en.xen.wiki/index.php?title=Kartvelian_scales&oldid=203219"