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]] 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.}}
{| class="wikitable"
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.
|+'''Kartvelian scales'''
 
!
= 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
|[[Kartvelian ditonic|2]]
*1200.000
|[[Kartvelian Tetratonic|4]]
=== Kartvelian tetratonic ===
|[[Kartvelian Hexatonic|6]]
An alternating pattern of [[2edf]] and [[2ed4/3]].
|[[Kartvelian Octatonic|8]]
*350.978
|[[Kartvelian Decatonic|10]]
*701.955
|[[Kartvelian Dodecatonic|12]]
*950.978
|[[Kartvelian Tetradecatonic|14]]
*1200.000
|[[Kartvelian Hexadecatonic|16]]
 
|[[Kartvelian Octadecatonic|18]]
=== Kartvelian pentatonic ===
|[[Kartvelian Icositonic|20]]
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
|[[Kartvelian 21-tonic|21]]
*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
|[[Kartvelian Enneadecatonic|19]]
*701.955
|
*950.979
|-
*1200.000
|
 
|
=== Traditional [[Kartvelian scale]]===
|
An alternating pattern of [[4edf]] and [[3ed4/3]]. Inspired by scales used in [[Music of Georgia|Georgian folk music]].
|
*175.489
|
*350.978
|
*526.466
|
*701.955
|[[Kartvelian Heptadecatonic|17]]
*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
|[[Kartvelian Pentadecatonic|15]]
*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
|[[Kartvelian Triskaidekatonic|13]]
*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
|[[Kartvelian Hendecatonic|11]]
*421.173
|
*561.564
|
*701.955
|
*826.466
|
*950.978
|[[Kartvelian 22-tonic|22]]
*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
|[[Kartvelian Icositonic|20]]
*701.955
|
*867.970
|-
*1033.985
|
*1200.000
|
 
|
=== 5edf Kartvelian decatonic ===
|[[Kartvelian Enneatonic|9]]
An alternating pattern of [[5edf]] and [[5ed4/3]].
|
*140.391
|
*280.782
|
*421.173
|[[Kartvelian Octadecatonic|18]]
*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]].
|[[Kartvelian Hexadecatonic|16]]
*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
|[[Kartvelian 23-tonic|23]]
*233.985
|-
*350.978
|
*467.970
|
*584.963
|[[Kartvelian scale|7]]
*701.955
|
*801.564
|
*901.173
|[[Kartvelian Tetradecatonic|14]]
*1000.782
|
*1100.391
|
*1200.000
|[[Kartvelian 21-tonic|21]]
 
|
=== 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
|[[Kartvelian Enneadecatonic|19]]
*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
|[[Kartvelian Dodecatonic|12]]
*200.559
|
*300.838
|
*401.117
|
*501.396
|
*601.676
|[[Kartvelian 24-tonic|24]]
*701.955
|-
*801.564
|
*901.173
|
*1000.782
|
*1100.391
|
*1200.000
|
 
|
=== 8edf Kartvelian dodecatonic ===
|[[Kartvelian Heptadecatonic|17]]
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
|[[Kartvelian 22-tonic|22]]
 
|
=== 7edf Kartvelian triskaidekatonic ===
|-
An alternating pattern of [[7edf]] and [[6ed4/3]].
|
*100.279
|[[Kartvelian Pentatonic|5]]
*200.559
|
*300.838
|[[Kartvelian Decatonic|10]]
*401.117
|
*501.396
|[[Kartvelian Pentadecatonic|15]]
*601.676
|
*701.955
|[[Kartvelian Icositonic|20]]
*784.962
|
*867.970
|[[Kartvelian 25-tonic|25]]
*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
|[[Kartvelian 23-tonic|23]]
*350.978
|
*438.729
|-
*526.466
|
*614.211
|
*701.955
|
*801.564
|
*901.173
|
*1000.782
|
*1100.391
|[[Kartvelian Octadecatonic|18]]
*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
|[[Kartvelian Triskaidekatonic|13]]
*526.466
|
*614.211
|
*701.955
|
*784.962
|
*867.970
|[[Kartvelian 26-tonic|26]]
*950.978
|-
*1033.985
|
*1116.993
|
*1200.000
|
 
|
==== Subsets ====
|
Fennec scale
|
 
|
* 175.489
|[[Kartvelian 21-tonic|21]]
* 350.978
|
* 526.466
|
* 701.955
|-
* 784.962
|
* 1116.993
|
* 1200.000
|[[Kartvelian Octatonic|8]]
 
|
[[Kartvelian scale]]
|
* 175.489
|[[Kartvelian Hexadecatonic|16]]
* 350.978
|
* 526.466
|
* 701.955
|[[Kartvelian 24-tonic|24]]
* 867.970
|
* 1033.985
|-
* 1200.000
|
 
|
==== Music ====
|
* [https://m.youtube.com/watch?v=rzcuLiE3HhE Funny Snakecharmer] - [[Sven Karma]] (Dec 2023)
|
 
|
=== 9edf Kartvelian tetradecatonic ===
|
An alternating pattern of [[9edf]] and [[5ed4/3]].
|
*87.744
|
*175.489
|
*263.223
|[[Kartvelian 27-tonic|27]]
*350.978
|-
*438.729
|
*526.466
|
*614.211
|
*701.955
|
*801.564
|
*901.173
|
*1000.782
|[[Kartvelian Enneadecatonic|19]]
*1100.391
|
*1200.000
|
 
|
=== 8edf Kartvelian pentadecatonic ===
|-
An alternating pattern of [[8edf]] and [[7ed4/3]].
|
*87.744
|
*175.489
|
*263.223
|[[Kartvelian Hendecatonic|11]]
*350.978
|
*438.729
|
*526.466
|
*614.211
|[[Kartvelian 22-tonic|22]]
*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
|[[Kartvelian 25-tonic|25]]
*155.990
|
*233.985
|-
*311.980
|
*379.975
|
*467.970
|
*545.965
|
*623.965
|[[Kartvelian Tetradecatonic|14]]
*701.955
|
*784.962
|
*867.970
|
*950.978
|
*1033.985
|[[Kartvelian 28-tonic|28]]
*1116.993
|-
*1200.000
|
 
|
=== 9edf Kartvelian hexadecatonic ===
|
An alternating pattern of [[9edf]] and [[7ed4/3]].
|
*77.995
|
*155.990
|[[Kartvelian Heptadecatonic|17]]
*233.985
|
*311.980
|
*379.975
|
*467.970
|
*545.965
|-
*623.965
|
*701.955
|
*773.104
|
*842.254
|
*914.403
|
*986.552
|
*1057.701
|[[Kartvelian Icositonic|20]]
*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
|[[Kartvelian 23-tonic|23]]
*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]].
|[[Kartvelian 26-tonic|26]]
*77.995
|
*155.990
|-
*233.985
|
*311.980
|
*379.975
|
*467.970
|
*545.965
|
*623.965
|
*701.955
|
*764.211
|
*826.466
|
*888.722
|[[Kartvelian 29-tonic|29]]
*950.978
|-
*1013.233
|[[Kartvelian Tritonic|3]]
*1075.489
|[[Kartvelian Hexatonic|6]]
*1137.744
|[[Kartvelian Enneatonic|9]]
*1200.000
|[[Kartvelian Dodecatonic|12]]
 
|[[Kartvelian Pentadecatonic|15]]
=== 10edf Kartvelian heptadecatonic ===
|[[Kartvelian Octadecatonic|18]]
An alternating pattern of [[10edf]] and [[7ed4/3]]. Very close to [[17edo]].
|[[Kartvelian 21-tonic|21]]
*70.196
|[[Kartvelian 24-tonic|24]]
*140.391
|[[Kartvelian 27-tonic|27]]
*210.587
|[[Kartvelian Triacontatonic|30]]
*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
[[Category:Lists of scales]]
[[Category:EDF]]
[[Category:ED4/3]]
[[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
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