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Kartvelian scales: Difference between revisions

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Merged all the individual pages into one central page, and split the scales into separate subheadings (e.g. instead of just calling both scales "Kartvelian triacontatonic", I split them into "18edf Kartvelian triacontatonic" and "17edf Kartvelian triacontatonic". Added to a few categories, including Gamelan because the original articles and the new article both mention two of the scales' similarity to slendro and pelog respectively.
Line 1: Line 1:
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.
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.
{| class="wikitable"
 
|+'''Kartvelian scales'''
= 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
|[[Kartvelian ditonic|2]]
*1200.000
|[[Kartvelian Tetratonic|4]]
 
|[[Kartvelian Hexatonic|6]]
== Kartvelian tetratonic ==
|[[Kartvelian Octatonic|8]]
An alternating pattern of [[2edf]] and [[2ed4/3]].
|[[Kartvelian Decatonic|10]]
*350.978
|[[Kartvelian Dodecatonic|12]]
*701.955
|[[Kartvelian Tetradecatonic|14]]
*950.978
|[[Kartvelian Hexadecatonic|16]]
*1200.000
|[[Kartvelian Octadecatonic|18]]
 
|[[Kartvelian Icositonic|20]]
== 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
|[[Kartvelian 21-tonic|21]]
*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
|[[Kartvelian Enneadecatonic|19]]
*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
|[[Kartvelian Heptadecatonic|17]]
*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
|[[Kartvelian Pentadecatonic|15]]
*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
|[[Kartvelian Triskaidekatonic|13]]
*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
|[[Kartvelian Hendecatonic|11]]
*280.872
|
*421.173
|
*561.564
|
*701.955
|
*826.466
|[[Kartvelian 22-tonic|22]]
*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
|[[Kartvelian Icositonic|20]]
*584.963
|
*701.955
|-
*867.970
|
*1033.985
|
*1200.000
|
 
|[[Kartvelian Enneatonic|9]]
== 5edf Kartvelian decatonic ==
|
An alternating pattern of [[5edf]] and [[5ed4/3]].
|
*140.391
|
*280.782
|[[Kartvelian Octadecatonic|18]]
*421.173
|
*561.564
|
*701.955
|-
*801.564
|
*901.173
|
*1000.782
|
*1100.391
|
*1200.000
|
 
|
== 6edf Kartvelian decatonic ==
|[[Kartvelian Hexadecatonic|16]]
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]].
|[[Kartvelian 23-tonic|23]]
*116.993
|-
*233.985
|
*350.978
|
*467.970
|[[Kartvelian scale|7]]
*584.963
|
*701.955
|
*801.564
|[[Kartvelian Tetradecatonic|14]]
*901.173
|
*1000.782
|
*1100.391
|[[Kartvelian 21-tonic|21]]
*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
|[[Kartvelian Enneadecatonic|19]]
*701.955
|
*826.466
|
*950.978
|-
*1075.489
|
*1200.000
|
 
|
== 7edf Kartvelian dodecatonic ==
|
An alternating pattern of [[7edf]] and [[5ed4/3]].
|[[Kartvelian Dodecatonic|12]]
*100.279
|
*200.559
|
*300.838
|
*401.117
|
*501.396
|[[Kartvelian 24-tonic|24]]
*601.676
|-
*701.955
|
*801.564
|
*901.173
|
*1000.782
|
*1100.391
|
*1200.000
|
 
|[[Kartvelian Heptadecatonic|17]]
== 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
|[[Kartvelian 22-tonic|22]]
*1200.000
|
 
|-
== 7edf Kartvelian triskaidekatonic ==
|
An alternating pattern of [[7edf]] and [[6ed4/3]].
|[[Kartvelian Pentatonic|5]]
*100.279
|
*200.559
|[[Kartvelian Decatonic|10]]
*300.838
|
*401.117
|[[Kartvelian Pentadecatonic|15]]
*501.396
|
*601.676
|[[Kartvelian Icositonic|20]]
*701.955
|
*784.962
|[[Kartvelian 25-tonic|25]]
*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
|[[Kartvelian 23-tonic|23]]
*263.223
|
*350.978
|-
*438.729
|
*526.466
|
*614.211
|
*701.955
|
*801.564
|
*901.173
|
*1000.782
|[[Kartvelian Octadecatonic|18]]
*1100.391
|
*1200.000
|
 
|
== 8edf Kartvelian tetradecatonic ==
|-
An alternating pattern of [[8edf]] and [[6ed4/3]].
|
*87.744
|
*175.489
|
*263.223
|
*350.978
|[[Kartvelian Triskaidekatonic|13]]
*438.729
|
*526.466
|
*614.211
|
*701.955
|
*784.962
|[[Kartvelian 26-tonic|26]]
*867.970
|-
*950.978
|
*1033.985
|
*1116.993
|
*1200.000
|
 
|
== 9edf Kartvelian tetradecatonic ==
|
An alternating pattern of [[9edf]] and [[5ed4/3]].
|
*87.744
|[[Kartvelian 21-tonic|21]]
*175.489
|
*263.223
|
*350.978
|-
*438.729
|
*526.466
|
*614.211
|[[Kartvelian Octatonic|8]]
*701.955
|
*801.564
|
*901.173
|[[Kartvelian Hexadecatonic|16]]
*1000.782
|
*1100.391
|
*1200.000
|[[Kartvelian 24-tonic|24]]
 
|
== 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
|[[Kartvelian 27-tonic|27]]
*842.254
|-
*914.403
|
*986.552
|
*1057.701
|
*1128.851
|
*1200.000
|
 
|
== 9edf Kartvelian pentadecatonic ==
|[[Kartvelian Enneadecatonic|19]]
An alternating pattern of [[9edf]] and [[6ed4/3]].
|
*77.995
|
*155.990
|
*233.985
|-
*311.980
|
*379.975
|
*467.970
|
*545.965
|[[Kartvelian Hendecatonic|11]]
*623.965
|
*701.955
|
*784.962
|
*867.970
|[[Kartvelian 22-tonic|22]]
*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
|[[Kartvelian 25-tonic|25]]
*467.970
|
*545.965
|-
*623.965
|
*701.955
|
*773.104
|
*842.254
|
*914.403
|[[Kartvelian Tetradecatonic|14]]
*986.552
|
*1057.701
|
*1128.851
|
*1200.000
|
 
|[[Kartvelian 28-tonic|28]]
== 10edf Kartvelian hexadecatonic ==
|-
An alternating pattern of [[10edf]] and [[6ed4/3]].
|
*70.196
|
*140.391
|
*210.587
|
*280.782
|
*350.978
|[[Kartvelian Heptadecatonic|17]]
*421.173
|
*491.396
|
*561.564
|
*631.760
|
*701.955
|-
*784.962
|
*867.970
|
*950.978
|
*1033.985
|
*1116.993
|
*1200.000
|
 
|[[Kartvelian Icositonic|20]]
== 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
|[[Kartvelian 23-tonic|23]]
*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
|[[Kartvelian 26-tonic|26]]
*210.587
|
*280.782
|-
*350.978
|
*421.173
|
*491.396
|
*561.564
|
*631.760
|
*701.955
|
*773.104
|
*842.254
|
*914.403
|
*986.552
|[[Kartvelian 29-tonic|29]]
*1057.701
|-
*1128.851
|[[Kartvelian Tritonic|3]]
*1200.000
|[[Kartvelian Hexatonic|6]]
 
|[[Kartvelian Enneatonic|9]]
== 10edf Kartvelian octadecatonic ==
|[[Kartvelian Dodecatonic|12]]
An alternating pattern of [[10edf]] and [[8ed4/3]].
|[[Kartvelian Pentadecatonic|15]]
*70.196
|[[Kartvelian Octadecatonic|18]]
*140.391
|[[Kartvelian 21-tonic|21]]
*210.587
|[[Kartvelian 24-tonic|24]]
*280.782
|[[Kartvelian 27-tonic|27]]
*350.978
|[[Kartvelian Triacontatonic|30]]
*421.173
|}
*491.396
[[Category:Kartvelian]]
*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
 
[[Category:Lists of scales]]
[[Category:Scales by family]]
[[Category:Scales by family]]
[[Category:EDF]]
[[Category:ED4/3]]
[[Category:Gamelan]]
Retrieved from "https://en.xen.wiki/w/Kartvelian_scales"