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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.}}
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 =
(Intervals given in [[cents]].)
(Intervals given in [[cents]].)
 
 
== 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 ===
An alternating pattern of [[2edf]] and [[1ed4/3]].
An alternating pattern of [[2edf]] and [[1ed4/3]].
*350.978
*350.978
*701.955
*701.955
*1200.000
*1200.000
== Kartvelian tetratonic ==
=== Kartvelian tetratonic ===
An alternating pattern of [[2edf]] and [[2ed4/3]].
An alternating pattern of [[2edf]] and [[2ed4/3]].
*350.978
*350.978
Line 20: Line 21:
*1200.000
*1200.000


== Kartvelian pentatonic ==
=== Kartvelian pentatonic ===
An alternating pattern of [[3edf]] and [[2ed4/3]]. Approximates the [[Slendro]] scale.
An alternating pattern of [[3edf]] and [[2ed4/3]]. Approximates the [[Slendro]] scale.
*233.985
*233.985
Line 28: Line 29:
*1200.000
*1200.000


== 3edf Kartvelian hexatonic ==
=== 3edf Kartvelian hexatonic ===
An alternating pattern of [[3edf]] and [[3ed4/3]].
An alternating pattern of [[3edf]] and [[3ed4/3]].
*233.985
*233.985
Line 37: Line 38:
*1200.000
*1200.000


== 4edf Kartvelian hexatonic ==
=== 4edf Kartvelian hexatonic ===
An alternating pattern of [[4edf]] and [[2ed4/3]].
An alternating pattern of [[4edf]] and [[2ed4/3]].
*175.489
*175.489
Line 46: Line 47:
*1200.000
*1200.000


== 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


== 4edf Kartvelian octatonic ==
=== 4edf Kartvelian octatonic ===
An alternating pattern of [[4edf]] and [[4ed4/3]].
An alternating pattern of [[4edf]] and [[4ed4/3]].
*175.489
*175.489
Line 68: Line 68:
*1200.000
*1200.000


== 5edf Kartvelian octatonic ==
=== 5edf Kartvelian octatonic ===
An alternating pattern of [[5edf]] and [[3ed4/3]].
An alternating pattern of [[5edf]] and [[3ed4/3]].
*140.391
*140.391
Line 79: Line 79:
*1200.000
*1200.000


== 5edf Kartvelian enneatonic ==
=== 5edf Kartvelian enneatonic ===
An alternating pattern of [[5edf]] and [[4ed4/3]]. Approximates the 9-tone [[Pelog]] scale.
An alternating pattern of [[5edf]] and [[4ed4/3]]. Approximates the 9-tone [[Pelog]] scale.
*140.391
*140.391
Line 91: Line 91:
*1200.000
*1200.000


== 6edf Kartvelian enneatonic ==
=== 6edf Kartvelian enneatonic ===
An alternating pattern of [[6edf]] and [[3ed4/3]].
An alternating pattern of [[6edf]] and [[3ed4/3]].
*116.993
*116.993
Line 103: Line 103:
*1200.000
*1200.000


== 5edf Kartvelian decatonic ==
=== 5edf Kartvelian decatonic ===
An alternating pattern of [[5edf]] and [[5ed4/3]].
An alternating pattern of [[5edf]] and [[5ed4/3]].
*140.391
*140.391
Line 116: Line 116:
*1200.000
*1200.000


== 6edf Kartvelian decatonic ==
=== 6edf Kartvelian decatonic ===
An alternating pattern of [[6edf]] and [[4ed4/3]].
An alternating pattern of [[6edf]] and [[4ed4/3]].
*116.993
*116.993
Line 129: Line 129:
*1200.000
*1200.000


== 6edf Kartvelian hendecatonic ==
=== 6edf Kartvelian hendecatonic ===
An alternating pattern of [[6edf]] and [[5ed4/3]].
An alternating pattern of [[6edf]] and [[5ed4/3]].
*116.993
*116.993
Line 143: Line 143:
*1200.000
*1200.000


== 7edf Kartvelian hendecatonic ==
=== 7edf Kartvelian hendecatonic ===
An alternating pattern of [[7edf]] and [[4ed4/3]].
An alternating pattern of [[7edf]] and [[4ed4/3]].
*100.279
*100.279
Line 157: Line 157:
*1200.000
*1200.000


== 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 172: Line 172:
*1200.000
*1200.000


== 8edf Kartvelian dodecatonic ==
=== 8edf Kartvelian dodecatonic ===
An alternating pattern of [[8edf]] and [[4ed4/3]].
An alternating pattern of [[8edf]] and [[4ed4/3]].
*87.744
*87.744
Line 187: Line 187:
*1200.000
*1200.000


== 7edf Kartvelian triskaidekatonic ==
=== 7edf Kartvelian triskaidekatonic ===
An alternating pattern of [[7edf]] and [[6ed4/3]].
An alternating pattern of [[7edf]] and [[6ed4/3]].
*100.279
*100.279
Line 203: Line 203:
*1200.000
*1200.000


== 8edf Kartvelian triskaidekatonic ==
=== 8edf Kartvelian triskaidekatonic ===
An alternating pattern of [[8edf]] and [[5ed4/3]].
An alternating pattern of [[8edf]] and [[5ed4/3]].
*87.744
*87.744
Line 219: Line 219:
*1200.000
*1200.000


== 8edf Kartvelian tetradecatonic ==
=== 8edf Kartvelian tetradecatonic ===
An alternating pattern of [[8edf]] and [[6ed4/3]].
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
*87.744
*175.489
*175.489
Line 236: Line 236:
*1200.000
*1200.000


== 9edf Kartvelian tetradecatonic ==
==== 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 ===
An alternating pattern of [[9edf]] and [[5ed4/3]].
An alternating pattern of [[9edf]] and [[5ed4/3]].
*87.744
*87.744
Line 252: Line 275:
*1200.000
*1200.000


== 8edf Kartvelian pentadecatonic ==
=== 8edf Kartvelian pentadecatonic ===
An alternating pattern of [[8edf]] and [[7ed4/3]].
An alternating pattern of [[8edf]] and [[7ed4/3]].
*87.744
*87.744
Line 270: Line 293:
*1200.000
*1200.000


== 9edf Kartvelian pentadecatonic ==
=== 9edf Kartvelian pentadecatonic ===
An alternating pattern of [[9edf]] and [[6ed4/3]].
An alternating pattern of [[9edf]] and [[6ed4/3]].
*77.995
*77.995
Line 288: Line 311:
*1200.000
*1200.000


== 9edf Kartvelian hexadecatonic ==
=== 9edf Kartvelian hexadecatonic ===
An alternating pattern of [[9edf]] and [[7ed4/3]].
An alternating pattern of [[9edf]] and [[7ed4/3]].
*77.995
*77.995
Line 307: Line 330:
*1200.000
*1200.000


== 10edf Kartvelian hexadecatonic ==
=== 10edf Kartvelian hexadecatonic ===
An alternating pattern of [[10edf]] and [[6ed4/3]].
An alternating pattern of [[10edf]] and [[6ed4/3]].
*70.196
*70.196
Line 326: Line 349:
*1200.000
*1200.000


== 9edf Kartvelian heptadecatonic ==
=== 9edf Kartvelian heptadecatonic ===
An alternating pattern of [[9edf]] and [[8ed4/3]].
An alternating pattern of [[9edf]] and [[8ed4/3]].
*77.995
*77.995
Line 346: Line 369:
*1200.000
*1200.000


== 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 366: Line 389:
*1200.000
*1200.000


== 10edf Kartvelian octadecatonic ==
==== Subsets ====
''See [[17edo#Scales]]''
 
=== 10edf Kartvelian octadecatonic ===
An alternating pattern of [[10edf]] and [[8ed4/3]].
An alternating pattern of [[10edf]] and [[8ed4/3]].
*70.196
*70.196
Line 387: Line 413:
*1200.000
*1200.000


== 11edf Kartvelian octadecatonic ==
=== 11edf Kartvelian octadecatonic ===
An alternating pattern of [[11edf]] and [[7ed4/3]].
An alternating pattern of [[11edf]] and [[7ed4/3]].
*63.814
*63.814
Line 408: Line 434:
*1200.000
*1200.000


== 11edf Kartvelian enneadecatonic ==
=== 11edf Kartvelian enneadecatonic ===
An alternating pattern of [[11edf]] and [[8ed4/3]].
An alternating pattern of [[11edf]] and [[8ed4/3]].
*63.814
*63.814
Line 430: Line 456:
*1200.000
*1200.000


== 12edf Kartvelian enneadecatonic ==
=== 12edf Kartvelian enneadecatonic ===
An alternating pattern of [[12edf]] and [[7ed4/3]].
An alternating pattern of [[12edf]] and [[7ed4/3]].
*58.496
*58.496
Line 452: Line 478:
*1200.000
*1200.000


== 11edf Kartvelian icositonic ==
=== 11edf Kartvelian icositonic ===
An alternating pattern of [[11edf]] and [[9ed4/3]].
An alternating pattern of [[11edf]] and [[9ed4/3]].
*63.814
*63.814
Line 475: Line 501:
*1200.000
*1200.000


== 12edf Kartvelian icositonic ==
=== 12edf Kartvelian icositonic ===
An alternating pattern of [[12edf]] and [[8ed4/3]].
An alternating pattern of [[12edf]] and [[8ed4/3]].
*58.496
*58.496
Line 498: Line 524:
*1200.000
*1200.000


== 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 522: Line 548:
*1200.000
*1200.000


== 13edf Kartvelian 21-tonic ==
==== 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]].
An alternating pattern of [[13edf]] and [[8ed4/3]].
*53.997
*53.997
Line 546: Line 582:
*1200.000
*1200.000


== 12edf Kartvelian 22-tonic ==
=== 12edf Kartvelian 22-tonic ===
An alternating pattern of [[12edf]] and [[10ed4/3]].
An alternating pattern of [[12edf]] and [[10ed4/3]].
*58.496
*58.496
Line 570: Line 606:
*1200.000
*1200.000


== 13edf Kartvelian 22-tonic ==
=== 13edf Kartvelian 22-tonic ===
An alternating pattern of [[13edf]] and [[9ed4/3]].
An alternating pattern of [[13edf]] and [[9ed4/3]].
*53.997
*53.997
Line 595: Line 631:
*1200.000
*1200.000


== 13edf Kartvelian 23-tonic ==
=== 13edf Kartvelian 23-tonic ===
An alternating pattern of [[13edf]] and [[10ed4/3]].
An alternating pattern of [[13edf]] and [[10ed4/3]].
*53.997
*53.997
Line 621: Line 657:
*1200.000
*1200.000


== 14edf Kartvelian 23-tonic ==
=== 14edf Kartvelian 23-tonic ===
An alternating pattern of [[14edf]] and [[9ed4/3]].
An alternating pattern of [[14edf]] and [[9ed4/3]].
*50.140
*50.140
Line 647: Line 683:
*1200.000
*1200.000


== 13edf Kartvelian 24-tonic ==
=== 13edf Kartvelian 24-tonic ===
An alternating pattern of [[13edf]] and [[11ed4/3]].
An alternating pattern of [[13edf]] and [[11ed4/3]].
*53.997
*53.997
Line 674: Line 710:
*1200.000
*1200.000


== 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 701: Line 737:
*1200.000
*1200.000


== 14edf Kartvelian 25-tonic ==
==== Subsets ====
''See [[24edo#Scales_.2F_modes]]''
 
=== 14edf Kartvelian 25-tonic ===
An alternating pattern of [[14edf]] and [[11ed4/3]].
An alternating pattern of [[14edf]] and [[11ed4/3]].
*50.140
*50.140
Line 729: Line 768:
*1200.000
*1200.000


== 15edf Kartvelian 25-tonic ==
=== 15edf Kartvelian 25-tonic ===
An alternating pattern of [[15edf]] and [[10ed4/3]].
An alternating pattern of [[15edf]] and [[10ed4/3]].
*46.797
*46.797
Line 757: Line 796:
*1200.000
*1200.000


== 15edf Kartvelian 26-tonic ==
=== 15edf Kartvelian 26-tonic ===
An alternating pattern of [[15edf]] and [[11ed4/3]].
An alternating pattern of [[15edf]] and [[11ed4/3]].
*46.797
*46.797
Line 786: Line 825:
*1200.000
*1200.000


== 16edf Kartvelian 26-tonic ==
=== 16edf Kartvelian 26-tonic ===
An alternating pattern of [[16edf]] and [[10ed4/3]].
An alternating pattern of [[16edf]] and [[10ed4/3]].
*43.872
*43.872
Line 815: Line 854:
*1200.000
*1200.000


== 15edf Kartvelian 27-tonic ==
=== 15edf Kartvelian 27-tonic ===
An alternating pattern of [[15edf]] and [[12ed4/3]].
An alternating pattern of [[15edf]] and [[12ed4/3]].
*46.797
*46.797
Line 845: Line 884:
*1200.000
*1200.000


== 16edf Kartvelian 27-tonic ==
=== 16edf Kartvelian 27-tonic ===
An alternating pattern of [[16edf]] and [[11ed4/3]].
An alternating pattern of [[16edf]] and [[11ed4/3]].
*43.872
*43.872
Line 875: Line 914:
*1200.000
*1200.000


== 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 906: Line 945:
*1200.000
*1200.000


== 17edf Kartvelian 28-tonic ==
==== 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]].
An alternating pattern of [[17edf]] and [[11ed4/3]].
*41.291
*41.291
Line 937: Line 997:
*1200.000
*1200.000


== 16edf Kartvelian 29-tonic ==
=== 16edf Kartvelian 29-tonic ===
An alternating pattern of [[16edf]] and [[13ed4/3]].
An alternating pattern of [[16edf]] and [[13ed4/3]].
*43.872
*43.872
Line 969: Line 1,029:
*1200.000
*1200.000


== 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 1,001: Line 1,061:
*1200.000
*1200.000


== 17edf Kartvelian triacontatonic ==
==== Subsets ====
''See [[29edo#Scales]]''
 
=== 17edf Kartvelian triacontatonic ===
An alternating pattern of [[17edf]] and [[13ed4/3]].
An alternating pattern of [[17edf]] and [[13ed4/3]].
*41.291
*41.291
Line 1,034: Line 1,097:
*1200.000
*1200.000


== 18edf Kartvelian triacontatonic ==
=== 18edf Kartvelian triacontatonic ===
An alternating pattern of [[18edf]] and [[12ed4/3]].
An alternating pattern of [[18edf]] and [[12ed4/3]].
*38.998
*38.998
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]]
Retrieved from "https://en.xen.wiki/w/Kartvelian_scales"