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 22: 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 30: 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 39: 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 48: 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 55: 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 70: 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 81: 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 93: 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 105: 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 118: 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 131: 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 145: 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 159: 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 174: 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 189: 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 205: 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 221: 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 238: 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 254: 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 272: 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 290: 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 309: 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 328: 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 348: 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 368: 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 389: 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 410: 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 432: 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 454: 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 477: 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 500: 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 524: 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 548: 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 572: 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 597: 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 623: 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 649: 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 676: 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 703: 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 731: 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 759: 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 788: 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 817: 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 847: 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 877: 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 908: 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 939: 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 971: 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 1,003: 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 1,036: 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 1,068: 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"