66edo: Difference between revisions

(6 intermediate revisions by 5 users not shown)

Line 3:

== Theory ==

The [[patent val]] of 66edo is [[contorted]] in the 5-limit, [[tempering out]] the same [[comma]]s ([[250/243]], [[2048/2025]], [[3125/3072]], etc.) as [[22edo]]. In the 7-limit it tempers out [[686/675]] and [[1029/1024]], in the 11-limit [[55/54]], [[100/99]] and [[121/120]], in the 13-limit [[91/90]], [[169/168]], [[196/195]] and in the 17-limit [[136/135]] and [[256/255]]. It provides the [[optimal patent val]] for the 11- and 13-limit [[ammonite]] temperament. Otherwise, 66edo is not exceptional when it comes to approximating prime harmonics; however, it contains a quite accurate approximation to the 5:7:9:11:13 chord and can therefore be used for various [[over-5]] scales.

The [[patent val]] of 66edo is [[contorted]] in the 5-limit, [[tempering out]] the same [[comma]]s ([[250/243]], [[2048/2025]], [[3125/3072]], etc.) as [[22edo]]. In the 7-limit it tempers out [[686/675]] and [[1029/1024]], in the 11-limit [[55/54]], [[100/99]] and [[121/120]], in the 13-limit [[91/90]], [[169/168]], [[196/195]] and in the 17-limit [[136/135]] and [[256/255]]. It provides the [[optimal patent val]] for the 11- and 13-limit [[ammonite]] temperament. Otherwise, 66edo is not exceptional when it comes to approximating prime harmonics; however, it contains a quite accurate approximation to the 5:7:9:11:13 chord and can therefore be used for various [[primodal]] [[over-5]] scales.

The 66b val tempers out [[16875/16384]] in the 5-limit, [[126/125]], [[1728/1715]] and [[2401/2400]] in the 7-limit, [[99/98]] and [[385/384]] in the 11-limit, and [[105/104]], [[144/143]] and [[847/845]] in the 13-limit.

Line 50:

In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

[[~~Category~~:~~Ammonite~~]]

== Instruments ==

=== Lumatone ===

[[Lumatone mapping for 66edo]]

=== Skip fretting ===

'''Skip fretting system 66 7 11''' is a [[skip fretting]] system for [[66edo]]. All examples on this page are for 7-string [[guitar]].

; Prime harmonics

1/1: string 2 open

2/1: string 1 fret 11 and string 7 fret 11

3/2: string 3 fret 4

5/4: string 2 fret 3

7/4: string 3 fret 6

11/8: string 5 fret 9

13/8: string 3 fret 5

17/16: string 6 fret 4

19/16: string 5 fret 7

23/16: string 2 fret 5

29/16: string 4 fret 5

31/16: string 2 fret 9

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/jHwtQg0aR14 ''Spring Yard Zone (microtonal version in 66edo) - Sonic The Hedgehog''] (2022)

* [https://www.youtube.com/shorts/Cn28RJSSgQ0 ''microtonal improvisation in 66edo''] (2025)

@@ Line 3: / Line 3: @@
 == Theory ==
-The [[patent val]] of 66edo is [[contorted]] in the 5-limit, [[tempering out]] the same [[comma]]s ([[250/243]], [[2048/2025]], [[3125/3072]], etc.) as [[22edo]]. In the 7-limit it tempers out [[686/675]] and [[1029/1024]], in the 11-limit [[55/54]], [[100/99]] and [[121/120]], in the 13-limit [[91/90]], [[169/168]], [[196/195]] and in the 17-limit [[136/135]] and [[256/255]]. It provides the [[optimal patent val]] for the 11- and 13-limit [[ammonite]] temperament. Otherwise, 66edo is not exceptional when it comes to approximating prime harmonics; however, it contains a quite accurate approximation to the 5:7:9:11:13 chord and can therefore be used for various [[over-5]] scales.
+The [[patent val]] of 66edo is [[contorted]] in the 5-limit, [[tempering out]] the same [[comma]]s ([[250/243]], [[2048/2025]], [[3125/3072]], etc.) as [[22edo]]. In the 7-limit it tempers out [[686/675]] and [[1029/1024]], in the 11-limit [[55/54]], [[100/99]] and [[121/120]], in the 13-limit [[91/90]], [[169/168]], [[196/195]] and in the 17-limit [[136/135]] and [[256/255]]. It provides the [[optimal patent val]] for the 11- and 13-limit [[ammonite]] temperament. Otherwise, 66edo is not exceptional when it comes to approximating prime harmonics; however, it contains a quite accurate approximation to the 5:7:9:11:13 chord and can therefore be used for various [[primodal]] [[over-5]] scales.
 The 66b val tempers out [[16875/16384]] in the 5-limit, [[126/125]], [[1728/1715]] and [[2401/2400]] in the 7-limit, [[99/98]] and [[385/384]] in the 11-limit, and [[105/104]], [[144/143]] and [[847/845]] in the 13-limit.
@@ Line 50: / Line 50: @@
 In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
-[[Category:Ammonite]]
+== Instruments ==
+=== Lumatone ===
+[[Lumatone mapping for 66edo]]
+=== Skip fretting ===
+'''Skip fretting system 66 7 11''' is a [[skip fretting]] system for [[66edo]]. All examples on this page are for 7-string [[guitar]].
+; Prime harmonics
+/1: string 2 open
+/1: string 1 fret 11 and string 7 fret 11
+/2: string 3 fret 4
+/4: string 2 fret 3
+/4: string 3 fret 6
+/8: string 5 fret 9
+/8: string 3 fret 5
+/16: string 6 fret 4
+/16: string 5 fret 7
+/16: string 2 fret 5
+/16: string 4 fret 5
+/16: string 2 fret 9
+== Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/jHwtQg0aR14 ''Spring Yard Zone (microtonal version in 66edo) - Sonic The Hedgehog''] (2022)
+* [https://www.youtube.com/shorts/Cn28RJSSgQ0 ''microtonal improvisation in 66edo''] (2025)