199edo: Difference between revisions

(7 intermediate revisions by 6 users not shown)

Line 1:

'''199edo''' is the [[EDO|equal division of the octave]] into 199 parts of 6.0302 cents each. It tempers out 2109375/2097152 (semicomma) and 31381059609/30517578125 ([[15edt|mowgli comma]]) in the 5-limit. Using the patent val, it tempers out 225/224 and 1728/1715 in the 7-limit; 243/242, 2420/2401, 3025/3024, and 161051/160000 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 2704/2695 in the 13-limit. Using the 199bef val, it tempers out 245/243, 65536/64827, and 390625/387072 in the 7-limit; 1375/1372, 2560/2541, 5632/5625, and 6875/6804 in the 11-limit; 364/363, 640/637, 676/675, 1625/1617, and 3200/3159 in the 13-limit. Using the 199d val, it tempers out 3136/3125, 33075/32768, and 177147/175000 in the 7-limit; 243/242, 385/384, 3773/3750, and 12005/11979 in the 11-limit; 351/350, 847/845, 1287/1280, and 1575/1573 in the 13-limit.

~~199edo is~~ the ~~46th~~ [[~~prime EDO~~]].

== Theory ==

Using the [[patent val]], the equal temperament [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and 31381059609/30517578125 ([[mowgli comma]]) in the 5-limit; [[225/224]] and [[1728/1715]] in the 7-limit; [[243/242]], 2420/2401, [[3025/3024]], and 161051/160000 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and 2704/2695 in the 13-limit. Using the 199bef val, it tempers out [[245/243]], 65536/64827, and 390625/387072 in the 7-limit; 1375/1372, 2560/2541, [[5632/5625]], and 6875/6804 in the 11-limit; [[364/363]], [[640/637]], [[676/675]], 1625/1617, and 3200/3159 in the 13-limit. Using the 199d val, it tempers out [[3136/3125]], [[33075/32768]], and 177147/175000 in the 7-limit; [[243/242]], [[385/384]], 3773/3750, and 12005/11979 in the 11-limit; [[351/350]], [[847/845]], 1287/1280, and [[1575/1573]] in the 13-limit.

[[~~Category:Edo~~]]

=== Odd harmonics ===

[[~~Category:Prime EDO~~]]

=== Subsets and supersets ===

199edo is the 46th [[prime edo]].

== Instruments ==

=== Skip fretting ===

'''Skip fretting system 199 11 16''' is a [[skip fretting]] system for 199edo. All examples on this page are for 7-string [[guitar]].

; Harmonics

1/1: string 2 open

2/1: string 7 fret 9

3/2: not easily accesssible

5/4: string 2 fret 4

7/4: string 5 fret 8

11/8: string 3 fret 5

13/8: string 3 fret 8

17/16: not easily accessible

@@ Line 1: / Line 1: @@
-'''199edo''' is the [[EDO|equal division of the octave]] into 199 parts of 6.0302 cents each. It tempers out 2109375/2097152 (semicomma) and 31381059609/30517578125 ([[15edt|mowgli comma]]) in the 5-limit. Using the patent val, it tempers out 225/224 and 1728/1715 in the 7-limit; 243/242, 2420/2401, 3025/3024, and 161051/160000 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 2704/2695 in the 13-limit. Using the 199bef val, it tempers out 245/243, 65536/64827, and 390625/387072 in the 7-limit; 1375/1372, 2560/2541, 5632/5625, and 6875/6804 in the 11-limit; 364/363, 640/637, 676/675, 1625/1617, and 3200/3159 in the 13-limit. Using the 199d val, it tempers out 3136/3125, 33075/32768, and 177147/175000 in the 7-limit; 243/242, 385/384, 3773/3750, and 12005/11979 in the 11-limit; 351/350, 847/845, 1287/1280, and 1575/1573 in the 13-limit.
+{{Infobox ET}}
+{{ED intro}}
-edo is the 46th [[prime EDO]].
+== Theory ==
+Using the [[patent val]], the equal temperament [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and 31381059609/30517578125 ([[mowgli comma]]) in the 5-limit; [[225/224]] and [[1728/1715]] in the 7-limit; [[243/242]], 2420/2401, [[3025/3024]], and 161051/160000 in the 11-limit; [[1001/1000]], [[1188/1183]], [[1287/1280]], and 2704/2695 in the 13-limit. Using the 199bef val, it tempers out [[245/243]], 65536/64827, and 390625/387072 in the 7-limit; 1375/1372, 2560/2541, [[5632/5625]], and 6875/6804 in the 11-limit; [[364/363]], [[640/637]], [[676/675]], 1625/1617, and 3200/3159 in the 13-limit. Using the 199d val, it tempers out [[3136/3125]], [[33075/32768]], and 177147/175000 in the 7-limit; [[243/242]], [[385/384]], 3773/3750, and 12005/11979 in the 11-limit; [[351/350]], [[847/845]], 1287/1280, and [[1575/1573]] in the 13-limit.
-[[Category:Edo]]
+=== Odd harmonics ===
-[[Category:Prime EDO]]
+{{Harmonics in equal|199}}
+=== Subsets and supersets ===
+edo is the 46th [[prime edo]].
+== Instruments ==
+=== Skip fretting ===
+'''Skip fretting system 199 11 16''' is a [[skip fretting]] system for 199edo. All examples on this page are for 7-string [[guitar]].
+; Harmonics
+/1: string 2 open
+/1: string 7 fret 9
+/2: not easily accesssible
+/4: string 2 fret 4
+/4: string 5 fret 8
+/8: string 3 fret 5
+/8: string 3 fret 8
+/16: not easily accessible