223edo: Difference between revisions

(5 intermediate revisions by 5 users not shown)

Line 1:

~~'''~~223edo~~''' is the [[EDO|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It~~ contains an excellent proportion of [[hornbostel]] temperament (via ~~7L2s~~), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is ~~inconsistent~~ to the 5-limit and higher limit, with three mappings possible for the 5-limit:

* {{val| 223 353 518 }} (patent val),

223edo contains an excellent proportion of [[hornbostel]] temperament (via [[7L 2s]]), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is in[[consistent]] to the [[5-odd-limit]] and higher limit, with three mappings possible for the 5-limit:

* {{val| 223 353 518 }} ([[patent val]]),

* {{val| 223 '''354''' 518 }} (223b),

* {{val| 223 353 '''517''' }} (223c).

Line 6:

Line 9:

Using the patent val, it tempers out 393216/390625 ([[würschmidt comma]]) and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.

Using the 223be val, it tempers out 15625/15552 ([[kleisma]]) and {{monzo| 58 -38 1 }} in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit.

Using the 223be val, it tempers out 15625/15552 ([[kleisma]]) and {{monzo| 58 -38 1 }} in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit.

Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit.

Using the 223c val, it tempers out the 129140163/128000000 ([[graviton]]) and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit.

Line 14:

Line 15:

Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

~~223edo is the 48th [[prime EDO]].~~

=== Odd harmonics ===

223 ~~is also the number of lunar months in an astronomical concept known as [[Wikipedia:Saros (astronomy)~~|~~saros]].~~

~~[[Category:Equal divisions of~~ the ~~octave]]~~

=== Subsets and supersets ===

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

223edo is the 48th [[prime edo]].

@@ Line 1: / Line 1: @@
-'''223edo''' is the [[EDO|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of [[hornbostel]] temperament (via 7L2s), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit:
+{{Infobox ET}}
-* {{val| 223 353 518 }} (patent val),
+{{ED intro}}
+edo contains an excellent proportion of [[hornbostel]] temperament (via [[7L 2s]]), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is in[[consistent]] to the [[5-odd-limit]] and higher limit, with three mappings possible for the 5-limit:
+* {{val| 223 353 518 }} ([[patent val]]),
 * {{val| 223 '''354''' 518 }} (223b),
 * {{val| 223 353 '''517''' }} (223c).
@@ Line 6: / Line 9: @@
 Using the patent val, it tempers out 393216/390625 ([[würschmidt comma]]) and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.
-Using the 223be val, it tempers out 15625/15552 ([[kleisma]]) and {{monzo| 58 -38 1 }} in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit.
+Using the 223be val, it tempers out 15625/15552 ([[kleisma]]) and {{monzo| 58 -38 1 }} in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit.
-Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit.
 Using the 223c val, it tempers out the 129140163/128000000 ([[graviton]]) and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit.
@@ Line 14: / Line 15: @@
 Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.
-edo is the 48th [[prime EDO]].
+=== Odd harmonics ===
+{{Harmonics in equal|223|columns=11}}
-is also the number of lunar months in an astronomical concept known as [[Wikipedia:Saros (astronomy)|saros]].
-[[Category:Equal divisions of the octave]]
+=== Subsets and supersets ===
-[[Category:Prime EDO]]
+edo is the 48th [[prime edo]].