203edo: Difference between revisions

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{{EDO intro}}  
{{EDO intro}}  


It is inconsistent to the 5-limit and higher, with three mappings possible for the 7-limit: <203 322 471 570| (patent val), <203 321 471 569| (203bd), and <203 322 472 570| (203c). Using the patent val, it tempers out the semicomma, 2109375/2097152 and 97656250000/94143178827 in the 5-limit; 4000/3969, 10976/10935, and 2100875/2097152 in the 7-limit; 385/384, 1331/1323, and 4000/3993 in the 11-limit; 352/351, 676/675, 1573/1568, and 1625/1617 in the 13-limit. Using the 203c val, it tempers out the sensipent comma, 78732/78125 and [[29-comma]] in the 5-limit; 5120/5103, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 1331/1323, 8019/8000, and 26411/26244 in the 11-limit. Using the 203ce val, it tempers out 441/440, 896/891, and 3388/3375 in the 11-limit. Using the 203cef val, it tempers out 196/195, 352/351, 364/363, 676/675, and 78732/78125 in the 13-limit.
203edo is in[[consistent]] to the [[5-odd-limit]] and higher, with three mappings possible for the 7-limit: {{val| 203 322 471 570 }} ([[patent val]]), {{val| 203 '''321''' 471 '''569''' }} (203bd), and {{val| 203 322 '''472''' 570 }} (203c). Using the patent val, it [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and {{monzo| 4 -23 14 }} in the 5-limit; [[4000/3969]], [[10976/10935]], and [[2100875/2097152]] in the 7-limit; [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit; [[352/351]], [[676/675]], [[1573/1568]], and 1625/1617 in the 13-limit. Using the 203c val, it tempers out 78732/78125 ([[sensipent comma]]) and [[29-comma]] in the 5-limit; [[5120/5103]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], 1331/1323, [[8019/8000]], and 26411/26244 in the 11-limit. Using the 203ce val, it tempers out [[441/440]], [[896/891]], and [[3388/3375]] in the 11-limit. Using the 203cef val, it tempers out [[196/195]], 352/351, [[364/363]], 676/675, and 78732/78125 in the 13-limit.


==Harmonics==
=== Odd harmonics ===
{{Harmonics in equal|203}}
{{Harmonics in equal|203}}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Revision as of 12:08, 13 April 2024

← 202edo 203edo 204edo →
Prime factorization 7 × 29
Step size 5.91133 ¢ 
Fifth 119\203 (703.448 ¢) (→ 17\29)
Semitones (A1:m2) 21:14 (124.1 ¢ : 82.76 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO intro

203edo is inconsistent to the 5-odd-limit and higher, with three mappings possible for the 7-limit: 203 322 471 570] (patent val), 203 321 471 569] (203bd), and 203 322 472 570] (203c). Using the patent val, it tempers out 2109375/2097152 (semicomma) and [4 -23 14 in the 5-limit; 4000/3969, 10976/10935, and 2100875/2097152 in the 7-limit; 385/384, 1331/1323, and 4000/3993 in the 11-limit; 352/351, 676/675, 1573/1568, and 1625/1617 in the 13-limit. Using the 203c val, it tempers out 78732/78125 (sensipent comma) and 29-comma in the 5-limit; 5120/5103, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 1331/1323, 8019/8000, and 26411/26244 in the 11-limit. Using the 203ce val, it tempers out 441/440, 896/891, and 3388/3375 in the 11-limit. Using the 203cef val, it tempers out 196/195, 352/351, 364/363, 676/675, and 78732/78125 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 203edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.49 -2.08 +0.63 -2.92 -1.56 -1.12 -0.58 +1.45 -1.95 +2.13 -1.67
Relative (%) +25.3 -35.1 +10.7 -49.5 -26.5 -18.9 -9.9 +24.5 -32.9 +36.0 -28.3
Steps
(reduced)
322
(119)
471
(65)
570
(164)
643
(34)
702
(93)
751
(142)
793
(184)
830
(18)
862
(50)
892
(80)
918
(106)