445edo

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Revision as of 09:30, 18 January 2024 by Francium (talk | contribs) (Created page with "{{Infobox ET}} {{EDO intro|445}} == Theory == 445et is consistent to the 7-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 48828125/48771072, 95703...")
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← 444edo 445edo 446edo →
Prime factorization 5 × 89
Step size 2.69663 ¢ 
Fifth 260\445 (701.124 ¢) (→ 52\89)
Semitones (A1:m2) 40:35 (107.9 ¢ : 94.38 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

Theory

445et is consistent to the 7-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 48828125/48771072, 95703125/95551488 and 2401/2400 in the 7-limit; 78121827/77948684, 56723625/56689952, 10333575/10307264, 35156250/35153041, 234375/234256, 1366875/1362944, 104162436/103984375, 1953125/1951488, 151263/151250, 472392/471625, 137781/137500, 24057/24010, 8019/8000, 3025/3024, 41503/41472, 539055/537824, 35937/35840, 244515348/244140625, 805255/802816, 39135393/39062500 in the 11-limit. It supports misneb.

Odd harmonics

Approximation of odd harmonics in 445edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.83 -0.70 -0.74 +1.03 -1.21 +0.82 +1.17 +0.21 -0.88 +1.13 +0.04
Relative (%) -30.8 -25.8 -27.3 +38.3 -44.7 +30.4 +43.4 +7.9 -32.8 +41.9 +1.5
Steps
(reduced)
705
(260)
1033
(143)
1249
(359)
1411
(76)
1539
(204)
1647
(312)
1739
(404)
1819
(39)
1890
(110)
1955
(175)
2013
(233)

Subsets and supersets

445 factors into 5 × 89, with 5edo and 89edo as its subset edos.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-141 89 [445 705]] 0.2623 0.2623 9.73
2.3.5 [-28 25 -5, [-29 -11 20 [445 705 1033]] 0.2748 0.2149 7.97
2.3.5.7 2401/2400, 48828125/48771072, 43046721/42875000 [445 705 1033 1249]] 0.2716 0.1862 6.90
2.3.5.7.11 3025/3024, 2401/2400, 8019/8000, 234375/234256 [445 705 1033 1249 1539]] 0.2870 0.1694 6.28

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 13\445 35.06 1990656/1953125 Gammic
1 42\445 113.26 16/15 Misneb
1 216\445 582.47 7/5 Neptune
5 185\445
(7\445)
498.88
(18.88)
4/3
(81/80)
Pental

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct