# 449edo

 ← 448edo 449edo 450edo →
Prime factorization 449 (prime)
Step size 2.67261¢
Fifth 263\449 (702.895¢)
Semitones (A1:m2) 45:32 (120.3¢ : 85.52¢)
Dual sharp fifth 263\449 (702.895¢)
Dual flat fifth 262\449 (700.223¢)
Dual major 2nd 76\449 (203.118¢)
Consistency limit 7
Distinct consistency limit 7

449 equal divisions of the octave (abbreviated 449edo or 449ed2), also called 449-tone equal temperament (449tet) or 449 equal temperament (449et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 449 equal parts of about 2.67 ¢ each. Each step represents a frequency ratio of 21/449, or the 449th root of 2.

## Theory

449edo is consistent to the 7-odd-limit, but the errors of harmonics 3, 5, and 7 are all quite large, giving us the option of treating it as a full 7-limit temperament, or a 2.9.15.21.11.13 subgroup temperament.

Using the patent val, the equal temperament tempers out 4375/4374 and 26873856/26796875 in the 7-limit; 41503/41472, 160083/160000, 539055/537824, 805255/802816, and 825000/823543 in the 11-limit.

### Odd harmonics

Approximation of odd harmonics in 449edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.94 +1.21 +1.33 -0.79 -0.76 -1.33 -0.52 -0.72 -0.85 -0.40 -0.21
Relative (%) +35.2 +45.4 +49.8 -29.6 -28.5 -49.7 -19.4 -27.1 -31.9 -15.1 -7.9
Steps
(reduced)
712
(263)
1043
(145)
1261
(363)
1423
(76)
1553
(206)
1661
(314)
1754
(407)
1835
(39)
1907
(111)
1972
(176)
2031
(235)

### Subsets and supersets

449edo is the 87th prime edo. 898edo, which doubles it, gives a good correction to the harmonic 3, 5 and 7.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [-1423 449 [449 1423]] 0.1249 0.1249 4.67

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 127\449 339.421 243\200 Amity (7-limit)

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

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