303edo

 ← 302edo 303edo 304edo →
Prime factorization 3 × 101
Step size 3.9604¢
Fifth 177\303 (700.99¢) (→59\101)
Semitones (A1:m2) 27:24 (106.9¢ : 95.05¢)
Consistency limit 3
Distinct consistency limit 3

303 equal divisions of the octave (abbreviated 303edo or 303ed2), also called 303-tone equal temperament (303tet) or 303 equal temperament (303et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 303 equal parts of about 3.96 ¢ each. Each step represents a frequency ratio of 21/303, or the 303rd root of 2.

Theory

303edo is inconsistent to the 5-odd-limit with three mappings possible for the 7-limit:

• 303 480 704 851] (patent val)
• 303 480 703 851] (303c val)
• 303 480 703 850] (303cd val)

The patent val tempers out 4294967296/4271484375 and 31381059609/30517578125 in the 5-limit; 3136/3125, 177147/175000 and 10616832/10504375 in the 7-limit, supporting gregorian leap day.

Using the 303c val, it tempers out 15625/15552 and [-83 48 3 in the 5-limit; 225/224, 4375/4374 and [36 -7 5 -13 in the 7-limit, supporting catakleismic

Using the 303cd val, it tempers out 15625/15552 and [-83 48 3 in the 5-limit; 1029/1024 and 43046721/43025920 in the 7-limit, supporting tritikleismic.

Prime harmonics

Approximation of prime harmonics in 303edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.96 +1.81 +1.47 -0.82 -0.92 +1.98 -0.48 +1.43 +0.13 -0.48
Relative (%) +0.0 -24.4 +45.6 +37.1 -20.8 -23.3 +49.9 -12.2 +36.1 +3.2 -12.1
Steps
(reduced)
303
(0)
480
(177)
704
(98)
851
(245)
1048
(139)
1121
(212)
1239
(27)
1287
(75)
1371
(159)
1472
(260)
1501
(289)

Subsets and supersets

303 factors into 3 × 101, with 3edo and 101edo as its subset edos. 606edo, which doubles it, gives a good correction to the harmonics 5 and 7.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-160 101 [303 480]] 0.3044 0.3045 7.69