225edo

← 224edo

225edo

226edo →

Prime factorization	32 × 52
Step size	5.33333 ¢
Fifth	132\225 (704 ¢) (→ 44\75)
Semitones (A1:m2)	24:15 (128 ¢ : 80 ¢)
Dual sharp fifth	132\225 (704 ¢) (→ 44\75)
Dual flat fifth	131\225 (698.667 ¢)
Dual major 2nd	38\225 (202.667 ¢)
Consistency limit	3
Distinct consistency limit	3

225 equal divisions of the octave (abbreviated 225edo or 225ed2), also called 225-tone equal temperament (225tet) or 225 equal temperament (225et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 225 equal parts of about 5.33 ¢ each. Each step represents a frequency ratio of 2^1/225, or the 225th root of 2.

Theory

225edo is inconsistent to the 5-odd-limit and higher limits, with rather large errors in harmonics 3, 5, 7, 11, and 13. It has three mappings possible for the 7-limit:

• ⟨225 357 522 632] (patent val),
• ⟨225 356 522 631] (225bd),
• ⟨225 357 523 632] (225c).

Using the patent val, it tempers out 20000/19683 and 2109375/2097152 in the 5-limit; 3125/3087, 10976/10935, and 589824/588245 in the 7-limit.

Using the 225bd val, it tempers out 78732/78125 (sensipent comma) and [-52 27 4⟩ in the 5-limit; 225/224, 177147/175000, and 40353607/40000000 in the 7-limit.

Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.

Odd harmonics

Approximation of odd harmonics in 225edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+2.04	-2.31	+1.84	-1.24	-1.98	+2.14	-0.27	+1.71	+1.15	-1.45	+1.06
	Relative (%)	+38.3	-43.4	+34.5	-23.3	-37.2	+40.1	-5.0	+32.1	+21.6	-27.1	+19.9
Steps (reduced)		357 (132)	522 (72)	632 (182)	713 (38)	778 (103)	833 (158)	879 (204)	920 (20)	956 (56)	988 (88)	1018 (118)

Scales

• Bossier scales