1700edo

← 1699edo

1700edo

1701edo →

Prime factorization	22 × 52 × 17
Step size	0.705882 ¢
Fifth	994\1700 (701.647 ¢) (→ 497\850)
Semitones (A1:m2)	158:130 (111.5 ¢ : 91.76 ¢)
Dual sharp fifth	995\1700 (702.353 ¢) (→ 199\340)
Dual flat fifth	994\1700 (701.647 ¢) (→ 497\850)
Dual major 2nd	289\1700 (204 ¢) (→ 17\100)
Consistency limit	5
Distinct consistency limit	5

1700 equal divisions of the octave (abbreviated 1700edo or 1700ed2), also called 1700-tone equal temperament (1700tet) or 1700 equal temperament (1700et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1700 equal parts of about 0.706 ¢ each. Each step represents a frequency ratio of 2^1/1700, or the 1700th root of 2.

Theory

1700edo is only consistent in the 5-odd-limit, and there is a large relative delta on the harmonic 3. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 subgroup, or if the harmonic 5 is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 subgroup (not including either 5 or 15).

Odd harmonics

Approximation of odd harmonics in 1700edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.308	-0.196	+0.351	+0.090	-0.024	+0.178	+0.202	+0.221	-0.337	+0.043	-0.039
	Relative (%)	-43.6	-27.8	+49.7	+12.7	-3.4	+25.2	+28.6	+31.3	-47.7	+6.0	-5.5
Steps (reduced)		2694 (994)	3947 (547)	4773 (1373)	5389 (289)	5881 (781)	6291 (1191)	6642 (1542)	6949 (149)	7221 (421)	7467 (667)	7690 (890)

Subsets and supersets

Since 1700 factors into 2² × 5² × 17, 1700edo has subset edos 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, and 850.

One step of 1700edo is the relative cent for 17edo. It has been named iota by Margo Schulter and George Secor.