5280edo

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5280edo

5281edo →

Prime factorization	25 × 3 × 5 × 11
Step size	0.227273¢
Fifth	3089\5280 (702.045¢)
Semitones (A1:m2)	503:395 (114.3¢ : 89.77¢)
Dual sharp fifth	3089\5280 (702.045¢)
Dual flat fifth	3088\5280 (701.818¢) (→193\330)
Dual major 2nd	897\5280 (203.864¢) (→299\1760)
Consistency limit	7
Distinct consistency limit	7

5280 equal divisions of the octave (abbreviated 5280edo or 5280ed2), also called 5280-tone equal temperament (5280tet) or 5280 equal temperament (5280et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 5280 equal parts of about 0.227 ¢ each. Each step represents a frequency ratio of 2^1/5280, or the 5280th root of 2.

5280edo is consistent in the 7-odd-limit. On the patent val, it tempers out the comma [-103 -22 0 22 22⟩, which associates 77/48 to 15\22.

Odd harmonics

Approximation of odd harmonics in 5280edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.0905	+0.0499	+0.0377	-0.0464	+0.0457	-0.0731	-0.0869	+0.0446	-0.0130	-0.0991	-0.0925
	Relative (%)	+39.8	+22.0	+16.6	-20.4	+20.1	-32.2	-38.2	+19.6	-5.7	-43.6	-40.7
Steps (reduced)		8369 (3089)	12260 (1700)	14823 (4263)	16737 (897)	18266 (2426)	19538 (3698)	20628 (4788)	21582 (462)	22429 (1309)	23191 (2071)	23884 (2764)

Subsets and supersets

Since 5280 factors as 2⁵ × 3 × 5 × 11, 5280edo has subset edos 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640.