User:Francium/3593edo

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3593edo

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Prime factorization	3593 (prime)
Step size	0.333983 ¢
Fifth	2102\3593 (702.032 ¢)
Semitones (A1:m2)	342:269 (114.2 ¢ : 89.84 ¢)
Consistency limit	13
Distinct consistency limit	13

3593 equal divisions of the octave (abbreviated 3593edo or 3593ed2), also called 3593-tone equal temperament (3593tet) or 3593 equal temperament (3593et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3593 equal parts of about 0.334 ¢ each. Each step represents a frequency ratio of 2^1/3593, or the 3593rd root of 2.

Theory

3593edo is consistent to the 13-limit, tempering out 4096/4095, 6656/6655, 105644/105625, 1063348/1063125 and 21437500/21434787. It supports lafa.

Odd harmonics

Approximation of odd harmonics in 3593edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.077	+0.104	+0.058	+0.153	+0.088	+0.107	-0.153	-0.085	+0.066	+0.135	-0.053
	Relative (%)	+23.0	+31.2	+17.4	+45.9	+26.2	+32.0	-45.8	-25.4	+19.6	+40.3	-15.8
Steps (reduced)		5695 (2102)	8343 (1157)	10087 (2901)	11390 (611)	12430 (1651)	13296 (2517)	14037 (3258)	14686 (314)	15263 (891)	15782 (1410)	16253 (1881)

Subsets and supersets

3593edo is the 503rd prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[5695 -3593⟩	[⟨3593 5695]]	−0.0242	0.0242	7.25
2.3.5	[77 -31 -12⟩, [19 -116 71⟩	[⟨3593 5695 8343]]	−0.0311	0.0220	6.59
2.3.5.7	78125000/78121827, 962072674304/961083984375, 3391115364245/3389154437772	[⟨3593 5695 8343 10087]]	−0.0285	0.0196	5.87
2.3.5.7.11	151263/151250, 21437500/21434787, 2097152/2096325, 4274192384/4271484375	[⟨3593 5695 8343 10087 12430]]	−0.0279	0.0176	5.27
2.3.5.7.11.13	4096/4095, 6656/6655, 105644/105625, 1063348/1063125, 21437500/21434787	[⟨3593 5695 8343 10087 12430 13296]]	−0.0280	0.0161	4.82

Music

Francium

• "even go in of glass houses" from have nice day (2025) – Spotify | Bandcamp | YouTube – in Lafa, 3593edo tuning