239edo

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239edo

240edo →

Prime factorization	239 (prime)
Step size	5.02092 ¢
Fifth	140\239 (702.929 ¢)
Semitones (A1:m2)	24:17 (120.5 ¢ : 85.36 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

239edo has a sharp tendency, with prime harmonics 3 through 11 all tuned sharp. The equal temperament tempers out 2401/2400, 5120/5103, and 29360128/29296875 in the 7-limit, supporting the hemififths temperament and providing an excellent tuning. It also supports and provides a good tuning for quasiorwell and alphaquarter. In the 11-limit, it tempers out 3025/3024, 4000/3993, 5632/5625, and 12005/11979.

Prime harmonics

Approximation of prime harmonics in 239edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.97	+0.30	+0.21	+0.98	-2.03	+0.48	-1.28	-0.66	-0.29	-0.27
	Relative (%)	+0.0	+19.4	+5.9	+4.2	+19.6	-40.5	+9.6	-25.5	-13.1	-5.7	-5.3
Steps (reduced)		239 (0)	379 (140)	555 (77)	671 (193)	827 (110)	884 (167)	977 (21)	1015 (59)	1081 (125)	1161 (205)	1184 (228)

Subsets and supersets

239edo is the 52nd prime edo.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [379 -239⟩ | [⟨239 379]] | −0.307 | 0.307 | 6.12 |- | 2.3.5 | [3 -18 11⟩, [32 -7 -9⟩ | [⟨239 379 555]] | −0.247 | 0.265 | 5.27 |- | 2.3.5.7 | 2401/2400, 5120/5103, 29360128/29296875 | [⟨239 379 555 671]] | −0.204 | 0.241 | 4.80 |- | 2.3.5.7.11 | 2401/2400, 3025/3024, 4000/3993, 5120/5103 | [⟨239 379 555 671 827]] | −0.220 | 0.218 | 4.34 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 3\239 | 15.06 | 121/120 | Yarman I (239) |- | 1 | 7\239 | 35.15 | 1990656/1953125 | Gammic (5-limit) |- | 1 | 9\239 | 45.19 | 250/243 | Quartonic (5-limit) |- | 1 | 11\239 | 55.23 | 33/32 | Escapade / alphaquarter |- | 1 | 35\239 | 175.73 | 72/65 | Quadrafifths (239f) |- | 1 | 54\239 | 271.13 | 90/77 | Quasiorwell (239) |- | 1 | 70\239 | 351.46 | 49/40 | Hemififths (7-limit) |- | 1 | 79\239 | 396.65 | 44/35 | Squarschmidt |- | 1 | 83\239 | 416.74 | 14/11 | Unthirds (239f) |- | 1 | 116\239 | 582.43 | 7/5 | Neptune (7-limit) Template:Rank-2 end Template:Orf

Music

Francium

• "thatyounglighthouseboi" from albumwithoutspaces (2024) – Spotify | Bandcamp | YouTube
• "Bath And A Nice Dream" from You Are A... (2024) – Spotify | Bandcamp | YouTube