User:Overthink/Sandbox

Marvel

Subgroups	2.3.5.7, 2.3.5.7.11
Comma basis	225/224 (7-limit); 225/224, 385/384 (11-limit)
Reduced mapping	⟨1; 1 0 2 -1; 0 1 2 -3]
ET join	19 & 22 & 31
Generators (CWE)
MOS scales	n/a
Ploidacot	n/a
Pergen	(P8, P5, ^1)
Color name	Ruyoyoti
Minimax error	9-odd-limit: 2.57 ¢; 11-limit 21-odd-limit: 3.86 ¢
Target scale size	9-odd-limit: ? notes; 11-limit 21-odd-limit: ? notes

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User:Overthink/Test template

← 11edo

12edo

13edo →

Prime factorization	22 × 3 (highly composite)
Step size	100 ¢ (by definition)
Fifth	7\12 (700 ¢) (convergent)
Semitones (A1:m2)	1:1 (100 ¢ : 100 ¢)
Consistency limit	9
Distinct consistency limit	5

12 equal divisions of the octave (abbreviated 12edo or 12ed2), also called 12-tone equal temperament (12tet) or 12 equal temperament (12et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 12 equal parts of exactly 100 ¢ each. Each step represents a frequency ratio of 2^1/12, or the 12th root of 2.

Theory

Approximation of prime harmonics in 12edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	-2.0	+13.7	+31.2	+48.7	-40.5	-5.0	+2.5	-28.3	-29.6	-45.0
	Relative (%)	+0.0	-2.0	+13.7	+31.2	+48.7	-40.5	-5.0	+2.5	-28.3	-29.6	-45.0
Steps (reduced)		12 (0)	19 (7)	28 (4)	34 (10)	42 (6)	44 (8)	49 (1)	51 (3)	54 (6)	58 (10)	59 (11)