Xenharmonic Wiki

User:Overthink/Sandbox

< User:Overthink
Revision as of 00:13, 13 February 2026 by Overthink (talk | contribs) (see how subst-ing this will work)
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

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 21/12, 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)
Retrieved from "https://en.xen.wiki/index.php?title=User:Overthink/Sandbox&oldid=223898"