User:Overthink/Sandbox: Difference between revisions
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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
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
→Theory: try |
see how subst-ing this will work |
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{{ | {{Infobox ET|12edo|debug=1}} | ||
{{ED intro|12edo}} | |||
== Theory == | |||
{{Harmonics in equal|12}} <!-- not yet working --> | |||
Revision as of 00:13, 13 February 2026
| Marvel |
225/224, 385/384 (11-limit)
11-limit 21-odd-limit: 3.86 ¢
11-limit 21-odd-limit: ? notes
- Kite's Genchain mode numbering
- Kite's Thoughts on 41edo Note Names and Key Signatures
- Kite's color notation
- Kite's color notation/Catalog of rank-2 temperaments
- Kite's color notation/Temperament names
- Kite's color notation/Translations
- Kite's list of uniform solfeges for EDOs
- Kite's list of uniform solfeges for pergens
- Kite's thoughts on 31edo brass instruments
- Kite's thoughts on 41edo Lattices
- Kite's thoughts on 41edo brass instruments
- Kite's thoughts on Stern-Brocot ancestors and rank 2 temperaments
- Kite's thoughts on antipodes
- Kite's thoughts on enharmonic unisons
- Kite's thoughts on enharmonic unisons in ups and downs notation
- Kite's thoughts on fifthspans
- Kite's thoughts on harmonic and subharmonic nomenclature
- Kite's thoughts on hi-lo notation
- Kite's thoughts on how to read 41-equal scores
- Kite's thoughts on negative intervals
- Kite's thoughts on numeric solfege
- Kite's thoughts on pergens
- Kite's thoughts on ring number
- Kite's thoughts on shadows
- Kite's thoughts on the V-I cadence in higher prime limits
- Kite's thoughts on the arrows of ups and down notation
- Kite's thoughts on the mathematical basis For the kite guitar
- Kite's thoughts on tuning a kite guitar to 31edo or 62edo
- Kite's thoughts on twin squares
- Kite's thoughts on ups and downs notation for rank-3 JI
- Kite's uniform solfege
- Kite's ups and downs notation
| ← 11edo | 12edo | 13edo → |
(convergent)
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
| 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) | |