12ed12/5: Difference between revisions

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!Cents
!Cents
!"Macrodiatonic" (5L 2s<12/5>) notation
!"Macrodiatonic" (5L 2s<12/5>) notation
!Approximate ratios
|-
|-
|0
|0
|0.00
|0.00
|C
|C
|[[1/1]]
|-
|-
|1
|1
|126.303
|126.303
|C#, Db
|C#, Db
|
|-
|-
|2
|2
|252.607
|252.607
|D
|D
|
|-
|-
|3
|3
|378.910
|378.910
|D#, Eb
|D#, Eb
|[[5/4]]
|-
|-
|4
|4
|505.214
|505.214
|E
|E
|[[4/3]]
|-
|-
|5
|5
|631.517
|631.517
|F
|F
|[[36/25]]
|-
|-
|6
|6
|757.821
|757.821
|F#, Gb
|F#, Gb
|
|-
|-
|7
|7
|884.124
|884.124
|G
|G
|[[5/3]]
|-
|-
|8
|8
|1010.428
|1010.428
|G#, Ab
|G#, Ab
|[[9/5]]
|-
|-
|9
|9
|1136.731
|1136.731
|A
|A
|[[48/25]]
|-
|-
|10
|10
|1263.034
|1263.034
|A#, Bb
|A#, Bb
|
|-
|-
|11
|11
|1398.338
|1398.338
|B
|B
|
|-
|-
|12
|12
|1515.641
|1515.641
|C
|C
|[[12/5]]
|}
|}

Revision as of 02:26, 23 May 2023

← 11ed12/5 12ed12/5 13ed12/5 →
Prime factorization 22 × 3 (highly composite)
Step size 126.303 ¢ 
Octave 10\12ed12/5 (1263.03 ¢) (→ 5\6ed12/5)
Twelfth 15\12ed12/5 (1894.55 ¢) (→ 5\4ed12/5)
Consistency limit 2
Distinct consistency limit 2

12 equal divisions of 12/5 (12ed12/5) is the tuning system that divides the classic minor tenth (12/5) into a number of equal steps.

Temperaments

12ed12/5 supports the "macro-meantone" temperament which tempers out 15625/15552 in the 12/5.3.4 subgroup. By a weird coincidence, this temperament is very close to a version of meantone with all intervals stretched by about 26%, such that 2/1 becomes approximately 12/5, 3/2 becomes approximately 5/3, and 5/4 becomes approximately 4/3. The ~4:5:6 chord becomes stretched to the point where it is a ~3:4:5 chord. Even MOS patterns are similar to meantone.

Intervals

Degrees Cents "Macrodiatonic" (5L 2s<12/5>) notation Approximate ratios
0 0.00 C 1/1
1 126.303 C#, Db
2 252.607 D
3 378.910 D#, Eb 5/4
4 505.214 E 4/3
5 631.517 F 36/25
6 757.821 F#, Gb
7 884.124 G 5/3
8 1010.428 G#, Ab 9/5
9 1136.731 A 48/25
10 1263.034 A#, Bb
11 1398.338 B
12 1515.641 C 12/5