12ed12/5: Difference between revisions
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| Line 9: | Line 9: | ||
!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 → |
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 |