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{{Infobox ET}} | {{Infobox ET}} | ||
'''12 equal divisions of 12/5''' (12ed12/5) is the tuning system that divides the [[12/5|classic minor tenth (12/5)]] into a number of [[equal]] steps. | '''12 equal divisions of 12/5''' (12ed12/5) is the tuning system that divides the [[12/5|classic minor tenth (12/5)]] into a number of [[equal]] steps. It is very closely approximated by every second step of [[19edo]]. | ||
== Temperaments == | == Temperaments == | ||
12ed12/5 supports the "macro-meantone" temperament which tempers out 15625/15552 in the 12/5.3.4 subgroup. By a weird coincidence, | 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 == | |||
{|class="wikitable" | |||
|- | |||
!Degrees | |||
!Cents | |||
!"Macrodiatonic" (5L 2s<12/5>) notation | |||
!Approximate ratios | |||
|- | |||
|0 | |||
|0.00 | |||
|C | |||
|[[1/1]] | |||
|- | |||
|1 | |||
|126.303 | |||
|C#, Db | |||
|[[27/25]] | |||
|- | |||
|2 | |||
|252.607 | |||
|D | |||
|125/108 | |||
|- | |||
|3 | |||
|378.910 | |||
|D#, Eb | |||
|[[5/4]] | |||
|- | |||
|4 | |||
|505.214 | |||
|E | |||
|[[4/3]] | |||
|- | |||
|5 | |||
|631.517 | |||
|F | |||
|[[36/25]] | |||
|- | |||
|6 | |||
|757.821 | |||
|F#, Gb | |||
|[[25/16]], 125/81, [[192/125]] | |||
|- | |||
|7 | |||
|884.124 | |||
|G | |||
|[[5/3]] | |||
|- | |||
|8 | |||
|1010.428 | |||
|G#, Ab | |||
|[[9/5]] | |||
|- | |||
|9 | |||
|1136.731 | |||
|A | |||
|[[48/25]] | |||
|- | |||
|10 | |||
|1263.034 | |||
|A#, Bb | |||
|25/12 | |||
|- | |||
|11 | |||
|1398.338 | |||
|B | |||
|20/9 | |||
|- | |||
|12 | |||
|1515.641 | |||
|C | |||
|[[12/5]] | |||
|} | |||
Latest revision as of 02:40, 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. It is very closely approximated by every second step of 19edo.
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 | 27/25 |
| 2 | 252.607 | D | 125/108 |
| 3 | 378.910 | D#, Eb | 5/4 |
| 4 | 505.214 | E | 4/3 |
| 5 | 631.517 | F | 36/25 |
| 6 | 757.821 | F#, Gb | 25/16, 125/81, 192/125 |
| 7 | 884.124 | G | 5/3 |
| 8 | 1010.428 | G#, Ab | 9/5 |
| 9 | 1136.731 | A | 48/25 |
| 10 | 1263.034 | A#, Bb | 25/12 |
| 11 | 1398.338 | B | 20/9 |
| 12 | 1515.641 | C | 12/5 |