12ed12/5: Difference between revisions
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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. | ||
== 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, 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. | 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 | |||
|- | |||
|0 | |||
|0.00 | |||
|C | |||
|- | |||
|1 | |||
|126.303 | |||
|C#, Db | |||
|- | |||
|2 | |||
|252.607 | |||
|D | |||
|- | |||
|3 | |||
|378.910 | |||
|D#, Eb | |||
|- | |||
|4 | |||
|505.214 | |||
|E | |||
|- | |||
|5 | |||
|631.517 | |||
|F | |||
|- | |||
|6 | |||
|757.821 | |||
|F#, Gb | |||
|- | |||
|7 | |||
|884.124 | |||
|G | |||
|- | |||
|8 | |||
|1010.428 | |||
|G#, Ab | |||
|- | |||
|9 | |||
|1136.731 | |||
|A | |||
|- | |||
|10 | |||
|1263.034 | |||
|A#, Bb | |||
|- | |||
|11 | |||
|1398.338 | |||
|B | |||
|- | |||
|12 | |||
|1515.641 | |||
|C | |||
|} | |||