12ed12/5: Difference between revisions

CompactStar (talk | contribs)
No edit summary
CompactStar (talk | contribs)
No edit summary
 
(12 intermediate revisions by the same user not shown)
Line 1: Line 1:
{{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, the approxmiations of 12/5, 5/3, and 4/3 in this temperament are very close to stretched 2/1, 3/2, and 5/4, so the ETs supported by macro-meantone are mostly identical to those that support meantone, but with the equave as 12/5 instead of 2/1 (so 12ed12/5, 19ed12/5, etc. instead of 12edo, 19edo, etc.). Even the MOS scales like 5L 2s are the same. The tempered 4:5:6 chords in meantone become stretched to the point where they are tempered 3:4:5 chords.
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]]
|}