12ed5: Difference between revisions
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'''[[Ed5|Division of the 5th harmonic]] into | {{Infobox ET}} | ||
'''[[Ed5|Division of the 5th harmonic]] into 12 equal parts''' (12ed5) is related to the [[Meantone family|mothra temperament]] and the [[Semicomma family|quadrawell temperament]]. The step size about 232.1928 cents, corresponding to 5.1681 [[edo]], very nearly every 6th step of [[31edo]]. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. | |||
[[ | == Intervals == | ||
[[ | {| class="wikitable" | ||
|- | |||
! | degree | |||
! | cents value | |||
! | corresponding <br>JI intervals | |||
! | comments | |||
|- | |||
| | 0 | |||
| | 0.0000 | |||
| | '''exact [[1/1]]''' | |||
| | | |||
|- | |||
| | 1 | |||
| | 232.1928 | |||
| | [[8/7]] | |||
| | | |||
|- | |||
| | 2 | |||
| | 464.3856 | |||
| | 17/13 | |||
| | | |||
|- | |||
| | 3 | |||
| | 696.5784 | |||
| | | |||
| | meantone fifth <br>(pseudo-[[3/2]]) | |||
|- | |||
| | 4 | |||
| | 928.7712 | |||
| | 65/38 | |||
| | | |||
|- | |||
| | 5 | |||
| | 1160.9640 | |||
| | 45/23 | |||
| | | |||
|- | |||
| | 6 | |||
| | 1393.1569 | |||
| | [[19/17|38/17]], 85/38 | |||
| | meantone major second plus an octave | |||
|- | |||
| | 7 | |||
| | 1625.3497 | |||
| | 23/9 | |||
| | | |||
|- | |||
| | 8 | |||
| | 1857.5425 | |||
| | [[19/13|38/13]] | |||
| | | |||
|- | |||
| | 9 | |||
| | 2089.7353 | |||
| | | |||
| | meantone major sixth plus an octave <br>(pseudo-[[10/3]]) | |||
|- | |||
| | 10 | |||
| | 2321.9281 | |||
| | 65/17 | |||
| | | |||
|- | |||
| | 11 | |||
| | 2554.1209 | |||
| | 35/8 | |||
| | | |||
|- | |||
| | 12 | |||
| | 2786.3137 | |||
| | '''exact [[5/1]]''' | |||
| | just major third plus two octaves | |||
|} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 12 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 12 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||