48ed5: Difference between revisions
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{{Infobox ET}} | |||
'''[[Ed5|Division of the 5th harmonic]] into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. | '''[[Ed5|Division of the 5th harmonic]] into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4. | ||
{| class="wikitable" | == Intervals == | ||
{| class="wikitable mw-collapsible" | |||
|+ Intervals of 48ed5 | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 253: | Line 256: | ||
| | just major third plus two octaves | | | just major third plus two octaves | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 48 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 48 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
==48ed5 as a generator== | ==48ed5 as a generator== | ||
48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val). | 48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val). | ||
{{todo|expand}} | |||