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28ed4/3: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''28ed4/3''' can be thought of as a [[2.3.7.11 subgroup]] analogue to [[20edf]] or [[Carlos Gamma]]. It very closely approximates the intervals of [[8/7]] (at 13 steps) and [[7/6]] (at 15 steps), along with [[11/8]] (at 31 steps). This tuning is close to every other step of [[135edo]] or to [[107edt]].
'''28ed4/3''' can be thought of as a [[2.3.7.11 subgroup]] analogue to [[20edf]] or [[Carlos Gamma]]. It very closely approximates the intervals of [[8/7]] (at 13 steps) and [[7/6]] (at 15 steps), along with [[11/8]] (at 31 steps); these approximations are related to the temperament in this subgroup tempering out [[117649/117612]] and [[67110351/67108864]], which is the subgroup restriction of [[keenanose]]. This tuning is close to every other step of [[135edo]] or to [[107edt]].
 
==Intervals==
These are the intervals up to a perfect fourth up.
{| class="wikitable mw-collapsible"
|+ Intervals of 28ed4/3
|-
! Degrees
! 2.3.7.11.97 subgroup approximation
! Cents
|-
|1
|[[99/98]], 98/97, 97/96
|17.8
|-
|2
|[[49/48]], 99/97
|35.6
|-
|3
|[[33/32]]
|53.4
|-
|4
|1067/1024, 1617/1552
|71.1
|-
|5
|539/512
|88.9
|-
|6
|1089/1024
|106.7
|-
|7
|8192/7623
|124.5
|-
|8
|4096/3773
|142.3
|-
|9
|3584/3267
|160.1
|-
|10
|256/231
|177.9
|-
|11
|384/343, 776/693
|195.7
|-
|12
|112/99, 388/343, 768/679
|213.4
|-
|13
|[[8/7]]
|231.2
|-
|14
|[[97/84]], 112/97, 343/297, 396/343
|249.0
|-
|15
|[[7/6]]
|266.8
|-
|16
|[[33/28]]
|284.6
|-
|17
|231/194, 343/288
|302.4
|-
|18
|[[77/64]]
|320.2
|-
|19
|1089/896
|338.0
|-
|20
|3773/3072
|355.7
|-
|21
|2541/2048
|373.5
|-
|22
|4096/3267
|391.3
|-
|23
|2048/1617
|409.1
|-
|24
|3072/2401
|426.9
|-
|25
|[[128/99]]
|444.7
|-
|26
|[[64/49]], 388/297
|462.5
|-
|27
|[[128/97]], 194/147, 392/297
|480.3
|-
|'''28'''
|[[4/3]]
|'''498.0'''
|}


== Harmonics ==
== Harmonics ==
Retrieved from "https://en.xen.wiki/w/28ed4/3"