28ed4/3: Difference between revisions
Created page with "{{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..." |
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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 | |||
|426.89571354395364193329708622509 | |||
|- | |||
|25 | |||
|[[128/99]] | |||
|444.68303494161837701385113148447 | |||
|- | |||
|26 | |||
|[[64/49]], 388/297 | |||
|462.47035633928311209440517674385 | |||
|- | |||
|27 | |||
|[[128/97]], 194/147, 392/297 | |||
|480.25767773694784717495922200323 | |||
|- | |||
|'''28''' | |||
|[[4/3]] | |||
|'''498.04499913461258225551326726261''' | |||
|} | |||
== Harmonics == | == Harmonics == | ||