4ed5/2: Difference between revisions
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{{Mathematical interest}} | |||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
== Theory == | |||
4ed5/2 is [[3edo]] with the [[2/1|octave]] compressed by about 10 cents, or [[7ed5]] with the [[5/1|5th harmonic]] compressed by the same amount. It therefore can be considered as an overcompressed 2.5-subgroup temperament tempering out [[128/125]]. | |||
=== Harmonics === | |||
{{Harmonics in equal|4|5|2}} | |||
=== Subsets and supersets === | |||
4ed5/2 is the first composite ed5/2, containing 2ed5/2 as the only nontrivial subset ed5/2. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable center-1 right-2" | ||
|+ | |+ | ||
! | ! # | ||
!Cents | ! Cents | ||
! | ! Approximated ratio | ||
|- | |- | ||
|0 | | 0 | ||
|0 | | 0 | ||
|1/1 | | 1/1 | ||
|- | |- | ||
|1 | | 1 | ||
| | | 397 | ||
|5/4 | | 5/4 | ||
|- | |- | ||
|2 | | 2 | ||
|793 | | 793 | ||
|8/5 | | 8/5 | ||
|- | |- | ||
|3 | | 3 | ||
| | | 1190 | ||
|2/1 | | 2/1 | ||
|- | |- | ||
|4 | | 4 | ||
|1586 | | 1586 | ||
|5/2 | | 5/2 | ||
|} | |} | ||