5L 4s: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 40: | Line 40: | ||
== Tuning ranges == | == Tuning ranges == | ||
=== Hard-of-basic === | === Hard-of-basic === | ||
Hard-of-basic tunings have [[Semifourth|semifourths]] as generators, between 1\5 ( | Hard-of-basic tunings have [[Semifourth|semifourths]] as generators, between 1\5 (240{{c}}) and 3\14 (257.14{{c}}), where two of them create a diatonic 4th. The generator could be viewed as a 15/13, and the resulting "ultramajor" chords and "inframinor" triads could be viewed as approximating 10:13:15 and 26:30:39. See [[Arto and Tendo Theory]]. | ||
==== Hypohard ==== | ==== Hypohard ==== | ||
| Line 76: | Line 76: | ||
This range is notable for having many simple tunings that are close to being "eigentunings" (tunings that tune a certain JI interval exactly): | This range is notable for having many simple tunings that are close to being "eigentunings" (tunings that tune a certain JI interval exactly): | ||
* 33edo semiquartal has close 7/5 (error −0. | * 33edo semiquartal has close 7/5 (error −0.69{{c}}), 9/5 (error −0.59{{c}}) and 9/7 (error +1.28{{c}}), thus can be used for the close 5:7:9 in the two Locrian-like modes 1|7 and 0|8 | ||
* 52edo semiquartal has close 22/19 (error +0. | * 52edo semiquartal has close 22/19 (error +0.04{{c}}) | ||
* 19edo semiquartal has close 6/5 (error +0. | * 19edo semiquartal has close 6/5 (error +0.15{{c}}) and 28/27 (error +0.20{{c}}) | ||
However, for the more complex intervals such as 22/19 and 28/27, you might want to use the exact eigentuning for the full effect, unless you specifically need an edo for modulatory purposes. | However, for the more complex intervals such as 22/19 and 28/27, you might want to use the exact eigentuning for the full effect, unless you specifically need an edo for modulatory purposes. | ||
| Line 109: | Line 109: | ||
=== Soft-of-basic === | === Soft-of-basic === | ||
Soft-of-basic tunings have semifourths that are between 3\14 (257. | Soft-of-basic tunings have semifourths that are between 3\14 (257.14{{c}}) and 2\9 (266.67{{c}}), creating a "[[mavila]]" or "[[superdiatonic]]" 4th. [[23edo]]'s 5\23 (260.87{{c}}) is an example of this generator. | ||
The sizes of the generator, large step and small step of 5L 4s are as follows in various soft-of-basic tunings. | The sizes of the generator, large step and small step of 5L 4s are as follows in various soft-of-basic tunings. | ||