27edt: Difference between revisions
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== Theory == | |||
27edt corresponds to 17.035…edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]]. In fact, the [[prime edo]]s that approximate the 3-limit well often correspond to composite edts: e.g. [[19edo]] → [[30edt]], [[29edo]] → [[46edt]] and [[31edo]] → [[49edt]]. | |||
Compared to 17edo, 27edt approximates the [[prime interval|primes]] [[7/1|7]], [[11/1|11]], and [[13/1|13]] better; it approximates prime [[5/1|5]] equally poorly, but maps it to 40 steps rather than 39 in the [[patent val]], corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third, and 5 has the same sharp tendency as 7 and 11. | |||
From a purely tritave-based perspective, it [[support]]s the [[minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup. | |||
== | === Harmonics === | ||
{{Harmonics in equal|27|3|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|27|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 27edt (continued)}} | |||
=== Subsets and supersets === | |||
Since 27 factors into primes as 3<sup>3</sup>, 27edt contains [[3edt]] and [[9edt]] as subset edts. | |||
=== Miscellany === | |||
27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for {{w|Klingon}} music since the tradtional Klingon number system is also based on 3. The rather harsh harmonic character of 27edt would suit very well, too<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_86909.html Yahoo! Tuning Group | ''the evil 27 equal temp scale from outer space'']</ref><ref>[https://web.archive.org/web/20100624113458/https://www.klingon.org/smboard/index.php?topic=1810.0 Klingon Imperial Forums | ''klingon music theory'']</ref>. | |||
This being said, such a proposal is rather short-sighted from a general cultural perspective, since any kind of living creature would most likely gravitate towards some form of [[low-complexity JI]], and while 27edt will gain appreciation in base-3 cultures at some point, it may not be the first temperament they discover. That would be like aliens assuming dominant tuning in human music is [[100ed10]] (or 1000ed10 or variation thereof) just because we count in base 10. | |||
== Intervals == | |||
{{Interval table}} | |||
== See also == | |||
* [[10edf]] – relative edf | |||
* [[17edo]] – relative edo | |||
* [[44ed6]] – relative ed6 | |||
== Notes == | |||
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