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'''27edt''' means '''division of the tritave ([[3/1]]) into 27 equal parts'''.
{{ED intro}}
 
== 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]].


Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.4428 [[cent]]s, corresponding 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 edos that approximate [[Pythagorean tuning]] commonly become 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.  


Compared to 17edo, 27edt approximates the primes 7, 11, and 13 better; it approximates prime 5 equally poorly, but maps 5/1 to 40 steps rather than 39, 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 supports [[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.
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.


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 [https://en.wikipedia.org/wiki/Klingon 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.
=== 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)}}


See, e.g., http://launch.dir.groups.yahoo.com/group/tuning/message/86909 and http://www.klingon.org/smboard/index.php?topic=1810.0.
=== Subsets and supersets ===
Since 27 factors into primes as 3<sup>3</sup>, 27edt contains [[3edt]] and [[9edt]] as subset edts.  


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.  
=== 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>.


==Harmonics==
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.
{{Harmonics in equal|27|3|1|prec=2|columns=15}}


== Intervals ==
== Intervals ==
{{Interval table}}
{{Interval table}}


[[Category:Edt]]
== See also ==
[[Category:Nonoctave]]
* [[10edf]] – relative edf
* [[17edo]] – relative edo
* [[44ed6]] – relative ed6
 
== Notes ==
Retrieved from "https://en.xen.wiki/w/27edt"