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{{Infobox ET}}
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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 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"