27edt: Difference between revisions

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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 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. 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.

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.

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 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 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. 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.
 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.