18edt: Difference between revisions
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'''18edt''' is the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. | '''18edt''' is the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. | ||
== | == Harmonics == | ||
{{Harmonics in equal | |||
| steps = 18 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 18 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
Note that this tuning is fairly close to [[1ed17/16]], although by [[patent val]] [[mapping]] 18edt maps ~[[17/16]] inconsistently to 2\18edt instead of 1\18edt, while 1ed17/16 maps its own [[equave]] even more inconsistently, to 3\1ed17/16. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
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|} | |} | ||
== | == Temperaments == | ||
As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament. | |||
18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case its approximation to [[13/11]] is very sharp. | |||
== See also == | |||
[[1ed17/16]] — relative ed17/16 | |||
[[category:macrotonal]] | [[category:macrotonal]] | ||
[[category:tritave]] | [[category:tritave]] | ||