65edo: Difference between revisions
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'''65edo''' divides the [[octave]] into 65 equal parts of 18.4615 cents each. | |||
== Theory == | |||
65et can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[würschmidt comma]]. In the [[7-limit]], there are two different maps; the first is {{val| 65 103 151 '''182''' }}, [[tempering out]] [[126/125]], [[245/243]] and [[686/675]], so that it supports [[sensi]] temperament, and the second is {{val| 65 103 151 '''183''' }} (65d), tempering out [[225/224]], 3125/3087, 4000/3969 and [[5120/5103]], so that it supports [[garibaldi]] temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[würschmidt]] temperament (wurschmidt and worschmidt) these two mappings provide. | |||
65edo approximates the intervals [[3/2]], [[5/4]], [[11/8]], [[19/16]], [[23/16]] and [[31/16]] well, so that it does a good job representing the 2.3.5.11.19.23.31 [[just intonation subgroup]]. To this one may want to add [[17/16]] and [[29/16]], giving the [[31-limit]] no-7's no-13's subgroup 2.3.5.11.17.19.23.29.31. Also of interest is the [[19-limit]] [[k*N subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as the [[zeta]] edo [[130edo]]. | 65edo approximates the intervals [[3/2]], [[5/4]], [[11/8]], [[19/16]], [[23/16]] and [[31/16]] well, so that it does a good job representing the 2.3.5.11.19.23.31 [[just intonation subgroup]]. To this one may want to add [[17/16]] and [[29/16]], giving the [[31-limit]] no-7's no-13's subgroup 2.3.5.11.17.19.23.29.31. Also of interest is the [[19-limit]] [[k*N subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as the [[zeta]] edo [[130edo]]. | ||
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65edo contains [[13edo]] as a subset. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see [https://soundcloud.com/andrew_heathwaite/rubble-a-xenuke-unfolded Rubble: a Xenuke Unfolded]. | 65edo contains [[13edo]] as a subset. The offset between a just perfect fifth at 702 cents and the 13edo superfifth at 738.5 cents, is approximately 2 degrees of 65edo. Therefore, an instrument fretted to 13edo, with open strings tuned to 3-limit intervals such as 4/3, 3/2, 9/8, 16/9 etc, will approximate a subset of 65edo. For an example of this, see [https://soundcloud.com/andrew_heathwaite/rubble-a-xenuke-unfolded Rubble: a Xenuke Unfolded]. | ||
=== Prime harmonics === | |||
{{Primes in edo|65|columns=11}} | {{Primes in edo|65|columns=11}} | ||
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! [[Degree|Degree]] | ! [[Degree|Degree]] | ||
![[cent|Cents]] | ![[cent|Cents]] | ||
! colspan="2" |[[Ups and Downs Notation | ! colspan="2" |[[Ups and Downs Notation]] | ||
|- | |- | ||
| style="text-align:center;" | 0 | | style="text-align:center;" | 0 | ||
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|} | |} | ||
=Scales= | == Scales == | ||
* [[ | * [[Photia7]] | ||
* [[ | * [[Photia12]] | ||
[[Category:65edo]] | [[Category:65edo]] | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Theory]] | |||
[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Subgroup]] | |||
[[Category:Schismic]] | [[Category:Schismic]] | ||
[[Category:Sensipent]] | [[Category:Sensipent]] | ||
[[Category:Würschmidt]] | [[Category:Würschmidt]] | ||
{{todo| | {{todo| unify precision }} | ||