8edo: Difference between revisions
8 edo is a weird and special case so I implemented it a bit differently here but made it as similar as possible. All other pages will be way more normal and Standardised than this. |
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=== Octave stretch and compression === | === Octave stretch and compression === | ||
8edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1187 cents gives the tuning called [[29ed12]]. | 8edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1187 cents gives the tuning called [[ed12|29ed12]]. | ||
Of all prime [[harmonic]]s up to 31, pure-octave 8edo only manages to approximate 2/1 and 19/1 within 15 [[cents]], completely missing all the others. | Of all prime [[harmonic]]s up to 31, pure-octave 8edo only manages to approximate 2/1 and 19/1 within 15 [[cents]], completely missing all the others. | ||
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{{Harmonics in equal|8|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 8edo (continued)}} | {{Harmonics in equal|8|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 8edo (continued)}} | ||
; [[29ed12]] | ; [[ed12|29ed12]] | ||
* Step size: 148.343{{c}}, octave size: 1186.746{{c}} | * Step size: 148.343{{c}}, octave size: 1186.746{{c}} | ||
{{Harmonics in equal|29|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 29ed12}} | {{Harmonics in equal|29|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 29ed12}} | ||