49edo: Difference between revisions

21st century: Add Bryan Deister's ''microtonal improv in 49edo'' (2024)
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=== Interval mappings ===
=== Interval mappings ===
{{Q-odd-limit intervals|49}}
{{Q-odd-limit intervals|49}}
{{Q-odd-limit intervals|49.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 49f val mapping}}


=== Zeta peaks ===
=== Zeta peaks ===
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== Octave stretch or compression ==
== Octave stretch or compression ==
49edo's [[prime]]s 3, 5, 7 and 11 are all tuned sharp, so 49edo can benefit from [[octave shrinking]]. Some compressed-octave tunings of 49edo include (least to most compression): [[ed12|176ed12]], [[ed5|114ed5]], [[zpi|233zpi]], [[ed6|127ed6]], [[ed7|138ed7]] and [[78edt]].
49edo's [[prime]]s 3, 5, 7 and 11 are all tuned sharp, so 49edo can benefit from [[octave shrinking]]. Some compressed-octave tunings of 49edo include (least to most compression): [[ed12|176ed12]], [[ed5|114ed5]], [[zpi|233zpi]], [[ed6|127ed6]], [[ed7|138ed7]] and [[78edt]].
=== Nonoctave temperament ===
The TE-optimized [[Triple BP|triple Bohlen–Pierce scale]] is obtained by taking every second degree of 49edo with the octave compressed by 3.861 cents to 1196.139 cents. It realizes the Tenney–Euclidean regular temperament on the 3.5.7.11.13 subgroup mapped as [⟨78 114 138 170 182]]. Under this compression, the primes map to the 49fgh val in the 23-limit.


== Scales ==
== Scales ==