49edo: Difference between revisions
→21st century: Add Bryan Deister's ''microtonal improv in 49edo'' (2024) |
m Text replacement - "[[The Riemann zeta function and tuning|" to "[[Riemann zeta function|" |
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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 === | ||
The strongest [[ | The strongest [[Riemann zeta function|local zeta peak]] around 49edo is its second closest, 49.141 edo. One step is 24.419 cents, and two steps, 48.839 cents, is a good generator for [[Triple BP]]. | ||
== Approximation to irrational intervals == | == Approximation to irrational intervals == | ||
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| 19\49 | | 19\49 | ||
| 465.3 | | 465.3 | ||
| 55 | | 72/55 | ||
| [[Semisept]] | | [[Semisept]] | ||
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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 == | ||
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* [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026) | * [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026) | ||
* [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026) | * [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026) | ||
* ''Prelude in 49edo'' (2026) | |||
** [https://www.youtube.com/watch?v=aNswQ1-1nlM&list=WL&index=275 <nowiki>[short clip]</nowiki>] (2026) (Lumatone view) | |||
** [https://www.youtube.com/watch?v=j1FEWPvHlGo <nowiki>[full version]</nowiki>] (2026) | |||
; [[Mercury Amalgam]] | ; [[Mercury Amalgam]] | ||