49edo: Difference between revisions
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| 10 | | 10 | ||
| 244.898 | | 244.898 | ||
| 125/108, 144/125 | | [[125/108]], [[144/125]] | ||
| {{UDnote|step=10}} | | {{UDnote|step=10}} | ||
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| 19 | | 19 | ||
| 465.306 | | 465.306 | ||
| 125/96, ''162/125'' | | [[72/55]], [[125/96]], ''[[162/125]]'' | ||
| {{UDnote|step=19}} | | {{UDnote|step=19}} | ||
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| 30 | | 30 | ||
| 734.694 | | 734.694 | ||
| ''125/81'', 192/125 | | ''[[55/36]], [[125/81]]'', [[192/125]] | ||
| {{UDnote|step=30}} | | {{UDnote|step=30}} | ||
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| 39 | | 39 | ||
| 955.102 | | 955.102 | ||
| 125/72, 216/125 | | [[125/72]], [[216/125]] | ||
| {{UDnote|step=39}} | | {{UDnote|step=39}} | ||
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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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=== Nonoctave temperament === | === 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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{{main|List of MOS scales in 49edo}} | {{main|List of MOS scales in 49edo}} | ||
* Bohpier[8]: 6 6 6 6 7 6 6 6 | * [[Bohpier]][8]: 6 6 6 6 7 6 6 6 | ||
* Catalan[7]: 3 10 3 10 3 10 10 (vaugely diminished-like) | * [[Catalan]][7]: 3 10 3 10 3 10 10 (vaugely diminished-like) | ||
* Catalan[11]: 3 7 3 3 7 3 3 7 3 3 7 | * Catalan[11]: 3 7 3 3 7 3 3 7 3 3 7 | ||
* Catalan[19]: 3 3 1 3 3 3 3 1 3 3 3 1 3 3 3 3 1 3 3 | * Catalan[19]: 3 3 1 3 3 3 3 1 3 3 3 1 3 3 3 3 1 3 3 | ||
* Clyde[5]: 5 13 5 13 13 (mysterious, adventurous) | * [[Clyde]][5]: 5 13 5 13 13 (mysterious, adventurous) | ||
* Didacus[6]: 8 8 8 8 8 9 (like the whole tone scale) | * [[Didacus]][6]: 8 8 8 8 8 9 (like the whole tone scale) | ||
* Didacus[13]: 1 7 1 7 1 7 1 7 1 7 1 7 1 | * Didacus[13]: 1 7 1 7 1 7 1 7 1 7 1 7 1 | ||
* Infraorwell[5]: 11 11 5 11 11 | * [[Infraorwell]][5]: 11 11 5 11 11 | ||
* Infraorwell[22]: 1 4 1 4 1 1 4 1 4 1 1 4 1 4 1 4 1 1 4 1 4 1 | * Infraorwell[22]: 1 4 1 4 1 1 4 1 4 1 1 4 1 4 1 4 1 1 4 1 4 1 | ||
* Kleiboh[5]: 12 12 12 12 1 | * [[Kleiboh]][5]: 12 12 12 12 1 | ||
* Kleiboh[13]: 1 10 1 1 10 1 1 1 10 1 1 10 1 | * Kleiboh[13]: 1 10 1 1 10 1 1 1 10 1 1 10 1 | ||
* Magus[7]: 1 15 1 15 1 15 1 (vaguely augmented-like) | * [[Magus]][7]: 1 15 1 15 1 15 1 (vaguely augmented-like) | ||
* Passion[12]: 4 4 4 4 4 4 5 4 4 4 4 4 (like [[12edo]]) | * [[Passion]][12]: 4 4 4 4 4 4 5 4 4 4 4 4 (like [[12edo]]) | ||
* Passion[23]: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 | * Passion[23]: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 | ||
* Sevond[21]/Seville[21]: 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 | * [[Sevond]][21]/[[Seville]][21]: 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 1 5 1 | ||
* Superpyth[5]: 11 9 9 11 9 (in between minor pentatonic and [[equipentatonic]]) | * [[Superpyth]][5]: 11 9 9 11 9 (in between minor pentatonic and [[equipentatonic]]) | ||
* Superpyth[7]: 9 2 9 9 9 2 9 (Dorian mode; rotate for other modes) | * Superpyth[7]: 9 2 9 9 9 2 9 (Dorian mode; rotate for other modes) | ||
* Superpyth[12]: 2 7 2 7 2 2 7 2 7 2 7 2 (same melodic shape as [[12edo]] but much more [[xenharmonic]] harmonies) | * Superpyth[12]: 2 7 2 7 2 2 7 2 7 2 7 2 (same melodic shape as [[12edo]] but much more [[xenharmonic]] harmonies) | ||
* Superpyth[27]: 2 2 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 2 | * Superpyth[27]: 2 2 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 2 2 | ||
* [[6afdo]]: 11 9 9 7 7 6 | |||
=== Other scales === | === Other 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]] | ||