Xenharmonic Wiki

49edo: Difference between revisions

← Older edit
VisualWikitext
→Music: Add Bryan Deister's ''49edo improv'' (2026)
Tags: Mobile edit Mobile web edit Advanced mobile edit
 
(15 intermediate revisions by 3 users not shown)
Line 3: Line 3:


== Theory ==
== Theory ==
49edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit.
49edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]], [[540/539]], and [[1375/1372]] in the 11-limit. In the 13-limit, its [[patent val]] {{val| 49 78 114 138 170 181 }}, has a rather flat (by relative error) harmonic [[13/1|13]], which leads to inconsistent mappings; but using the 49f val {{val| 49 78 114 138 170 182 }} improves 13-limit consistency, and in this val it tempers out [[364/363]] and [[847/845]].


=== Harmonics ===
=== Harmonics ===
Line 9: Line 9:


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 49 factors into {{factorization|49}}, 49edo contains [[7edo]] as its only nontrivial subset. 49edo is the first square edo with a [[enfactoring|non-enfactored]] diatonic fifth.
Since 49 factors into primes as 7<sup>2</sup>, 49edo contains [[7edo]] as its only nontrivial subset. 49edo is the first square edo with a [[enfactoring|non-enfactored]] diatonic fifth. Doubling it produces [[98edo]], a respectable (if overly complex) [[meantone]] tuning.  


== Intervals ==
== Intervals ==
Line 66: Line 66:
| 9
| 9
| 220.408
| 220.408
| [[8/7]], ''[[9/8]]''
| [[8/7]], ''[[9/8]]'', [[25/22]]
| {{UDnote|step=9}}
| {{UDnote|step=9}}
|-
|-
Line 221: Line 221:
| 40
| 40
| 979.592
| 979.592
| [[7/4]], ''[[16/9]]''
| [[7/4]], ''[[16/9]]'', [[44/25]]
| {{UDnote|step=40}}
| {{UDnote|step=40}}
|-
|-
Line 309: Line 309:
=== 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 ===
Line 480: Line 481:
== 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 ==
Line 529: Line 533:


== Music ==
== Music ==
; [[Mercury Amalgam]]
=== Modern renderings ===
* [https://www.youtube.com/watch?v=c_kzhcMMHWM&pp=ygUFNDllZG8%3D ''Wrong Generation (Demo, January 2022)''] (2023)
; {{W|The Cure}}
 
* [https://www.youtube.com/watch?v=GHslu-ZWspk ''Boys Don't Cry''] (1979) – Lumatone cover by [[YoVariable]] (2025)
; [[Cam Taylor]]
* [https://www.youtube.com/watch?v=fns6688IRpg ''49-equal: 7-equal meets superpyth''] (2023)


=== 21st century ===
; [[Bryan Deister]]
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023)
* [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023)
* [https://www.youtube.com/shorts/V8t7MyP2Nuo ''microtonal improv in 49edo''] (2024)
* [https://www.youtube.com/shorts/zb1Z6o-Uvuw ''weathergirl - FLAVOR FOLEY (microtonal cover in 49edo)''] (2025)
* [https://www.youtube.com/shorts/zb1Z6o-Uvuw ''weathergirl - FLAVOR FOLEY (microtonal cover in 49edo)''] (2025)
* [https://www.youtube.com/shorts/73PfAAWubVs ''I'm Your Captain Now (The Ancients) - The Recovery System (microtonal cover in 49edo)''] (2026)
* [https://www.youtube.com/shorts/73PfAAWubVs ''I'm Your Captain Now (The Ancients) - The Recovery System (microtonal cover in 49edo)''] (2026) {{todo|research|comment=Identify the original composers.}}
* [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026)
* [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026)
* [https://www.youtube.com/shorts/_yNrDI6nS1I ''49edo riff''] (2026)
* [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026)
* [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026)


; [[YoVariable]]
; [[Mercury Amalgam]]
* [https://www.youtube.com/watch?v=GHslu-ZWspk The Cure - ''Boys Don't Cry'' (cover)] (2025)
* [https://www.youtube.com/watch?v=c_kzhcMMHWM&pp=ygUFNDllZG8%3D ''Wrong Generation''] (2022 demo version)
 
; [[Cam Taylor]]
* [https://www.youtube.com/watch?v=fns6688IRpg ''49-equal: 7-equal meets superpyth''] (2023)


[[Category:Archytas]]
[[Category:Archytas]]
Retrieved from "https://en.xen.wiki/w/49edo"