49edt: Difference between revisions

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'''[[Edt|Division of the third harmonic]] into 49 equal parts''' (49EDT) is related to [[31edo|31 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 3.2777 cents stretched and the step size about 38.8154 cents. It is consistent through the [[11-odd-limit|12-integer limit]].

~~Lookalikes:~~ [[~~18edf~~]], [[31edo]], [[~~39cET~~]], [[~~80ed6~~]]

== Theory ==

49edt is related to [[31edo]], but with the 3/1 rather than the [[2/1]] being just, which stretches the octave by about 3.28{{c}}. Like 31edo, 49edt is [[consistent]] through the [[integer limit|12-integer-limit]], but it has a sharp tendency, with [[prime harmonic]]s 2, [[5/1|5]], [[7/1|7]], and [[11/1|11]] all tuned sharp.

=== Harmonics ===

{{Harmonics in equal|49|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 49edt (continued)}}

=== Subsets and supersets ===

Since 49 factors into primes as 7<sup>2</sup>, 49edt contains [[7edt]] as its only nontrivial subset edt.

== Intervals ==

== ~~Harmonics~~ ==

== Music ==

~~{{Harmonics~~ in ~~equal~~

; [[User:Rperlner|Ray Perlner]]

~~| steps~~ = 49

* [https://www.youtube.com/watch?v=2DIZlqLS1O8 ''Fugue in 49EDT for Harpsichord Mintaka<nowiki>[7]</nowiki> LLLsLLs "Macro-Lydian"''] (2025)

~~| num~~ = 3

~~| denom~~ = 1

== See also ==

~~| intervals = integer~~

* [[18edf]] – relative edf

}}

* [[31edo]] – relative edo

~~{{Harmonics in equal~~

* [[72ed5]] – relative ed5

~~| steps = 49~~

* [[80ed6]] – relative ed6

~~| num = 3~~

* [[87ed7]] – relative ed7

~~| denom = 1~~

* [[107ed11]] – relative ed11

~~| start = 12~~

* [[111ed12]] – relative ed12

~~| collapsed = 1~~

* [[138ed22]] – relative ed22

~~| intervals = integer~~

* [[204ed96]] – close to the zeta-optimized tuning for 31edo

}}

* [[39cET]]

[[Category:~~Edonoi~~]]

[[Category:31edo]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''[[Edt|Division of the third harmonic]] into 49 equal parts''' (49EDT) is related to [[31edo|31 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 3.2777 cents stretched and the step size about 38.8154 cents. It is consistent through the [[11-odd-limit|12-integer limit]].
+{{ED intro}}
-Lookalikes: [[18edf]], [[31edo]], [[39cET]], [[80ed6]]
+== Theory ==
+edt is related to [[31edo]], but with the 3/1 rather than the [[2/1]] being just, which stretches the octave by about 3.28{{c}}. Like 31edo, 49edt is [[consistent]] through the [[integer limit|12-integer-limit]], but it has a sharp tendency, with [[prime harmonic]]s 2, [[5/1|5]], [[7/1|7]], and [[11/1|11]] all tuned sharp.
+=== Harmonics ===
+{{Harmonics in equal|49|3|1|intervals=integer}}
+{{Harmonics in equal|49|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 49edt (continued)}}
+=== Subsets and supersets ===
+Since 49 factors into primes as 7<sup>2</sup>, 49edt contains [[7edt]] as its only nontrivial subset edt.
 == Intervals ==
 {{Interval table}}
-== Harmonics ==
+== Music ==
-{{Harmonics in equal
+; [[User:Rperlner|Ray Perlner]]
-| steps = 49
+* [https://www.youtube.com/watch?v=2DIZlqLS1O8 ''Fugue in 49EDT for Harpsichord Mintaka<nowiki>[7]</nowiki> LLLsLLs "Macro-Lydian"''] (2025)
-| num = 3
-| denom = 1
+== See also ==
-| intervals = integer
+* [[18edf]] – relative edf
-}}
+* [[31edo]] – relative edo
-{{Harmonics in equal
+* [[72ed5]] – relative ed5
-| steps = 49
+* [[80ed6]] – relative ed6
-| num = 3
+* [[87ed7]] – relative ed7
-| denom = 1
+* [[107ed11]] – relative ed11
-| start = 12
+* [[111ed12]] – relative ed12
-| collapsed = 1
+* [[138ed22]] – relative ed22
-| intervals = integer
+* [[204ed96]] – close to the zeta-optimized tuning for 31edo
-}}
+* [[39cET]]
-[[Category:Edonoi]]
+[[Category:31edo]]