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 ===

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

[[Category:~~Edonoi~~]]

=== Subsets and supersets ===

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

== Intervals ==

== See also ==

* [[18edf]] – relative edf

* [[31edo]] – relative edo

* [[72ed5]] – relative ed5

* [[80ed6]] – relative ed6

* [[87ed7]] – relative ed7

* [[107ed11]] – relative ed11

* [[111ed12]] – relative ed12

* [[138ed22]] – relative ed22

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

* [[39cET]]

[[Category:31edo]]

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 {{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 ===
-{{Harmonics in equal|27|3|1|prec=2|columns=15}}
+{{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)}}
-[[Category:Edonoi]]
+=== 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}}
+== See also ==
+* [[18edf]] – relative edf
+* [[31edo]] – relative edo
+* [[72ed5]] – relative ed5
+* [[80ed6]] – relative ed6
+* [[87ed7]] – relative ed7
+* [[107ed11]] – relative ed11
+* [[111ed12]] – relative ed12
+* [[138ed22]] – relative ed22
+* [[204ed96]] – close to the zeta-optimized tuning for 31edo
+* [[39cET]]
+[[Category:31edo]]