84edt: Difference between revisions

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{{Infobox ET}}{{todo|expand}}
{{Infobox ET}}
'''[[Edt|Division of the third harmonic]] into 84 equal parts''' (84EDT) is practically identical to [[53edo|53 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.
{{ED intro}}


== Theory ==
== Theory ==
This tuning tempers out 99/98 and 121/120 in the 11-limit; and 120/119 in the 17-limit.
84edt is practically identical to [[53edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is about 0.0430 cents stretched. Like 53edo, 84edt is [[consistent]] to the [[integer limit|10-integer-limit]].
 
=== Harmonics ===
{{Harmonics in equal|84|3|1|intervals=integer}}
{{Harmonics in equal|84|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 84edt (continued)}}
 
=== Subsets and supersets ===
84 is a [[largely composite]] number. Since it factors into primes as {{nowrap| 2<sup>2</sup> × 3 × 7 }}, 84edt has subset edts {{EDs|equave=t| 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 }}.


== Intervals ==
== Intervals ==
{{Interval table}}
{{Interval table}}


== Harmonics ==
== See also ==
{{Harmonics in equal
* [[9ed9/8]] – relative ed9/8
| steps = 84
* [[31edf]] – relative edf
| num = 3
* [[53edo]] – relative edo
| denom = 1
* [[137ed6]] – relative ed6
| intervals = integer
}}
{{Harmonics in equal
| steps = 84
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = integer
}}
 
[[Category:Edt]]
[[Category:Edonoi]]