157edt: Difference between revisions

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'''[[Edt|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit|10-integer-limit]]. 157edt is notable for it's excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.

== Harmonics ==

== Theory ==

{{Harmonics in equal

157edt is related to [[99edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is [[stretched and compressed tuning|compressed]] by about 0.678 cents. 157edt is [[consistent]] to the [[integer limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 157edt is notable for its excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.

| ~~steps =~~ 157

| ~~num =~~ 3

=== Harmonics ===

| ~~denom =~~ 1

}}

{{Harmonics in equal|157|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 157edt (continued)}}

{{Harmonics in equal

| ~~steps =~~ 157

=== Subsets and supersets ===

| ~~num =~~ 3

157edt is the 37th [[prime equal division|prime edt]]. It does not contain any nontrivial edts as subsets.

| ~~denom~~ = 1

| start = 12

| collapsed = 1

}}

== See also ==

* [[~~99edo~~]]

* [[58edf]] – relative edf

* [[~~58edf~~]]

* [[99edo]] – relative edo

* [[256ed6]] – relative ed6

[[~~Category:Edt]]~~

~~[[Category:Edonoi]]~~

~~[[Category:99edo~~]]

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 {{Infobox ET}}
-'''[[Edt|Division of the third harmonic]] into 157 equal parts''' (157EDT) is related to [[99edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.6781 cents compressed and the step size is about 12.1144 cents. It is consistent to the [[11-odd-limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit|10-integer-limit]]. 157edt is notable for it's excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.
+{{ED intro}}
-== Harmonics ==
+== Theory ==
-{{Harmonics in equal
+edt is related to [[99edo]], but with the 3/1 rather than the [[2/1]] being just. The octave is [[stretched and compressed tuning|compressed]] by about 0.678 cents. 157edt is [[consistent]] to the [[integer limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 157edt is notable for its excellent 5/3, as a convergent to log<sub>3</sub>(5), and can be used effectively both with and without twos.
-| steps = 157
-| num = 3
+=== Harmonics ===
-| denom = 1
+{{Harmonics in equal|157|3|1}}
-}}
+{{Harmonics in equal|157|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 157edt (continued)}}
-{{Harmonics in equal
-| steps = 157
+=== Subsets and supersets ===
-| num = 3
+edt is the 37th [[prime equal division|prime edt]]. It does not contain any nontrivial edts as subsets.
-| denom = 1
-| start = 12
-| collapsed = 1
-}}
 == See also ==
-* [[99edo]]
+* [[58edf]] – relative edf
-* [[58edf]]
+* [[99edo]] – relative edo
+* [[256ed6]] – relative ed6
-[[Category:Edt]]
-[[Category:Edonoi]]
-[[Category:99edo]]