BudjarnLambeth/Ed257/128: Difference between revisions
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An '''equal division of reduced harmonic 257''' ('''ed257/128''') is an [[equal-step tuning]] in which the [[4/1|4ve]]-reduced 257th harmonic ([[257/128]]) is [[Just intonation|justly tuned]] and is divided in a given number of equal steps. 257/128 is very close to the [[octave]], 2/1, but it is slightly sharper. This makes it suitable as an alternative to edos whose consonances are too flat, such as [[7edo]]. | |||
Ed257/128s really only make sense for that purpose with 65 or fewer tones per [[pseudo-octave]]. With more tones than that, the relative error on 2/1 becomes unacceptably high and it makes more sense to switch to a different tuning like a [[zpi]] or ed513/256. | |||
Ed257/128s are the complementary opposite of [[ed255/128]]s. | |||
== 7ed257/128 == | == 7ed257/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|7|257|128|intervals= | {{Harmonics in equal|7|257|128|intervals=prime}} | ||
7edo, [[16ed5]], [[22ed9]] for comparison: | 7edo, [[16ed5]], [[22ed9]] for comparison: | ||
{{Harmonics in equal|7|intervals= | {{Harmonics in equal|7|intervals=prime|collapsed=1}} | ||
{{Harmonics in equal|16|5|1|intervals= | {{Harmonics in equal|16|5|1|intervals=prime|collapsed=1}} | ||
{{Harmonics in equal|22|9|1|intervals= | {{Harmonics in equal|22|9|1|intervals=prime|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 24: | Line 29: | ||
== 9ed257/128 == | == 9ed257/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|9|257|128|intervals= | {{Harmonics in equal|9|257|128|intervals=prime}} | ||
[[9edo]] for comparison: | [[9edo]] for comparison: | ||
{{Harmonics in equal|9|intervals= | {{Harmonics in equal|9|intervals=prime|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 44: | Line 49: | ||
== 14ed257/128 == | == 14ed257/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|14|257|128|intervals= | {{Harmonics in equal|14|257|128|intervals=prime}} | ||
[[14edo]] for comparison: | [[14edo]] for comparison: | ||
{{Harmonics in equal|14|intervals= | {{Harmonics in equal|14|intervals=prime|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 69: | Line 74: | ||
== 16ed257/128 == | == 16ed257/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|16|257|128|intervals= | {{Harmonics in equal|16|257|128|intervals=prime}} | ||
[[16edo]] for comparison: | [[16edo]] for comparison: | ||
{{Harmonics in equal|16|intervals= | {{Harmonics in equal|16|intervals=prime|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 96: | Line 101: | ||
== 19ed257/128 == | == 19ed257/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|19|257|128|intervals= | {{Harmonics in equal|19|257|128|intervals=prime}} | ||
[[19edo]] for comparison: | [[19edo]] for comparison: | ||
{{Harmonics in equal|19|intervals= | {{Harmonics in equal|19|intervals=prime|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 125: | Line 130: | ||
== 33ed257/128 == | == 33ed257/128 == | ||
This is an excellent tuning for [[Meantone family#Dreamtone|dreamtone]] temperament, much better than standard 33edo. It is almost exactly the TE tuning. | |||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|33|257|128|intervals= | {{Harmonics in equal|33|257|128|intervals=prime}} | ||
[[33edo]] for comparison: | [[33edo]] for comparison: | ||
{{Harmonics in equal|33|intervals= | {{Harmonics in equal|33|intervals=prime|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 167: | Line 174: | ||
* 1206.749 | * 1206.749 | ||
== 38ed257/128 == | == 38ed257/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|38|257|128|intervals= | {{Harmonics in equal|38|257|128|intervals=prime}} | ||
[[38edo]] for comparison: | [[38edo]] for comparison: | ||
{{Harmonics in equal|38|intervals= | {{Harmonics in equal|38|intervals=prime|collapsed=1}} | ||
== 42ed257/128 == | |||
''See [[42ed257/128]].'' | |||
== 45ed257/128 == | == 45ed257/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|45|257|128|intervals= | {{Harmonics in equal|45|257|128|intervals=prime}} | ||
[[45edo]] for comparison: | [[45edo]] for comparison: | ||
{{Harmonics in equal|45|intervals= | {{Harmonics in equal|45|intervals=prime|collapsed=1}} | ||
== 54ed257/128 == | |||
=== Harmonics === | |||
{{Harmonics in equal|54|257|128|intervals=prime}} | |||
[[45edo]] for comparison: | |||
{{Harmonics in equal|54|intervals=prime|collapsed=1}} | |||
== 59ed257/128 == | |||
=== Harmonics === | |||
{{Harmonics in equal|59|257|128|intervals=prime}} | |||
[[59edo]] for comparison: | |||
{{Harmonics in equal|59|intervals=prime|collapsed=1}} | |||
== 64ed257/128 == | |||
=== Harmonics === | |||
{{Harmonics in equal|64|257|128|intervals=prime}} | |||
[[64edo]] for comparison: | |||
{{Harmonics in equal|64|intervals=prime|collapsed=1}} | |||
== Related concepts == | == Related concepts == | ||
* [[Substitute harmonic]] | * [[Substitute harmonic]] | ||
* [[Equal-step tuning]] | * [[Equal-step tuning]] | ||
[[Category:Edonoi]][[Category:7edo]][[Category:7-tone scales]] | [[Category:Edonoi]][[Category:7edo]][[Category:7-tone scales]] | ||