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]]. | 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 == | ||
| Line 167: | Line 173: | ||
* 1170.181 | * 1170.181 | ||
* 1206.749 | * 1206.749 | ||
== 38ed257/128 == | == 38ed257/128 == | ||
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[[38edo]] for comparison: | [[38edo]] for comparison: | ||
{{Harmonics in equal|38|intervals=prime|collapsed=1}} | {{Harmonics in equal|38|intervals=prime|collapsed=1}} | ||
== 42ed257/128 == | == 42ed257/128 == | ||
''See [[42ed257/128]].'' | ''See [[42ed257/128]].'' | ||
== 45ed257/128 == | == 45ed257/128 == | ||
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[[45edo]] for comparison: | [[45edo]] for comparison: | ||
{{Harmonics in equal|45|intervals=prime|collapsed=1}} | {{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]] | ||