ALS: Difference between revisions
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== Relationship to other tunings == | == Relationship to other tunings == | ||
=== | === As shifted undertone series === | ||
By varying the undertone series step size to some | By varying the undertone series step size to some number other than 1, if that number is irrational you can produce an ALS, and if rational you can produce a US (which you could also call an ALS if you really wanted to). In other words, by shifting the undertone series by a constant amount of string length, the step sizes remain equal in terms of length, but their relationship in pitch changes. | ||
=== | === Vs. AFS === | ||
The analogous otonal equivalent of an ALS is an [[AFS|AFS (arithmetic frequency sequence)]]. | The analogous otonal equivalent of an ALS is an [[AFS|AFS (arithmetic frequency sequence)]]. | ||
=== | === Vs. US === | ||
A [[US|US, or utonal sequence]], is the | A [[US|US, or utonal sequence]], is the rational version of an ALS. | ||
=== | === Vs. ELD === | ||
By specifying n, your sequence will be equivalent to some [[ELD|ELD (equal length division)]]; specifically n-ALSp = n-ELD((p-1)/n). | By specifying n, your sequence will be equivalent to one period of some [[ELD|ELD (equal length division)]]; specifically n-ALSp = n-ELD((p-1)/n). | ||
== Examples == | == Examples == | ||
| Line 52: | Line 52: | ||
! 8 | ! 8 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(1) | |(1) | ||
|1.12 | |1.12 | ||
| Line 63: | Line 63: | ||
|7.73 | |7.73 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
|0.17 | |0.17 | ||
| Line 74: | Line 74: | ||
|2.95 | |2.95 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(1) | |(1) | ||
|0.89 | |0.89 | ||
| Line 101: | Line 101: | ||
! 8 | ! 8 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(1) | |(1) | ||
|0.54 | |0.54 | ||
| Line 112: | Line 112: | ||
|0.13 | |0.13 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
| -0.88 | | -0.88 | ||
| Line 123: | Line 123: | ||
| -2.95 | | -2.95 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(1 + 0/⁴√2) | |(1 + 0/⁴√2) | ||
|1 + 1/⁴√2 | |1 + 1/⁴√2 | ||
| Line 138: | Line 138: | ||
[[Category:Subharmonic series]] | [[Category:Subharmonic series]] | ||
[[Category:Utonality]] | [[Category:Utonality]] | ||
[[Category:Xenharmonic series]] | |||