US: Difference between revisions
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== Specification == | == Specification == | ||
The full specification of a US is (n-)USp: (n pitches of a) utonal sequence adding by p. The n is optional. If not provided, the sequence is open-ended. | The full specification of a US is (n-)USp: (n pitches of a) [[utonal]] sequence adding by p. The n is optional. If not provided, the sequence is open-ended. | ||
== Formula == | == Formula == | ||
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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. UD === | ||
By specifying n, your sequence will be equivalent to some [[UD|UD (utonal division)]]. E.g. 8-US3/4 = 8-UD7, because 8(3/4) = 6, so you will have traveled 6 away from the root of 1, and reached 7. | By specifying n, your sequence will be equivalent to some [[UD|UD (utonal division)]]. E.g. 8-US3/4 = 8-UD7, because 8(3/4) = 6, so you will have traveled 6 away from the root of 1, and reached 7. | ||
=== | === Vs. ALS === | ||
A US is the rational version of [[ALS|ALS, or arithmetic length sequence]]. | A US is the rational version of [[ALS|ALS, or arithmetic length sequence]]. | ||
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! 8 | ! 8 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(28/28) | |(28/28) | ||
|28/25 | |28/25 | ||
| Line 59: | Line 59: | ||
|7/1 | |7/1 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
|0.16 | |0.16 | ||
| Line 70: | Line 70: | ||
|2.81 | |2.81 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(28/28) | |(28/28) | ||
|25/28 | |25/28 | ||
| Line 97: | Line 97: | ||
! 8 | ! 8 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(1/1) | |(1/1) | ||
|4/7 | |4/7 | ||
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|1/7 | |1/7 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
| -0.81 | | -0.81 | ||
| Line 119: | Line 119: | ||
| -2.81 | | -2.81 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(4/4) | |(4/4) | ||
|7/4 | |7/4 | ||
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[[Category:Subharmonic]] | [[Category:Subharmonic]] | ||
[[Category:Subharmonic series]] | [[Category:Subharmonic series]] | ||
[[Category:Xenharmonic series]] | |||