ALS: Difference between revisions
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Cmloegcmluin (talk | contribs) No edit summary |
Cmloegcmluin (talk | contribs) No edit summary |
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{| class="wikitable" | {| class="wikitable" | ||
|+example: (1/⁴√2)-shifted undertone series segment = | |+example: (1/⁴√2)-shifted undertone series segment = 8-ALS(1/⁴√2) | ||
|- | |- | ||
! quantity | ! quantity | ||
! (0) | |||
! 1 | ! 1 | ||
! 2 | ! 2 | ||
| Line 17: | Line 18: | ||
! 7 | ! 7 | ||
! 8 | ! 8 | ||
|- | |- | ||
! frequency | ! frequency (f) | ||
|1.00 | |1.00 | ||
|1.12 | |1.12 | ||
| Line 30: | Line 30: | ||
|7.73 | |7.73 | ||
|- | |- | ||
! pitch | ! pitch (log₂f) | ||
|0.00 | |0.00 | ||
|0.17 | |0.17 | ||
| Line 41: | Line 41: | ||
|2.95 | |2.95 | ||
|- | |- | ||
! length | ! length (1/f) | ||
|1.00 | |1.00 | ||
|0.89 | |0.89 | ||
Revision as of 22:02, 22 March 2021
An ALS, or arithmetic length sequence, is a kind of arithmetic and monotonic tuning.
Is full specification is (n-)ALSp: (n pitches of an) arithmetic length sequence adding by p. It is equivalent to an undertone series shifted ± frequency.
A US, or utonal sequence, is a specific (rational) type of ALS. By varying the undertone series step size to some rational number (other than 1) you can produce a US, and by varying it to an irrational number you can produce an ALS. 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.
| quantity | (0) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| frequency (f) | 1.00 | 1.12 | 1.28 | 1.48 | 1.77 | 2.19 | 2.88 | 4.20 | 7.73 |
| pitch (log₂f) | 0.00 | 0.17 | 0.35 | 0.57 | 0.82 | 1.13 | 1.53 | 2.07 | 2.95 |
| length (1/f) | 1.00 | 0.89 | 0.78 | 0.67 | 0.56 | 0.46 | 0.35 | 0.24 | 0.13 |