US: Difference between revisions
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Cmloegcmluin (talk | contribs) No edit summary |
Cmloegcmluin (talk | contribs) No edit summary |
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| Line 20: | Line 20: | ||
|- | |- | ||
! frequency (f) | ! frequency (f) | ||
|28/28 | |(28/28) | ||
|28/25 | |28/25 | ||
|28/22 | |28/22 | ||
| Line 28: | Line 28: | ||
|28/10 | |28/10 | ||
|28/7 | |28/7 | ||
| | |28/4 | ||
|- | |- | ||
! pitch (log₂f) | ! pitch (log₂f) | ||
|0 | |(0) | ||
|0.16 | |0.16 | ||
|0.35 | |0.35 | ||
| Line 39: | Line 39: | ||
|1.49 | |1.49 | ||
|2.00 | |2.00 | ||
| | |2.81 | ||
|- | |- | ||
! length (1/f) | ! length (1/f) | ||
|28/28 | |(28/28) | ||
|25/28 | |25/28 | ||
|22/28 | |22/28 | ||
| Line 50: | Line 50: | ||
|10/28 | |10/28 | ||
|7/28 | |7/28 | ||
| | |4/28 | ||
|} | |} | ||
Revision as of 22:23, 22 March 2021
A US, or utonal sequence, is a kind of arithmetic and monotonic tuning.
The full specification of a US is (n-)USp: (n pitches of a) utonal sequence adding by p.
A US is a specific (rational) type of ALS, or arithmetic length sequence. By varying the undertone series step size to some rational number (other than 1) you can produce a US, and 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) | (28/28) | 28/25 | 28/22 | 28/19 | 28/16 | 28/13 | 28/10 | 28/7 | 28/4 |
| pitch (log₂f) | (0) | 0.16 | 0.35 | 0.56 | 0.81 | 1.11 | 1.49 | 2.00 | 2.81 |
| length (1/f) | (28/28) | 25/28 | 22/28 | 19/28 | 16/28 | 13/28 | 10/28 | 7/28 | 4/28 |