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 6: | Line 6: | ||
{| class="wikitable" | {| class="wikitable" | ||
|+example: | |+example: 8-US(3/4) | ||
|- | |- | ||
! quantity | ! quantity | ||
! (0) | |||
! 1 | ! 1 | ||
! 2 | ! 2 | ||
| Line 17: | Line 18: | ||
! 7 | ! 7 | ||
! 8 | ! 8 | ||
|- | |- | ||
! frequency | ! frequency (f) | ||
|28/28 | |28/28 | ||
|28/25 | |28/25 | ||
| Line 30: | Line 30: | ||
|(28/4) | |(28/4) | ||
|- | |- | ||
! pitch | ! pitch (log₂f) | ||
|0.00 | |0.00 | ||
|0.16 | |0.16 | ||
| Line 41: | Line 41: | ||
|(2.81) | |(2.81) | ||
|- | |- | ||
! length | ! length (1/f) | ||
|28/28 | |28/28 | ||
|25/28 | |25/28 | ||
Revision as of 22:03, 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) | 0.00 | 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) |