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 8: | Line 8: | ||
{| class="wikitable" | {| class="wikitable" | ||
|+example: | |+example: 9-US(3/4) | ||
|- | |- | ||
! quantity | ! quantity | ||
| Line 22: | Line 22: | ||
|- | |- | ||
! frequency | ! frequency | ||
| | |1/1 | ||
| | |28/25 | ||
| | |14/11 | ||
| | |28/19 | ||
| | |7/4 | ||
| | |28/13 | ||
| | |14/5 | ||
| | |4/1 | ||
| | |7/1 | ||
|- | |- | ||
! pitch | ! pitch | ||
| | |0.00 | ||
| | |0.16 | ||
| | |0.35 | ||
| | |0.56 | ||
| | |0.81 | ||
| | |1.11 | ||
| | |1.49 | ||
| | |2.00 | ||
| | |2.81 | ||
|- | |- | ||
! length | ! length | ||
| | |1/1 | ||
| | |25/28 | ||
| | |11/14 | ||
| | |19/28 | ||
| | |4/7 | ||
| | |13/28 | ||
| | |5/14 | ||
| | |1/4 | ||
| | |1/7 | ||
|} | |} | ||
Revision as of 01:51, 22 March 2021
A US, or utonal sequence, is a kind of arithmetic and monotonic tuning.
A US is a specific (rational) type of ALS.
(n-)USp: (n pitches of a) utonal sequence adding by p
The same principles that were just described for frequency are also possible for length: by varying the undertone series step size to some rational number you can produce a utonal sequence (US), and varying it to an irrational number you can produce an arithmetic length sequence (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 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| frequency | 1/1 | 28/25 | 14/11 | 28/19 | 7/4 | 28/13 | 14/5 | 4/1 | 7/1 |
| pitch | 0.00 | 0.16 | 0.35 | 0.56 | 0.81 | 1.11 | 1.49 | 2.00 | 2.81 |
| length | 1/1 | 25/28 | 11/14 | 19/28 | 4/7 | 13/28 | 5/14 | 1/4 | 1/7 |