US
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 |