US
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 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | (9) |
|---|---|---|---|---|---|---|---|---|---|
| frequency | 28/28 | 28/25 | 28/22 | 28/19 | 28/16 | 28/13 | 28/10 | 28/7 | (28/4) |
| pitch | 0.00 | 0.16 | 0.35 | 0.56 | 0.81 | 1.11 | 1.49 | 2.00 | (2.81) |
| length | 28/28 | 25/28 | 22/28 | 19/28 | 16/28 | 13/28 | 10/28 | 7/28 | (4/28) |