ALS

An ALS, or arithmetic length sequence, is a kind of arithmetic and monotonic tuning.

shifted undertone series (± frequency) (equivalent to ALS)

(n-)ALSp: (n pitches of an) arithmetic length sequence adding by p

A US is a specific (rational) type of ALS.

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.

example: (1/⁴√2)-shifted undertone series segment = 9-ALS(1/⁴√2)

quantity	1	2	3	4	5	6	7	8	9
frequency	1.00	1.12	1.28	1.48	1.77	2.19	2.88	4.20	7.73
pitch	0.00	0.17	0.35	0.57	0.82	1.13	1.53	2.07	2.95
length	1.00	0.89	0.78	0.67	0.56	0.46	0.35	0.24	0.13