Recursive structure of MOS scales: Difference between revisions
| Line 28: | Line 28: | ||
== Finding a generator == | == Finding a generator == | ||
The recursive structure also allows a recursive algorithm to find the generator: | |||
To find the generator you reduce to a simple pattern you know the generator of, then plug everything back in. | |||
If you do that to 5L 7s you get 5L 2s: LLLsLLs. You know that the generator of 5L 2s is LLLs, so using the above procedure for finding the pattern, the generator of 5L 7s is LsLsLss. If you don't know anything you just reduce all the way to 1L 1s and plug everything back in. | |||
== Tree of MOS patterns == | |||
MOS patterns have parents and children. If 1L 1s is the root of the tree, with any generator between 0\1 (for paucitonic 1L 1s) and 1\2 (for equalized 1L 1s) Every node aL bs has two children, aL (a+b)s and (a+b)L as (these MOS patterns are [[sister]] MOS patterns; they are called such because they have the same parent). The generator range of aL bs splits at the mediant of the endpoints of the parent interval (which is the generator size for [[MOS step ratio spectrum|basic]] aL bs), giving the generator ranges of the two child patterns. | |||
The tree of MOS patterns starts with: | |||
1L 1s | |||
1L 2s 2L 1s | |||
1L 3s 3L 1s 3L 2s 2L 3s | |||
The corresponding generator ranges are: | |||
(0\1, 1\2) | |||
(0\1, 1\3) (1\3, 1\2) | |||
(0\1, 1\4) (1\4, 1\3) (1\3, 2\5) (2\5, 1\2) | |||