Golden sequences and tuning: Difference between revisions
mNo edit summary |
m Move notes to be under the corresponding tables |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
[[File:GoldenMOS.png|thumb|555x555px|A visualization of the golden generators. Each cell is a MOS, containing its step formula on the top and its generator's step formula on the bottom. For visual clarity, they have been organized into eight branches, the colored squares on the right of which contain the tunings of the generators in cents.]] | |||
Golden sequences (the generalization of the Fibonacci sequence to have any two starting values) have a number of interesting properties relating to the tuning of MOS scales, and potentially can be used to determine a way to "naturally" tune a MOS (and thus generate a line of daughter MOSes). | Golden sequences (the generalization of the Fibonacci sequence to have any two starting values) have a number of interesting properties relating to the tuning of MOS scales, and potentially can be used to determine a way to "naturally" tune a MOS (and thus generate a line of daughter MOSes). | ||
| Line 77: | Line 78: | ||
| | | | ||
|} | |} | ||
<references group="note" /> | |||
This means that there is an inherent relationship between MOSes and golden sequences, and moreover that any given golden sequence can be uniquely identified by a pair of descending positive numbers. | This means that there is an inherent relationship between MOSes and golden sequences, and moreover that any given golden sequence can be uniquely identified by a pair of descending positive numbers. | ||
| Line 597: | Line 599: | ||
| 3L 16s | | 3L 16s | ||
|} | |} | ||
<references group="note" /> | |||
Exotemperaments are tuned to the simplest MOS that has a golden generator in the correct range. | Exotemperaments are tuned to the simplest MOS that has a golden generator in the correct range. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 724: | Line 728: | ||
| 1111.8816 | | 1111.8816 | ||
|} | |} | ||
[[Category:Golden ratio]] | [[Category:Golden ratio]] | ||
[[Category:Tuning]] | [[Category:Tuning]] | ||