Golden sequences and tuning: Difference between revisions

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[[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).

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| Magic

| 5/4

| 380.82{{c}}<ref group="note">Also has another tuning of 377.6 cents for 3L 13s. This results in a fifth almost as flat as in 7edo, but is a simpler scale of 16 notes rather than 19.</ref>

| 380.82{{c}}<ref group="note">Also has another tuning of 377.6 cents for 3L 13s (interpretable as [[muggles]] rather than septimal magic). This results in a fifth almost as flat as in 7edo, but is a simpler scale of 16 notes rather than 19.</ref>

| 3L 16s

|}

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+[[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).
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 | Magic
 | 5/4
-| 380.82{{c}}<ref group="note">Also has another tuning of 377.6 cents for 3L&nbsp;13s. This results in a fifth almost as flat as in 7edo, but is a simpler scale of 16 notes rather than 19.</ref>
+| 380.82{{c}}<ref group="note">Also has another tuning of 377.6 cents for 3L&nbsp;13s (interpretable as [[muggles]] rather than septimal magic). This results in a fifth almost as flat as in 7edo, but is a simpler scale of 16 notes rather than 19.</ref>
 | 3L&nbsp;16s
 |}