OS: Difference between revisions
Cmloegcmluin (talk | contribs) →Relationship to other tunings: address Flora's recent concerns about rationality vs. irrationality in this system |
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== Specification == | == Specification == | ||
Its full specification is (n-)OSp: (n pitches of an) otonal sequence adding by rational interval p. The "n" is optional. If unspecified, you describe an open-ended sequence. | Its full specification is (n-)OSp: (n pitches of an) [[otonal]] sequence adding by rational interval p. The "n" is optional. If unspecified, you describe an open-ended sequence. | ||
== Formula == | == Formula == | ||
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=== As shifted overtone series === | === As shifted overtone series === | ||
Both OS and AFS are equivalent to taking an overtone series and adding (or subtracting) a constant amount of frequency (for OS it is rational, for AFS it is probably irrational). By doing this, the step sizes remain equal in frequency, but their relationship in pitch changes. For a detailed explanation of this, see the later section on the [[OS#Derivation|derivation]]. | Both OS and AFS are equivalent to taking an overtone series and adding (or subtracting) a constant amount of frequency (for OS it is rational, for AFS it is probably irrational). By doing this, the step sizes remain equal in frequency, but their relationship in pitch changes. For a detailed explanation of this, see the later section on the [[OS#Derivation|derivation]]. | ||
=== Vs. | Yet another term for this structure is an [[isoharmonic series]]. | ||
=== Vs. OD === | |||
By specifying n, your OS will be equivalent to some [[OD|OD (otonal division)]]. E.g. 8-OS3/4 = 8-OD7, because 8(3/4) = 6, so you will have traveled 6 away from the root of 1, and reached 7. | By specifying n, your OS will be equivalent to some [[OD|OD (otonal division)]]. E.g. 8-OS3/4 = 8-OD7, because 8(3/4) = 6, so you will have traveled 6 away from the root of 1, and reached 7. | ||
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! 8 | ! 8 | ||
|- | |- | ||
! frequency (f) | ! frequency (''f'', ratio) | ||
|(4/4) | |(4/4) | ||
|7/4 | |7/4 | ||
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|28/4 | |28/4 | ||
|- | |- | ||
! pitch ( | ! pitch (log₂''f'', octaves) | ||
|(0) | |(0) | ||
|0.81 | |0.81 | ||
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|2.81 | |2.81 | ||
|- | |- | ||
! length (1/f) | ! length (1/''f'', ratio) | ||
|(1/1) | |(1/1) | ||
|4/7 | |4/7 | ||
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[[Category:Harmonic]] | [[Category:Harmonic]] | ||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||
[[Category:Xenharmonic series]] | |||