Cent values for each pitch class above the tonic (unison excluded). The unison (0¢) is prepended automatically if absent. At least one value is required.
Reference frequency for step 0 (A4). Default: 440 Hz.
Cent values for each pitch class above the tonic (unison excluded). The unison (0¢) is prepended automatically if absent. At least one value is required.
Display name: '12-TET', 'Ptolemaic Just Intonation', 'Werckmeister III'.
Number of steps that constitute one period (usually one octave, 2:1). For non-octave tunings (e.g. Bohlen-Pierce) this is steps per tritave.
Returns the frequency in Hz for a given step offset from A4.
Returns a note name for the given step: the 12-TET name of the note the step stands for
(getStandardStep), in sharps ("C#4", "A4"), or "Step N" when it stands for none.
Converts a 12-TET step pattern (successive steps, e.g. major [2, 2, 1, 2, 2, 2, 1]) to
this tuning. Each note's position above the first is mapped, not each step, so the
pattern keeps its span: in 22-EDO the major scale spans 22 steps (rounding each step
would give 24), and in a 7-note JI scale a semitone does not collapse to 0 steps.
A step comes out 0 only when two notes land on the same step of this tuning.
The 12-TET note a step stands for: the 12-TET step (A4 = 0) nearest in cents, when
getStepFromStandard maps that note back to this step. Names, chord qualities and Roman
numerals in any tuning are read through it.
The 12-TET step, or null when the step stands for no 12-TET note, and always
in a tuning that does not repeat at the octave.
Maps a 12-TET step to this tuning's step nearest in cents; one to one with 12 pitch classes.
The step of target that stands for the same 12-TET note as step does here
(getStandardStep on both sides): C4 is step -9 in 12-TET and step -23 in 31-EDO.
The step in target, or null when step stands for no note or target has
no step for it.
Cent-based tuning - pitch classes defined by exact cent offsets within one octave. Intended for historical temperaments (Werckmeister, Kirnberger, meantone, etc.) and any tuning system defined by cent deviations from equal temperament.
The octave is always treated as exactly 1200 cents (2:1), regardless of the last value in the array. Historical temperaments define pitch classes, not the octave itself.
Example: Werckmeister III (approximate)