MOS scale: Difference between revisions

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# [[Maximum variety]] 2: Ascending by a certain number of steps is equivalent to ascending by one of at most two intervals, and the maximum of two is achieved (i. e. it is not true that ascending by a certain number of steps is always equivalent to ascending by one interval.) For example, in the [[diatonic scale]], ascending by two steps can give you a major third tuned to 400c in 12edo or a minor third tuned to 300c in 12edo, but no other intervals.

# [[Binary]] and has a generator: The scale step comes in exactly two sizes, and the scale is formable from stacking some interval called a generator and octave-reducing.

# Mode of a Christoffel word: The scale can be formed by creating a 2D lattice where the octave is present ~~and~~ taking pitches by travelling vertically and horizontally as close to the line from the origin to the octave as possible without going above it ~~starting from the origin~~, then choosing any pitch within that collection of pitches as the root of the scale.

# Mode of a Christoffel word: The scale can be formed by creating a 2D lattice where the octave is present, then taking pitches by travelling vertically and horizontally from the origin, maintaining as close to the line from the origin to the octave as possible without going above it, then choosing any pitch within that collection of pitches as the root of the scale.

# Binary and [[distributionally even]], which is unhelpful as a definition (since distributional evenness is most conveniently defined in terms of MOS scales) but useful as a generalization.

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 # [[Maximum variety]] 2: Ascending by a certain number of steps is equivalent to ascending by one of at most two intervals, and the maximum of two is achieved (i. e. it is not true that ascending by a certain number of steps is always equivalent to ascending by one interval.) For example, in the [[diatonic scale]], ascending by two steps can give you a major third tuned to 400c in 12edo or a minor third tuned to 300c in 12edo, but no other intervals.
 # [[Binary]] and has a generator: The scale step comes in exactly two sizes, and the scale is formable from stacking some interval called a generator and octave-reducing.
-# Mode of a Christoffel word: The scale can be formed by creating a 2D lattice where the octave is present and taking pitches by travelling vertically and horizontally as close to the line from the origin to the octave as possible without going above it starting from the origin, then choosing any pitch within that collection of pitches as the root of the scale.
+# Mode of a Christoffel word: The scale can be formed by creating a 2D lattice where the octave is present, then taking pitches by travelling vertically and horizontally from the origin, maintaining as close to the line from the origin to the octave as possible without going above it, then choosing any pitch within that collection of pitches as the root of the scale.
 # Binary and [[distributionally even]], which is unhelpful as a definition (since distributional evenness is most conveniently defined in terms of MOS scales) but useful as a generalization.