Math formulas

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Contents 1 Variable Reference 1.1 Variables 1.2 Constants 1.3 Ordered Sets 1.4 Important Cardinalities 2 Counting Functions 2.1 Beats 3 Time Functions 3.1 Composition Length in Seconds 4 Permutations 4.1 Modal Inversion 5 Reference

Variable Reference

Variables

• b = number of beats
• c = true length of a composition expressed in seconds
• d = number of dimensions
• m = number of measures
• n = number of notes
• p = modal pitch class (i.e. scale degree in relation to the tonic)
• s = number of sections
• t = tempo
• v = duration value
• x = numerator of the time signature
• y = denominator of the time signature

Constants

• B = 120: the true time duration of a note with duration value v=1 in relation to MIDI tempo
• C = 60: the number of seconds in a minute, used for clarity when calculating T from bpm
• D = 480: the number of MIDI clock pulses per quarter note; 480 is standard
• Z = 1/16 or 16th note: the applied duration of a note with duration value v=1, where Z = ((B/D)/4)

Ordered Sets

P = the ordered set of modal pitch classes p composing a sequence:

V = the ordered set of durations v:

Important Cardinalities

= the number of pitch classes in a sequence

= the number of duration values in a duration set

Counting Functions

Beats

Where b represents the number of beats in a note with duration v:

Where b represents the number of beats in a sequence with durations V:

Time Functions

Composition Length in Seconds

Permutations

Modal Inversion

Where x is a modal pitch class, and n is a mode of the tonic scale acting as the focal point for reflection:

Reference

• Summation
• Modulo
• Matrix
• Musical Set Theory
• Combinatorics
• Permutations
• Mathematical Sets
• Exponentiation