Back to: Glossary
Glossary
“a”
represents the smallest attack 
“T”
character used to represent time, may also be used to represent Tonic. 
“t”
smallest duration unit


A

A
character used for Attack Group 
a ÷ b
a ÷ b character used for Resultant of a and b, fractioned with symmetry around an axis. 
a ÷ b
character used for Resultant of a and b. 
Abscissa
refers to measurements horizontally, left to right stating the time dimension that is used in graphing. 
Amplitude
a measure of intensity (loudness of a sound). 
Attack
is the moment a musical event occurs. Attacks can be grouped into Attack Groups and Attack Groups can be further grouped into Attack Continuity. 
Attack Continuity
Attacks organized in a sequence which are identified in AttackGroups. 
A―> character used for Attack Continuity. 

B  
Balancing
adding a duration to the Resultant. For example using the generators a and b, the added duration is a (ab). 

Binary
The functions of two terms 
Binomial
groups containing two elements 

C  
Circular Permutation
a specific permutation produced by moving the original group one step at a time until it returns to its original form. For example circular permutation of abc would be abc to bca to cab and back to abc. 

Clock Time
measurement of time on a clock usually in seconds. 
Clockwise
replicating the circular motion of the clock hands. Transformation uses this to discern clockwise movements such as 135 to counterclockwise movements such as 513. 
Common Denominator (cd)
the smallest factor of a resultant 
Common Product (cp)
The product obtained by multiplying two or more numbers together. 
Complimentary Factors
when finding the resultants, the number of occurrences a generator makes 
Continuity the same types of elements organized in a sequence. Symbols used in composition are as follows: A―> Attack Continuity Δ―> Density group continuity T―> Durational or rhythmic continuity Ω―> Orchestral group continuity I―> Instrumental attack form continuity V―> Dynamic group continuity ∑―> Harmonic continuity, complete, or sigma continuity 
Contraction
Any rhythm group which moves from longer duration to shorter duration 
Counterclockwise
see Clockwise. 

D  
Distributive Cube
see Distributive Powers. 

Distributive Involution Group
a group of numbers containing a polynomial raised to a power and arranged distributively. See Distributive Powers 
Distributive Powers
mathematically distributing a power across an equation ex. (a+b)^{² }=a ² + ab+ba+b²

Distributive Square
see Distributive Powers. 
Duration
a measurement of time chronologically in Clock Time or in music by the time value of notes measured on a Graph extending along the Abscissa. 
Duration Continuity
a Continuity composed of Durational Groups. 
Duration Group
a group of one or more durations in time. 

E  
Expansion
Any rhythm group which moves from shorter duration to longer duration 



F  
Fractioning
Fragmenting a Duration usually in proportion to some polynomial of the Style Series. 



G  
Geometrical Projections
techniques of variation of musical material specifically Quadrant Rotation, Expansion, Contraction, Geometrical Expansion, Geometrical Contraction, Tonal Expansion, Tonal Contraction. 

Graph
see graphing. 
Graphing
notation of music in graph form where the ordinate (up & down) denoting pitch and the abscissa (left to right) denoting time. 

I  
Interference
The product of the synchronization of two waves which form a third wave. 



M  
Minor Generator
See Generator 

Monomial
A group containing only one element. 
Monomial Periodicity See Periodicity 

O  
Ordinate
the up and down measurement in a graph denotes pitch in music. 



P  
Periodicity
Repetition of notes, sounds, or attacks at regular intervals or periods on a continuous b axis. Groups attacks that continue in identical duration are called uniform periodicity which can include groups of more than one term. Monomial periodicity are attacks that involve only one term such as groupings of quarter notes, eighth notes, etc. 

Permutation
techniques of variation by rearranging variables in a sequence. General, circular (clockwise & counterclockwise) techniques are used. 
Piano Roll View
the graph view in most modern day software music sequencer 
pla
places in the attack group 
pli
places in the instrumental group 
Polynomial
groups containing more than one element. 
Power
the product of multiplying a number by itself a specific number of times. A zero power of any number is equal to 1. The first power of a number is the number. A negative power is the power of a number divided into the integer. Schillinger most always used powers as Distributive Powers. 
Power Series
a series in which elements are successive powers on constant numbers 
PRV PRV=Piano Roll View 

R


r
character denoting Resultant 

Resultant
A new pattern formed by the combination of a major generator and a minor generator which are synchronized. 
Resultant of Acceleration
a form of resultant where an acceleration series is synchronized with itself backwards. 
Rhythm
the arrangement in time of durations of elements in music. In the Schillinger System rhythm is the basis to all his theories. Schillinger refers to the division of time within each measure of small groups of measures fractional rhythm but also the organization of the measures themselves are called factorial rhythm. The Style Series breaks down the determinant and arranges them into the rhythm of the piece. His theory is then used 1.) Instrumental Rhythm 2.) Intonational Rhythm 3.) Harmonic Rhythm. 
Rhythm of ChordProgression
the rhythmic organization of a succession of chords. 

S  
Split Units
In rhythm a technique that divides a single duration by some divisor 

Style Series
the source of all rhythmic styles 
Summation Series
any number series where the third and subsequent numbers are the sum of the previous 2 numbers. 
Symmetry
a characteristic of any pattern or sequence when forward and reveres are identical. 
Synchronization
the process of creating 2 or more elements of the same duration that fits together. 

T


t
smallest duration unit 

T―>
character used to represent Duration Continuity or sequent group of durations. 
Terminology
In order for us to analyze and compose music it is necessary to reduce the rhythms to the lowest common denominator or fastest duration.
Terminology
T = one measure or bar. t = fastest duration. ex. t=1=1/8th note. 