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 Attack-Groups.

 

 

 

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 (a-b).

 

 

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 1-3-5 to counterclockwise movements such as 5-1-3.

 

 

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 Chord-Progression

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.

 

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