Transformations¶

Introduction¶

Transformations, also known as viewpoints [Conklin2001] or abstractions, are one of the core concepts in the MeloSpyLib. Starting from the basic representation of melodies, which consists of sequences of (onset, duration, pitch)-triplets, transformation are mappings either to sequences or to objects of fixed dimension (scalars, vectors, matrices). The first kind produces sequences of variable length, depending on the length of the original melody. For example, the duration class transformation ‘forgets’ first about pitch and onsets and classifies then each duration into one of five classes. The second kind of transformation produces object of fixed dimensions, e.g., a scalar (single value) or a vector (multiple values). For instance, the number of tones in a melody would be a scalar feature, whereas the relative frequency of tonal pitch classes can be seen as a fixed 12-dim vector. The second kind of transformations are usually called ‘feature’ in the literature. However, the distinction between features and transformatons cannot and should not be made fully rigid, mostly for practical reasons. Some of the transformations provided by MeloSpyLib are actually features in the above mentioned sense, on the other hand, some of the pre-defined features in the Feature Definition Files are more accurately classified as transformations (of the first kind). A more practical definition used in this documentation is, that those transformations (of first or second kind) provided by the MeloSpyLib on the library level are called transformations, whereas features are those defined in Feature Definition Files. Transformations form always the first element (the source) of a feature.

A large share of the transformations are based on a single dimension of the original core representations, e.g., they use only the pitch or the onset dimension. Other transformations are based not only on the core representation of a melody but rely on the provided metadata, hence, they are not fully general. For example, chordal pitch class requires for each tone a chord context. For the jazz solo data in the Weimar Jazz Database all annotations are guaranteed to be present. For the EsAC database only phrase and metrical annotations as well as metadata are provided, whereas chord, chorus, form, and beat annotations are missing.

In this document, transformations that are entirely based on annotations are called pseudo-transformations, whereas transformation of fixed length will be called degenerated.

Available transformations¶

The first column in the table holds the name of the transformations. The second column indicates the length of the transformation. $N$ always means the length of the original melody. ‘Var’ means that the length of result sequence is a non-trivial function of the length of the original sequences. Concrete integers mean here degenerate transformation, which result in a fixed scalar, vector or matrix of the indicated length. The third column gives the type of the elements of the resulting sequences, e.g., Real, Integer, Char, String, etc. along with possible constraints to the value set. The fourth colum gives the abbreviation of the transformation that has to be used in a feature defintions file. The fifth column finally indicates the necessary requirements, i.e., annotations.

Next part: Metrical System.

Transformation	Length	Type	Abbreviation(s)	Optional Parameter	Requirements
MIDI Pitch	$N$	Real (Integer)	`pitch`	–	None
Absolute Pitch Class	$N$	Integer [0:11]	`pc`, `pitch-class`	–	None
Chordal Pitch Class	$N$	Integer [0:11]	`cpc`, `chordal-pitch-class`	`KeepNC`	Chord annotation
Chordal Diatonic Pitch Class	$N$	Char (`1,2,3,4,5,6,7,<,>,T,L`)	`cdpc`, `chord-dpc`, `chordal-dpc`, `chordal-diatonic-pitch-class`	`KeepNC`	Chord annotation
Extended Chordal Diatonic Pitch Class	$N$	Char (`1, 2, 3, 4, 5, 6, 7, <, >, T, L, %, \`)	`cdpcx`, `chord-dpc-x`, `chordal-dpc-ext`, `chordal-diatonic-pitch-class-ext`	`KeepNC`	Chord annotation
Tonal Pitch Class	$N$	Integer [0:11]	`tpc`, `tonal-pitch-class`	–	Key annotations
Tonal Diatonic Pitch Class	$N$	Char (`1,2,3,4,5,6,7,<,>,T,L`)	`tdpc`, `tonal-dpc`, `tonal-diatonic-pitch-class`	–	Key annotation
Semitone Intervals	$N-1$	Integer	`interval`	–	None
Fuzzy Intervals (Refined Contour)	$N-1$	Integer [-4:4]	`fuzzyinterval`	–	None
Parsons Code (Contour)	$N-1$	Integer [-1:+1]	`parsons`	–	None
Huron Contour	Var	Integer [0:8] or labels `hor`, `hor-desc`, `hor-asc` etc.	`huroncontour`	`code`, `redcode`	None
Beat Track	Var	Real	`beats`, `beattrack`	–	Beat annotation
Chords	Var	String (Chord label)	`ch`, `chords`	`types`	Chord annotation
Chord Events	$N$	String (Chord label)	`che`, `chord-events`	–	Chord annotation
Phrase IDs	$N$	Integer	`phrid`, `phrase-ids`, `phraseids`	–	Phrase annotation
Phrase Boundary Markers	$N$	Integer [0, 1]	`phrbd`, `phrase-boundaries`, `phrasebounds`	–	Phrase annotation
Chorus IDs	$N$	Integer	`chorusid`, `chorus-ids`, `chorusids`	–	Chorus annotation
Metadata	1	String	`meta`	–	Metadata
Onsets	$N$	Real	`onsets`	–	None
Inter-onset Intervals	$N-1$	Real	`ioi`	–	None
Duration	$N$	Real	`duration`	–	None
Duration Tatum	$N$	Integer	`durtatum`	–	Metrical annotation
Duration Classes	$N$	Integer [-2:2]	`durclass`	`abs`, `rel`	None
Inter-onset Interval Classes	$N-1$	Integer [-2:2]	`ioiclass`	`abs`, `rel`	None
Total Duration	$1$	Float	`total-duration`	–	None
Total Metrical Duration	$1$	Float	`total-metrical-duration`	–	Metrical annotation
Metrical Position	$N$	String (Metrical position notation)	`meter`	–	Metrical annotation
Metrical Position Decimal	$N$	Real	`meter-decimal`	–	Metrical annotation
Metrical Circle Map	$N$	Integer	`mcm`	`<N>`	Metrical annotation
Bar Numbers	$N$	Integer	`bars`	–	Metrical annotation
Beat Indices	$N$	Integer	`beats`	–	Metrical annotation
Tatum Indices	$N$	Integer	`tatums`	–	Metrical annotation
Metrical Weights	$N$	Integer [0:2]	`metricalweights` , `weights`, `mw`	–	Metrical annotation
Swing Ratio	Var	Real [0,1]	`swing-ratios`	–	Metrical annotation
Accents	N	Integer 0,1/Real [0,1]	`accent<-TYPE>`	`<TYPE>`	Var

MIDI Pitch¶

Abbreviation: pitch
Length: $N$
Integer (Real) [0:127]
Optional Parameter: –
Requires: –

Raw MIDI Pitches of a medody (integers). All rhythm information is discarded.

Absolute Pitch Class¶

Abbreviations: pc, pitch-class
Length: $N$
Type: Integer [0:11]
Optional Parameter: –
Requires: –

MIDI pitch disregrading octave position (mod 12) with C = 0, C# = 1, D=2, …, B=11

Chordal Pitch Class¶

Abbreviation: cpc, chord-pc, chordal-pc, chordal-pitch-class
Length: $N$
Type: Integer [-1:11]
Optional Parameter: keepNC
Requires: Chord annotation

As Absolute Pitch Class, but with the root of the current chord context mapped to 0. Events without chord annotation will be left out, unless the optional parameter keepNC is set, in which case they will be represented by the value -1.

Chordal Diatonic Pitch Class¶

Abbreviation: cdpc, chordal-diatonic-pitch-class
Length: $N$
Type: Char (1,2,3,4,5,6,7,<,>,T,L)
Optional Parameter: keepNC
Requires: Chord annotation

As Chordal Pitch Class, but with a diatonic naming scheme:

Symbol	Chord tone
`1`	root
`2`	major/minor second
`3`	third:
`B`	minor third over major chord
`>`	major third over minor chord
`4`	fourth
`5`	fifth
`6`	major/minor sixth
`T`	tritone
`7`	seventh
`<`	minor seventh over major-seventh chord
`L`	major seventh over minor-seventh chord

Events without chord annotation will be left out, unless the optional parameter keepNC is set, in which case they will be represented by its raw MIDI pitch.

Extended Chordal Diatonic Pitch Class¶

Abbreviation: cdpcx, chord-dpc-x, chordal-dpc-ext, chordal-diatonic-pitch-class-ext
Length: $N$
Type: Char (1,\,2,3,B,>,4,5,%,6,T,7,<,L)
Optional Parameter: keepNC
Requires: Chord annotation

As Chordal Diatonic Pitch Class, but with two more classes:

Symbol	Chord tone
`1`	root
`\`	minor second
`2`	major second
`3`	third:
`B`	minor third over major chord
`>`	major third over minor chord
`4`	fourth
`5`	fifth
`%`	minor sixth
`6`	major sixth
`T`	tritone
`7`	seventh
`<`	minor seventh over maj-seventh chord
`L`	major seventh over minor-seventh chord

Events without chord annotation will be left out, unless the optional parameter keepNC is set, in which case they will be represented by its raw MIDI pitch.

Tonal Pitch Class¶

Abbreviation: tpc, tonal-pc, tonal-pitch-class
Length: $N$
Type: Integer [0:11]
Optional Parameter: –
Requires: Key annotation

As Chordal Pitch Class, but with the local key as reference instead of local chords.

Tonal Diatonic Pitch Class¶

Abbreviation: tdpc, tonal-dpc, tonal-diatonic-pitch-class
Length: $N$
Type: Integer [0:11]
Optional Parameter: –
Requires: Key annotation

As Chordal Diatonic Pitch Class, but with the local key as reference instead of local chords.

Semitone Intervals¶

Abbreviation: interval
Length: $N-1$
Type: Integer
Optional Parameter: –
Requires: –

Semitone intervals between subsequent pitches. All rhythm information is discarded.

Fuzzy Intervals (Refined Contour)¶

Abbreviation: fuzzy-interval
Length: $N-1$
Type: Integer [-4:+4]
Optional Parameter: –
Requires: –

Fuzzy intervals between subsequent pitches. All rhythm information is discarded. Fuzzy intervals (or refined) contour values come from a simple 5-fold classification of interval sizes:

Interval class name	Class borders	Numerical representation
big jump down	<-7	-4
jump down	[-7:-5]	-3
leap down	[-4:-3]	-2
step down	[-2:-1]	-1
repetition/unisone	0	0
step up	[1:2]	1
leap up	[3:4]	+2
jump up	[+5:+7]	+3
big jump up	>+7	+4

Parsons Code (Contour)¶

Abbreviation: parsons
Length: $N-1$
Type: Integer [-1:+1]
Optional Parameter: –
Requires: –

Parson’s code (often also called contour) codes the interval direction in three distinct classes:

Interval class name	Class borders	Numerical representation
down (D)	<0	-1
repetition/unisone (R)	0	0
up (U)	>0	1

Huron Contour¶

Abbreviation: huroncontour
Length: 1
Type: Integer [0:8] or labels
Optional Parameter: code, redcode
Requires: –

Huron contour is defined for sequences of pitch values and is determined based on three reference pitches: The first, the last and the average value of the pitches in between. The first and the average and the average and the last pitch are compared for magnitude. This yields nine possible combinations of the two magnitude relations with three possibilities each (greater (+), lesser (-) or equal (0)). These are coded to nine different contour values, as seen in Tab. Huron Contour Codes. (The numerical values are calculated using the formula $3c_1 + c_2$ , where $c_i$ are the comparison values coded as - -> -1, 0 -> 0, + ->1.) Default output are numerical values, if the optional parameter code is set, labels will be emitted. There is also a reduced version of the code by mapping the mixed horizontal classes to their ascending/descending part with can be accessed with the optional parameter redcode.

Huron Contour Codes¶
Relation	Full name	Contour code	Reduced code	Numerical value
(0,0)	Horizontal	`hor`	`hor`	0
(0,+)	Horizontal-ascending	`hor-asc`	`asc`	1
(0,-)	Horizontal-descending	`hor-desc`	`desc`	-1
(+,0)	Ascending-horizontal	`asc-hor`	`asc`	3
(-,0)	Descending-horizontal	`desc-hor`	`desc`	-3
(+,+)	Ascending	`asc`	`asc`	4
(-,-)	Descending	`desc`	`desc`	-4
(+,-)	Convex	`convex`	`convex`	2
(-,+)	Concave	`concave`	`concave`	-2

Beat Track¶

Abbreviation: beats, beattrack
Length: Var
Type: Real
Optional Parameter: –
Requires: Beat annotation

This transformation is a pseudo-transformation, not generated from the melody events themselves but from an annotated beat track - if available.

Chords¶

Abbreviation: ch, chords
Length: Var
Type: String (Chord labels (s. Chords)
Optional Parameter: type
Requires: Chord annotation

This transformation is a pseudo-transformation, not generated from the melody events themselves but from annotated chord symbols. This is the raw list of chords with no obvious relation to the events. If the optional parameter type is set, only the basic chord type will be used.

Chord Events¶

Abbreviation: che, chord-events
Length: $N$
Type: String (Chord labels)
Optional Parameter: –
Requires: Chord annotation

This transformation is a pseudo-transformation, not generated from the melody events themselves but from annotated chord symbols. This a list of chords of the same length as the melody, where the chord context of each event is returned.

Phrase IDs¶

Abbreviation: phrid, phrase-ids, phraseids
Length: $N$
Type: Integer
Optional Parameter: –
Requires: Phrase annotation

This transformation is a pseudo-transformation, not generated from the melody events themselves but from annotated phrase boundaries. Phrases are enumerated starting with index 1. For each event the ID of the phrase containing the event is returned.

Phrase Boundary Markers¶

Abbreviation: phrbd, phrase-boundaries, phrasebounds
Length: $N$
Type: Integer [0, 1] (Boolean)
Optional Parameter: –
Requires: Phrase annotation

This transformation is a pseudo-transformation, not generated from the melody events themselves but from annotated phrase boundaries. Each element is mapped to 1, if it starts a phrase (1) or to 0 if its an inner or end element of a phrase.

Chorus IDs¶

Abbreviation: chorusid, chorus-ids, chorusids
Length: $N$
Type: Integer
Optional Parameter: –
Requires: Chorus annotation

This transformation is a pseudo-transformation, not generated from the melody events themselves but from annotated choruses. Choruses are enumerated starting with index 1. For each event the ID of the chorus containing the event is returned.

Metadata¶

Abbreviation: meta.<FIELD>
Length: 1
Type: String
Optional Parameter: –
Requires: Metadata

If metadata is present in the SQL database, you access the field names by using the above syntax meta.<FIELD>, e.g., meta.title will return the title as stored in the database.

Onsets¶

Abbreviation: onsets
Length: $N$
Type: Real
Optional Parameter: –
Requires: –

This transformation belongs to the projection, i.e. it is the raw list of onsets of the melody events.

Inter-onset Intervals¶

Abbreviation: ioi
Length: $N-1$
Type: Real
Optional Parameter: –
Requires: –

This transformation returns interonset-intervals, i.e. the differences of consecutive onsets of the melody events.

Duration¶

Abbreviation: duration
Length: $N$
Type: Real
Optional Parameter: –
Requires: –

This transformation belongs to the projections, i.e., it is the raw list of durations of the melody events.

Duration Tatum¶

Abbreviation: durtatum
Length: $N$
Type: Integer
Optional Parameter: –
Requires: Metical annotation

Duration Classes¶

Abbreviation: durclass
Length: $N$
Type: Integer [-2:+2]
Optional parameter: abs or rel
Requires: –

Durations are mapped to duration classes by comparing them to a reference duration. There are two possibilities, specified by an optimal paramter: relative (rel) and absolute (abs) mode. In relative mode the reference duration is the beat duration of the surrounding beat, in absolute mode the value of 500ms is used, which correspond to the beat duration in a tempo of 120 bpm. The class definitions are displayed in Duration/IOI classes, expressed as percentage of the reference duration.

Duration/IOI classes¶
Class name	Class borders	Numerical value
very short	<35%	-2
short	35%-70%	-1
medium	70%-140%	0
long	140%-280%	1
very long	>280%	2

Inter-onset Interval Classes¶

Abbreviation: ioiclass
Length: $N-1$
Type: Integer [-2:+2]
Optional parameter: abs or rel
Requires: –

Inter-onset interval are mapped to IOI classes by comparing them to a reference duration. There are two possibilities, specified by an optimal parameter: relative (rel) and absolute (abs) mode. In relative mode the reference duration is the beat duration of the surrounding beat, in absolute mode the value of 500ms is used, which correspond to the beat duration in a tempo of 120 bpm. The class definitions are displayed in Duration/IOI classes.

Total Duration¶

Abbreviation: total-duration
Length: $1$
Type: Float
Optional parameter: –
Requires: –

This degenerated transformation retrieves the duration of a melody (in seconds).

Total Metrical Duration¶

Abbreviation: total-metrical-duration
Length: $1$
Type: Float
Optional parameter: –
Requires: Metrical annotation

This degenerated transformation retrieves the duration of a melody (in fractional metrical units, where each numerical unit represents one bar).

Metrical Position¶

Abbreviation: meter
Length: $N$
Type: String (Metrical position notation)
Optional parameter: –
Requires: Metrical annotation

Bar Numbers¶

Abbreviation: bars
Length: $N$
Type: Integer
Optional parameter: –
Requires: Metrical annotation

Beat Indices¶

Abbreviation: beats
Length: $N$
Type: Integer
Optional parameter: –
Requires: Metrical annotation

Tatum Indices¶

Abbreviation: tatum
Length: $N$
Type: Integer
Optional parameter: –
Requires: Metrical annotation

Metrical Position Decimal¶

Abbreviation: meter-decimal
Length: $N$
Type: Integer
Optional parameter: –
Requires: Metrical annotation

Metrical Inter-onset Intervals Decimal¶

Abbreviation: meter-ioi-decimal
Length: $N-1$
Type: Integer
Optional parameter: –
Requires: Metrical annotation

Calculates inter-onset intervals in decimal metrical units, where each numerical unit corresponds to one bar.

Metrical Circle Map¶

Abbreviation: mcm
Length: $N$
Type: Integer
Optional parameter: <N>
Requires: Metrical annotation

The optional parameter N defines how many segments in the circle representing a metrical bar will be used, defaults to N=48.

Metrical Weights¶

Abbreviation: metricalweights , weights, mw
Length: $N$
Type: Integer [0:2]
Optional parameter: –
Requires: Metrical annotation

Gives 2 for primary and secondary accents in the bar, 1 for other beat position and 0 for every subbeat position.

Swing Ratio¶

Abbreviation: swing-ratios
Length: Var
Type: Real
Optional parameter: –
Requires: Metrical annotation

Accents¶

Abbreviation: accent-<TYPE> or accent with optional parameter
Length: N
Type: Integer, Real [0,1]
Optional parameter: <TYPE>
Requires: Variable

Accents are mostly equivalent to boolean structural markers, which are True (1) if a structural condition is met, and False (0) if not. Sole exception is accent-thom, which is a probability value between 0 and 1. The labels in the following list need to be substituted for <TYPE> in accent-<TYPE>, e.g., accent-longpr or accent-long2pr etc.

Label	Type	Length	Condition	Requirement
`longpr`	Integer [0:1]	N	True for tones with longer IOI than the previous tone.
`long2pr`	Integer [0:1]	N	True for tones with an at least twice longer IOI than the previous tone.
`longmod`	Integer [0:1]	N	True for tones with a longer IOI than mode IOI of all tones.
`long2mod`	Integer [0:1]	N	True for tones with an at least twice longer IOI than mode IOI of all tones.
`longmod_win5`	Integer [0:1]	N	True for tones with IOI that is at least 41% longer than mean of the past 5 IOIs.
`long2mod_win5`	Integer [0:1]	N	True for tones with IOI that is at least twice as long than mean of the past 5 IOIs.
`longpr_abs`	Integer [0:1]	N	True for tones with an higher (longer) IOI class than the previous one.
`long2pr_abs`	Integer [0:1]	N	True for tones with an IOI class at least two classes away from that of the previous one.
`longmod_abs`	Integer [0:1]	N	True for tones with a higher/longer IOI class than the most frequent (mode) IOI class.
`long2mod_abs`	Integer [0:1]	N	True for tones with an IOI class at least two classes away from the most frequent (mode) IOI class.
`longmod_win5_abs`	Integer [0:1]	N	True for tones with an IOI class longer than mode IOI class of the past 5 IOIs.
`long2mod_win5_abs`	Integer [0:1]	N	True for tones with an IOI class at least two classes longer than the mode IOI class of the past 5 IOIs.
`longpr_rel`	Integer [0:1]	N	True for tones with an higher (longer) IOI class than the previous one.
`long2pr_rel`	Integer [0:1]	N	True for tones with an IOI class at least two classes away from that of the previous one.
`longmod_rel`	Integer [0:1]	N	True for tones with a higher/longer IOI class than the most frequent (mode) IOI class.
`long2mod_rel`	Integer [0:1]	N	True for tones with an IOI class at least two classes away from the most frequent (mode) IOI class.
`longmod_win5_rel`	Integer [0:1]	N	True for tones with an IOI class longer than mode IOI class of the past 5 IOIs.
`long2mod_win5_rel`	Integer [0:1]	N	True for tones with an IOI class at least two classes longer than the mode IOI class of the past 5 IOIs.
`triad`	Integer [0:1]	Var	True for chord tones (excluding upper structures).	Chord annotation
`inchord`	Integer [0:1]	Var	True for chord tones (including upper structures).	Chord annotation
`outchord`	Integer [0:1]	Var	True for non-chord tones.	Chord annotation
`jumpaft3`	Integer [0:1]	N	True for tones following a large pitch jump of at least 3 semi-tones (either direction).
`jumpaft4`	Integer [0:1]	N	True for tones following a large pitch jump of at least 4 semi-tones (either direction).
`jumpaft5`	Integer [0:1]	N	True for tones following a large pitch jump of at least 5 semi-tones (either direction).
`jumpbef3`	Integer [0:1]	N	True for tones before a large pitch jump of at least 3 semi-tones (either direction).
`jumpbef4`	Integer [0:1]	N	True for tones before a large pitch jump of at least 4 semi-tones (either direction).
`jumpbef5`	Integer [0:1]	N	True for tones before a large pitch jump of at least 5 semi-tones (either direction).
`jumpbea3`	Integer [0:1]	N	True for tones before and after a large pitch jump of at least 3 semi-tones (either direction).
`jumpbea4`	Integer [0:1]	N	True for tones before and after a large pitch jump of at least 4 semi-tones (either direction).
`jumpbea5`	Integer [0:1]	N	True for tones before and after a large pitch jump of at least 5 semi-tones (either direction).
`jumploc`	Integer [0:1]	N	True for tones after a pitch interval that is at least 1 semi-tone larger than the previous interval.
`jumploc2`	Integer [0:1]	N	True for tones after a pitch interval that is at least 2 semi-tone larger than the previous interval.
`thom`	Real [0,1]	N	Value according to Thomassen’s algorithm (1982), which is based on the seven possible pitch direction patterns that can be formed by 2-interval chains (3-note patterns). Values are not binary, but probabilities.
`thom_thr`	Integer [0:1]	N	Thresholded version of Thomassen accents with threshold, True if `accent-thom`>.75.
`beat1`	Integer [0:1]	N	True for primary accent (first beat) of a bar.
`beat3`	Integer [0:1]	N	True for secondary accent of a bar, if present, e.g., on the 3rd beat of a 4/4-measures.	Metrical annotation
`beat13`	Integer [0:1]	N	True for primary and secondary accents of a bar.	Metrical annotation
`beatall`	Integer [0:1]	N	True for all beat positions in a bar.	Metrical annotation
`sync1`	Integer [0:1]	N	True for all syncopations right before the primary accent in a bar (‘anticipated 1’).	Metrical annotation
`sync3`	Integer [0:1]	N	True for all syncopations right before the secondary accent in a bar (‘anticipated 3’).	Metrical annotation
`sync13`	Integer [0:1]	N	True for all syncopations right before primary and secondary accents in a bar (‘anticipated 1s and 3s’).	Metrical annotation
`sync1234`	Integer [0:1]	N	True for all syncopations right before all beats in a bar.	Metrical annotation
`syncall`	Integer [0:1]	N	True for all syncopations on every sub-beat metrical levels (i.e., excluding half-beat level).	Metrical annotation
`pextrem`	Integer [0:1]	N	True for pitch extrema (no restrictions).
`pextrmf`	Integer [0:1]	Var	True for pitch extrema (excluding proper cambiata).
`pextrst`	Integer [0:1]	N	True for pitch extrema (sensu Steinbeck, with at least two intervals before and after the extrema leading strictly to it).
`phrasbeg`	Integer [0:1]	N	True for first note in a phrase	Phrase annotation
`phrasend`	Integer [0:1]	N	True for last note in a phrase	Phrase annotation
`phrasbor`	Integer [0:1]	N	True for first and last note in a phrase	Phrase annotation

References¶

Conklin2001: Conklin & Anagnostopoulou Conklin, Darrell & Christina Anagnostopoulou (2001). Representation and discovery of multiple viewpoint patterns. Proceedings of the 2001 International Computer Music Conference. San Francisco: ICMA.