1. Representation and Discovery of Vertical Patterns in Music Darrell Conklin

2. Introduction oNeed a representation method to be able to manipulate and establish relationships between sequences in a musical piece. oIdentify recurrent patterns and ‘signatures’ using pattern discovery algorithm. oApplication in synthesis and classification of polyphonic pieces of music.

3. Terminologies oMusic Objects: Notes, Simultaneities (Sim), Sequences (Seq). oNote - MIDI integer defining pitch class and octave. oSeq (X) - joining music objects of type X that do not overlap in time. oSim (X) - layering objects of type X which have the same onset time.

4. Representation of Music Objects

5. Structuring and Partitioning of Music Pieces oTransformation from Sim(Seq) to Seq(Sim). [,, ] oNatural Partitioning creates new object when all voices have same onset time.

6. Viewpoints oViewpoint : Seq (X) --------> viewpoint elements oExample : Features of melodic segments- viewpoint of type Seq(Note) Feature lists(beat list, etc) - viewpoint elements

7. What does a Viewpoint element tell us? oExample : viewpoint ‘t’ :- t (join (c, o) ) = v ‘ music object o has the attribute value v in the context of sequence c’. oViewpoint element of an object depends on preceding objects in the sequence.

8. Viewpoint Sequences oSequence ‘s’ = [s1, s2,…, sn] oViewpoint ‘t’ applied to this sequence gives a viewpoint sequence [ t(s1), t(s2), …, t(sn) ]. [A,D,A,B,G,F#,F#] ---> [5,-5,2,-2,-2,-1,0] for the melodic interval viewpoint.

9. Viewpoint Patterns oIt is a recurring viewpoint sequence fragment in a corpus of pieces. oP-value of a pattern that occurs ‘n’ times in a corpus - Pr { pattern occurs ‘n’ or more times in a random corpus of the same size.} oP[2,-2]< P*[5,-5,2,-2,-1,0] oShortest & Longest Significant patterns.

10. Vertical Viewpoints Viewpoints can be linked together using a constructor to form complex viewpoints. Viewpoint ‘F’ must be transposition invariant F(X)=F(T(X)). Viewpoint of type NOTE can be ‘lifted’ to form vertical viewpoint of type Sim(NOTE).

11. RESULTS 185 Bach chorales--> expanded-->> pitch class interval viewpoint-->threaded at quarter note beat and lifted. 32 shortest significant patterns covering 142 pieces were detected.

12. Shortest Significant Patterns

13. Scope For Thought Not effective on free-form MIDI data. A new representation method : Notes are encoded as multidimensional vectors; repeated patterns in a piece are geometric translations of these vectors. Expansion of pieces can distort tonal harmony.