Counterpoint, harmony and polyphonic retrieval

1. Counterpoint, harmony and polyphonic retrieval ISMIR Graduate School, Barcelona 2004 Musicology 5-6 Frans Wiering, ICS, Utrecht University

2. Outline • polyphony • counterpoint • chords • tonality • polyphonic retrieval

3. Polyphony • what is polyhony • music where more than 1 pitch is sounding at the same time • most Western music is polyphonic • 2 ways of looking at polyphony: • counterpoint: combination of melodies • Palestrina • Bach fugues • harmony: chord succession • Bach Chorales, blues schema, fake book ex. • combination of 2: possible op to a certain leve • third category: heterophony • different versions of same melody at the same time • improvisation, Gamelan

4. Polyphony (2) • what makes polyphony interesting • overlap of melodies ->longer structures • voice separation is rewarding task for the brain (Huron 2001) • rules: succession of intervals/chords create tension and relaxation • this in turn generates emotion and meaning (Meyer 1956) • retrieval from polyphony • polyphony adds context to melody • chord progressions • complex queries, mostly for professionals • give me imitations in the 7th • lots of extra false positives • database size

5. Counterpoint • combination of 2 or more different melodies • progressions depend on rules of voice leading, such as (simplified) • intervals on strong beats should preferably be consonants • dissonants • weak beats • on strong beats prepared • must resolve • consonance, dissonance • leading note: relaxation of tension by semitone step • example: note pattern of tension and relaxation

6. Development in counterpoint • medieval counterpoint • few voices (2-3), different character • rhytmic contrast • user of contrasting instruments • different texts • change in late 15th century • more voices (4 and more) • similar in character • progressively sharing same melodic materials • culminates in fugue • 1 theme contrapuntally elaborated, realising its complete potential • J.S. Bach • C-minor fugue WTK 2 shows off lots of contrapuntal tricks • music schools: exercise

7. Counterpoint and perception • David Huron. Tone and Voice: A Derivation of the Rules of Voice-Leading from Perceptual Principles (2001) • object of study: 13 traditional rules of voice-leading (16th-18th century) • six core perceptual principles account for most of these • three additional principles: generate different styles • example rules: • avoid unisons • conjunct motion (i.e. melodies preferably move by steps) • consecutive perfect intervals forbidden (unison, fifth, octave)

8. Counterpoint and perception (2) • example core perceptual principles • toneness: use tones with a harmonic spectum • temporal continuity • minimum masking principle: avoid 2 notes in 1 spectral band • chord spacing: • average SAT notes given B (Haydn String Quartets) • probably calculated using Humdrum Toolkit • example auxiliary principle • limited density • trained musicians make almost no mistakes in estimating number of voices in music for less than 4 voices • except in ‘streaming’ • for 4 and more: number is consistently underestimated • switch from ‘contrapuntal’ to ‘harmonic’ listening streaming example Byrd and Crawford 2001

9. Streaming example streaming example Byrd and Crawford 2001

10. Formalization of counterpoint • Huron is first of all about contrapuntal rules rather than contrapuntal music • automatic generation of counterpoint • exists since 17th century (Athanasius Kircher’s composition machine) • problem is mainly the mediocrity of the melodies

11. Chords • simultaneous pitch events fuse into chords • happens for example in simple accompanyment • ‘harmonic background’ • chords are chains of thirds • triads: 2 thirds, like C-E-G • seventh chords: 3 thirds, like C-E-G-B • can be ‘spaced’ in many different ways that belong to same cognitive category • pitches that do not fit in: passing notes, anticipations etc.

12. Chords in music cognition • After Dirk-Jan Povel (2003) • 4 melodic fragments are perceived as very similar • reason: we infer the same chord progression • interesting property to use in retrieval

13. Chance hit in Orpheus • query produced group of rather similar melodies • can all be reduced to same melodic contour and stereotyped chord progression

14. Roman numeral system of harmony • Stereotyped chord progressions define key • a key has a triad as its tonal centre (Tonic) • 24 keys: 12 major and 12 minor • triads can be constructed on any note in the major and minor scale • scale degree indicated by Roman numeral • not an effective progression (I-II-V-I is effective) • other effective examples in persentation Fernando da Cruz

15. Harmonic functions simplified • In one key, there exist three harmonic functions: • Tonic: the tonal centre • Subdominant: moves away from tonic • Dominant: moves to tonic • All chords in one key belong to 1 or 2 of these classes S T D II IV VI I III V VII • Effective progressions in classical music are (in decreasing order) T-S-D-T, T-D-T, and T-S-T • tension/relaxation • strongest harmonic cliché: I - IV - V -I

16. Carol Krumhansl: key finding • Cognitive Foundations of Musical Pitch (1990) ISBN 0-19-514836-3 • Probe tone method • fragment is played • then probe tone • test subject rates the tone on 7-point scale • key profiles (p. 30)

17. Key finding algorithm • key-finding algorithm (Krumhansl-Schmuckler) • have profiles for all 24 major and minor keys (transposition) • sum total duration for each pitch class for the given fragment • calculate correlations with each key • decide • 91.7% success for 48 Bach preludes • Criticism (based on Temperley, The cognition of basic musical structures, 2001) • no concept of time: chunk is taken as one bag of pitches • pitch spelling not used • no concept of modulation (see next slide) • alternatives • Temperley’s revision of K-S • Vos & van Geenen (1996)

18. Modulation and key relationships • Modulation (in harmony): change of key • based on correlations between keys • can be rendered in 4D space • dimensions 1 and 2 emphasise fifth relationships between keys • dimensions 3 and 4 emphasise third relationships between keys • again, many other models (e.g. Arnold Schoenberg 1954) Krumhansl 1990, p. 43

19. Basic musical structures • Example basic musical structures include • chords • harmony • beat • meter • concepts of basical musical structures can be formalised relatively easily • Melody is not a basic musical structure • very hard for automatic processing

20. Harmonic matching (Pickens) • Jeremy Pickens et al. Polyphonic Score Retrieval Using Polyphonic Audio Queries: A Harmonic Modeling Approach (2003) • related to OMRAS • audio to symbolic matching • polyphonic aspect makes it particularly nice • main steps • Audio recording -> MIDI transcription • many errors • compare to MIDI representations of scores in database • output ranked results

21. The transcription and matching • each simultaneity is compared to all 24 triads (12 major, 12 minor) • no decision, but value for each tonality • employs Krumhansl’s 4-dimensional model fof inter-key relationships • out of the 24 values for each simultaneity, a Markov model for triads is generated • models of query and documents are compared • Language modelling: estimating probability of generating a query that conforms the model of the document • tested by means of retrieval of variations (Mozart, Ah, vous, Lachrimae, Folia) • very decent results (see article), evaluated by means of • mean average precision • average precision at top-5 • unites different approaches taught at ISMIR • signal processing • symbolic representation, study of ‘intertextual’ repertoire • experimental verification using IR performance measures

22. my preferred 5 % retention of ISMIR GS (musicology only) • fact from education research: one retains 5% only of the information presented in a lecture • what is the 5% I’d like you to remember • talking and thinking about music is an worthwhile activity • ‘classical’ musicology • lots of potentially useful knowledge (New Grove), • theoretical notions in particular • criteria for professional use of MIR systems • bias of musicology • computational musicology • interesting data (CCARH) • generation of music from musical grammars • music perception and cognition • MIR has a lot to do with what happens in the musical mind (Snyder) • models for basic musical structures (Krumhansl, Temperley) • musical similarity and meaning • types of musical similarity, and the gap we’re trying to fill • relation to the other fields • musical notions in signal processing • music information retrieval