Rameau: A System for Automatic Harmonic Analysis

Transcription

1 Rameau: A System for Automatic Harmonic Analysis Genos Computer Music Research Group Federal University of Bahia, Brazil ICMC 2008

2 1 How the system works

3 The input: LilyPond format \score { << \new Staff { << \new Voice { \voiceone \relative c { c4 b c2 }} \new Voice { \voicetwo \relative c { e4 d e2 }} >> } \new Staff { << \clef "bass" \new Voice { \voiceone \relative c { c4 b c2 }} \new Voice { \voicetwo \relative c { c4 g c2 }} >> } >> }

4 The input: LilyPond format 3 4

5 The answer sheet format For the previous example: C G C For the 1st phrase of Bach Chorale #1 {g g c/e [b] d/f# g bm/d bm7/d em c [b d] [b] f# /a g d g d/f# em7/g f# /a g/b am7/c d d7 g}

6 The output as a table # answer ES-tree EC-Knn ES-Knn ES-PB S-PB C C C C C C 2 G G G G G G 3 C C C C C C CORRECT(%)

7 The output as a score: Bach chorale #1 (Riemenschneider)

8 Comparison of results

9 Timing the program chorale #1 (80 segments) on my aging laptop: 14s for all 9 algorithms 0.2s for the fastest algorithm (neural network) 32s to analyze all 371 chorales using only the fastest algorithm

10 2 Problems

11 Pitch spelling equal not equal

12 Pitch class notation C=0, C =1, D=2, D =3,..., B=11 (or MIDI: 60, 62, ) problem: C = D

13 A codification for tonal music (Dr. Jamary Oliveira) c d e f g a b C=0, D=14, F =42, A =67

14 Segmentation (easy case) splitting the piece into chord spans

15 Segmentation (not easy) splitting the piece into chord spans

16 Chord labeling Labeling each chord with a name B 7 Eb D 7 Eb

17 Functional Analysis Assigning tonal functions to the chords in F major: F F C/E F/Eb Bb/D I I V V /IV IV 2

18 3 The analysis per se

19 The process is: parse a score into a list of events and simplify it to a list of pitches

20 Each algorithm converts the list of pitches into chords

21 4 The algorithms

22 Pardo and Birmingham s algorithm straight template-matching 0 4 = Major = Minor 7 And so on... (but we did extend it to have enough labels and be enharmonically savvy)

23 Temperley and Sleator s algorithm maximizing something over the piece Too slow. And too complex. And also too wrong, so we took it out.

24 Naïve Bayesian algorithm the chord that gives the highest probability to each sonority

25 Hidden Markov Model (Raphael) Bayesian, but also maximizes the probability of the entire piece in a Markov Model As you can see, it s the only one that can tell that a transition from Bm to D and then to Em is too unlikely.

26 K-Nearest Neighbors algorithm the most common chord label closest to the pitches being analyzed

27 Decision tree implicit rule-following If first pitch is 0 (a C) and second pitch is 28 (an E) and third pitch is 55 (a G), then the chord is a C major. If first pitch is 0 and second pitch is 27 (an E ) and third pitch is 55, then the chord is a C minor. And so on...

28 Neural networks (Tsui) pattern-matching over each sonority s pitches Currently the best algorithm is a neural network that only looks at one sonority at a time. Go figure.

29 5 Our Results

30 Average accuracies (10 chorales) Context-free neural net 95% ± 6 Context-free Knnn 94% ± 7 Context-considering knn 92% ± 8 Context-considering net 91% ± 10 Decision tree 89% ± 14 Naïve Bayesian 88% ± 19 Hidden Markov Model 83% ± 16 Pardo & Birmingham s 82% ± 21

31 Confusion matrix for the neural network M nc M7+ M7 m7 m ø7!!7 7 M x nc 2.8 x M x x 4.2 M7 x m7 x m x ø7 7.1 x! x! x 7 x

32 Precision (%) Decision tree Contextual neural network M nc M M m m ø

33 Recall (%) Decision tree Contextual neural network M nc M M m m ø

34 F-measure (%) Decision tree Contextual neural network M nc M M m m ø

35 6 Computational musicology

36 Range Bach Kostk a Soprano Alto Tenor Bass

37 Range highest pitch lowest pitch soprano alto tenor bass

38 Voice crossing (57% of Bach Chorales)

39 Consecutive octaves (4%)

40 Cadence detection: these are all the final cadences in the Bach chorales

41 Conclusion Pros free software: algorithms from literature and new algorithms good accuracy easy performance evaluation quite fast :-) Cons no functional analysis no explicit segmentation no non-chord tone analysis only Bach Chorales natural ambiguity in harmonic analysis input data must be 100% correct