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Christof Weiß Ringvorlesung TechTalk . Physics Diploma Philosophische Fakultät, FAU, WS 2019/20 Universität Würzburg . Composition Neue Wege für die Musikforschung mittels HfM Würzburg Digitaler Signalverarbeitung . Ph. D. in Media Technology Fraunhofer IDMT, Ilmenau Christof Weiß, Meinard Müller . Postdoc in Music Processing & Composer International Audio Laboratories Erlangen [email protected], [email protected] AudioLabs / Erlangen-Nürnberg University . 2018: KlarText award for science communication 2 Harmony Analysis Harmony Analysis . Different concepts . Different concepts . Concepts relate to different temporal granularity . Concepts relate to different temporal granularity Movement level Global key C major Global key detection Movement level Global key C major Global key detection Segment level C majorLocal key G major C major Local key detection Segment level C majorLocal key G major C major Local key detection Chord level CM GM7 Am Chords Chord recognition Chord level CM GM7 Am Chords Chord recognition Melody Melody Note level Middle voices Music transcription Note level Middle voices Music transcription Bass line Bass line 3 4 Harmony Analysis Harmony Analysis . The Beatles, Let it be – Chords . Different concepts . Concepts relate to different temporal granularity Movement level Global key C major Global key detection Segment level C majorLocal key G major C major Local key detection Chord level CM GM7 Am Chords Chord recognition Melody Note level Middle voices Music transcription Source: www.ultimate-guitar.com Bass line 5 6 Harmony Analysis: Local Keys Harmony Analysis: Local Keys . Johann Sebastian Bach, Choral “Durch Dein Gefängnis” . Johann Sebastian Bach, Choral “Durch Dein Gefängnis” (St. John’s Passion) – Local keys (St. John’s Passion) – Local keys E maj B maj E maj B maj E maj B maj E maj Modulation E maj . Musical form: Stollen Stollen Abgesang „Bar form“ 7 8 Harmony Analysis: Local Keys Harmony Analysis: Local Keys . Johann Sebastian Bach, Choral “Durch Dein Gefängnis” . Johann Sebastian Bach, Choral “Durch Dein Gefängnis” (St. John’s Passion) – Local keys (St. John’s Passion) – Local keys Circle of fifths Circle of fifths C C E maj B maj F G E maj B maj F G Am Am Dm Em Dm Em B♭ D B♭ D Gm Bm Gm Bm Series of fifths E♭ Cm ♭ ♯ F#m A Series of fifths E♭ Cm ♭ ♯ F#m A Fm C#m Fm C#m A ♭ E A ♭ E B ♭ m E ♭m G#m B ♭ m E ♭m G#m D#m D#m D♭ B 0 diatonic D♭ B G ♭ G ♭ F# F# 9 10 Harmony Analysis: Local Keys Harmony Analysis: Local Keys . Johann Sebastian Bach, Choral “Durch Dein Gefängnis” . Johann Sebastian Bach, Choral “Durch Dein Gefängnis” (St. John’s Passion) – Local keys (St. John’s Passion) – Local keys Circle of fifths Circle of fifths C C E maj B maj F G E maj B maj F G Am Am Dm Em Dm Em B♭ D B♭ D Gm Bm Gm Bm Series of fifths E♭ Cm ♭ ♯ F#m A Series of fifths E♭ Cm ♭ ♯ F#m A Fm C#m Fm C#m A ♭ E A ♭ E B ♭ m E ♭m G#m B ♭ m E ♭m G#m D#m D#m 1# diatonic D♭ B 2♭ diatonic D♭ B G ♭ G ♭ F# F# 11 12 Harmony Analysis: Local Keys Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Johann Sebastian Bach, Choral “Durch Dein Gefängnis” . Score – Piano reduction (St. John’s Passion) – Local keys Circle of fifths C F G 4# 5# Am Dm Em B♭ D Gm Bm Series of fifths E♭ Cm ♭ ♯ F#m A Fm C#m A ♭ E B ♭ m E ♭m G#m D#m D♭ B G ♭ F# 13 14 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Audio – Waveform (Scholars Baroque Ensemble, Naxos 1994) . Audio – Spectrogram (Scholars Baroque Ensemble, Naxos 1994) Time (seconds) 15 16 Visualization of Diatonic Scales Chroma Features . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Human perception of pitch is periodic . Audio – Chroma features (Scholars Baroque Ensemble, Naxos 1994) . Two components: tone height (octave) and chroma (pitch class) Shepard’s helix of pitch Chromatic circle 17 18 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Audio – Chroma features (Scholars Baroque Ensemble, Naxos 1994) . Chroma features – smoothing 19 20 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Chroma features – smoothing . Chroma features – smoothing 21 22 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Chroma features – smoothing . Re-ordering to perfect fifth series 23 24 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Re-ordering to perfect fifth series . Diatonic Scales (7 fifths) 4# 25 26 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Diatonic Scales (7 fifths) . Diatonic Scales – multiplication 5# 27 28 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Diatonic Scales – multiplication . Diatonic Scales – multiplication 29 30 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Diatonic Scales – multiplication . Diatonic Scales – shift to global key 4 # (E major) 4# 5# 4# 5# 4# 31 32 Visualization of Diatonic Scales Visualization of Diatonic Scales . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Example: J.S. Bach, Choral “Durch Dein Gefängnis” . Diatonic Scales – shift to global key . Diatonic Scales – relative [1] C. Weiß, J. Habryka, “Chroma-Based Scale Matching for Audio Tonality Analysis” Proc. Conference on Interdisciplinary Musicology, 2014. Modulation 4 # (E major) 33 34 Visualization of Diatonic Scales Visualization of Diatonic Scales . L. v. Beethoven – Sonata No. 10 op. 14 Nr. 2, 1. Allegro — 0 ≙ 1 . R. Wagner, Die Meistersinger von Nürnberg, Vorspiel — 0 ≙ 0 (Barenboim, EMI 1998) (Polish National Radio Symphony Orchestra, J. Wildner, Naxos 1993) Exposition Exposition Durchführung Reprise sonata form 35 36 Cooperation: Musicology Cross-Version Analysis . DFG-funded project: “Computer-Assisted Analysis of . 16 different performances (versions) Harmonic Structures” . Manual measure annotations for 3 versions . Harmony analysis and visualization No. Conductor Recording hh:mm:ss . 1st phase: 2014–2018, 2nd phase: 2019–2023 1 Barenboim 1991–92 14:54:55 2 Boulez 1980–81 13:44:38 3 Böhm 1967–71 13:39:28 . Partners: 1 2 3 4 4 Furtwängler 1953 15:04:22 . Rainer Kleinertz, Musicology Univ. Saarland 5 Haitink 1988–91 14:27:10 6 Janowski 1980–83 14:08:34 . Stephanie Klauk, Musicology Univ. Saarland 7 Karajan 1967–70 14:58:08 . Meinard Müller, AudioLabs FAU 8 Keilberth/Furtwängler 1952–54 14:19:56 . Christof Weiß, AudioLabs FAU 9 Krauss 1953 14:12:27 10 Levine 1987–89 15:21:52 11 Neuhold 1993–95 14:04:35 . Central work: Richard Wagner, Der Ring des Nibelungen 12 Sawallisch 1989 14:06:50 13 Solti 1958–65 14:36:58 14 Swarowsky 1968 14:56:34 . How is harmony organized at the large scale? 15 Thielemann 2011 14:31:13 16 Weigle 2010–12 14:48:46 37 38 Cross-Version Analysis Die Walküre WWV 86 B Act 1 . 16 different performances (versions) . Manual measure annotations for 3 versions Time (measures) Act 2 Amplitude Time (seconds) . Visualize cross-version consistency with gray scale Act 3 39 40 Die Walküre WWV 86 B Die Walküre WWV 86 B . Act 1, measures 955–1012 . Act 1, measures 955–1012 . Sieglinde’s narration . Sieglinde’s narration 41 42 Die Walküre WWV 86 B Die Walküre WWV 86 B Act 1 . Act 3, measures 724–789 . Wotan’s punishment Act 2 Act 3 43 44 Die Walküre WWV 86 B Die Walküre WWV 86 B A. Lorenz, 1924 . Act 3, measures 724–789 . Wotan’s punishment 45 46 Exploring Tonal-Dramatic Relationships Exploring Tonal-Dramatic Relationships . Histograms of Analysis over time Die Walküre – Sword motif Das Rheingold Die Walküre Siegfried Götterdämmerung WWV 86 A WWV 86 B WWV 86 C WWV 86 D 3897 measures 5322 measures 6682 measures 6040 measures Diatonic Scales Diatonic Scales Time (measures) 47 48 Exploring Tonal-Dramatic Relationships Exploring Tonal-Dramatic Relationships Siegfried – Sword motif Das Rheingold – Valhalla motif Diatonic Scales Chords 49 50 Exploring Tonal-Dramatic Relationships Die Walküre – Valhalla motif Corpus Analysis: Composer Styles Chords 51 52 Tonal Complexity Tonal Complexity . Global chroma statistics (audio) . Global chroma statistics (audio) . 1783 – W. A. Mozart, „Linz“ symphony KV 425, 1. Adagio / Allegro . 1883 – J. Brahms, Symphony No. 3, 1. Allegro con brio (F major) 1 1 0.8 0.8 0.6 0.6 0.4 0.4 Salience Salience 0.2 0.2 0 0 Eb Bb F C G D A E B F# C# G# Ab Eb Bb F C G D A E B F# C# Pitch class Pitch class Circle of fifths → Circle of fifths → 53 54 Tonal Complexity Tonal Complexity . Global chroma statistics (audio) . Realization of complexity measure Γ . 1940 – A. Webern, Variations for Orchestra op. 30 . Distribution over Circle of Fifths 1 0 1 0.6 0.8 0.6 0.4 Salience 0.2 0 Ab Eb Bb F C G D A E B F# C# Pitch class Circle of fifths → 1 ℎ .