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Mapping MIDI to the Spiral Array: Disambiguating Pitch Spelling

This study explores the application of the Spiral Array model for clarifying pitch spelling in MIDI files. By utilizing a systematic approach, it aims to enhance automatic transcription, key-finding, and style recognition in music analysis. The effectiveness of the method is evaluated through illustrative examples from Beethoven's Piano Sonata, Op. 109, and comparisons with existing literature demonstrate high success rates in pitch spelling accuracy. This research contributes significantly to the fields of music categorization and retrieval, and emphasizes the necessity of precise pitch interpretation in expressive performances.

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Mapping MIDI to the Spiral Array: Disambiguating Pitch Spelling

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  1. Mapping MIDI to the Spiral Array:Disambiguating Pitch Spelling Elaine CHEW Yun-Ching CHEN

  2. Pitch Structure pitch spelling chord ident. key-finding MIDI segmentation style recognition pattern processing Applications automatic transcription computer analysis of music categorization / retrieval expressive performance Time Structure beat tracking meter induction Motivation Pitch Spelling using the Spiral Array2/8

  3. Pitch Spelling • Each pitch read from the MIDI file will correspond to two or three letter names. Row spelling1 (index) spelling2 (index) spelling3 (index) 0 B# (12) C (0) Dbb (-12) 1 C# (7) Db (-5) B## (19) 2 C##(14)D(2)Ebb(-10) 3 D# (9) Eb (-3) Fbb (-15) 4 D## (16) E (4) Fb (-8) 5 E# (11) F (-1) Gbb (-13) 6 E## (18) F# (6) Gb (-6) 7 F## (13) G (1) Abb (-11) 8 G# (8) Ab(-4) 9 G## (15) A (3) Bbb (-9) 10 A# (10) Bb (-2) Cbb (-14) 11 A## (17) B (5) Cb (-7) * (index) refers to index of pitch in Spiral Array. Pitch Spelling using the Spiral Array3/8

  4. Opening bars of Beethoven’s Piano Sonata, Op.109 Bars 25 ½ - 33 ½ of Beethoven’s Piano Sonata, Op.109 Illustrative Examples Default { B, G, Bb, Eb, Ab, Db, Gb, Cb } Spelling 1(initialize c.e. at C major) { B, G, Bb, Eb, Ab, Db, Gb, Cb } Spelling 2 (initialize c.e. at g# minor) { B, F#, C#, G#, D#, A#, E#,F## } Pitch Spelling using the Spiral Array4/8

  5. Literature Review • Interval Optimization Approach - Automatic Pitch Spelling: From Numbers to Sharps and Flats Emilios Cambouropoulos (2001) • Evaluated on 8 complete piano sonatas by Mozart and had a success rate of 96.2% • Preference Rule Approach - The Cognition of Basic Musical Structure, David Temperley (2002) • Many possible interpretations are considered; • Each rule expresses an opinion as to how well it is satisfied by a given interpretation, and • Opinions are combined to yield the preferred analysis. • Evaluated on Kostka-Payne corpus and had success rate 98.8% Pitch Spelling using the Spiral Array5/8

  6. A# Our Method • c.e. acts as proxy for key context • Select spelling closest to c.e. c.e. Bb Pitch Spelling using the Spiral Array6/8

  7. Results Pitch Spelling using the Spiral Array7/8

  8. Discussion • Types of Errors: • Algorithm’s ignorance of linear motion • Insufficient sensitivity to key changes Linear motion in Op.109 resulting in spelling error in bar 10 (circled). Spelling error (circled) in bar 20 of Op.79 because the c.e. had not yet detected the E minor context. Pitch Spelling using the Spiral Array8/8

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