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Mapping MIDI to
the Spiral Array:
Disambiguating
Pitch Spelling
Elaine CHEW
Yun-Ching CHEN
Motivation
Pitch Structure
pitch spelling
chord ident.
key-finding
segmentation
style recognition
pattern processing
MIDI
Time Structure
beat tracking
meter induction
Applications
automatic transcription
computer analysis of music
categorization / retrieval
expressive performance
Pitch Spelling using the Spiral Array 2/8
Pitch Spelling

Each pitch read from the MIDI file will
correspond to two or three letter names.
Row
0
1
2
3
4
5
6
7
8
9
10
11
spelling1 (index)
B#
(12)
C#
(7)
C##
(14)
D#
(9)
D##
(16)
E#
(11)
E##
(18)
F##
(13)
G#
(8)
G##
(15)
A#
(10)
A##
(17)
spelling2 (index)
C
(0)
Db
(-5)
D
(2)
Eb
(-3)
E
(4)
F
(-1)
F#
(6)
G
(1)
Ab
(-4)
A
(3)
Bb
(-2)
B
(5)
* (index) refers to index of pitch in Spiral Array.
spelling3 (index)
Dbb
(-12)
B##
(19)
Ebb
(-10)
Fbb
(-15)
Fb
(-8)
Gbb
(-13)
Gb
(-6)
Abb
(-11)
Bbb
Cbb
Cb
(-9)
(-14)
(-7)
Pitch Spelling using the Spiral Array 3/8
Illustrative Examples
Opening bars of Beethoven’s Piano Sonata, Op.109
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## }
Bars 25 ½ - 33 ½ of Beethoven’s Piano Sonata, Op.109
Pitch Spelling using the Spiral Array 4/8
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 Array 5/8
A#
Our Method
c.e.

c.e. acts as proxy
for key context

Select spelling
closest to c.e.
Bb
Pitch Spelling using the Spiral Array 6/8
Results
•Piece
•notes
•correct spelling
•% correct
•Beethoven Op.79
•(3rd movement)
•1375
•1374
•99.93
•Beethoven Op.109
•(1st movement)
•1516
•1443
•95.18
•TOTAL
•2891
•2817
•97.44
Pitch Spelling using the Spiral Array 7/8
Discussion

Types of Errors:

Algorithm’s ignorance of linear motion
Linear motion in Op.109 resulting in spelling error in bar 10 (circled).

Insufficient sensitivity to key changes
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 Array 8/8