1. Maxime Convert†, Satoru Fukayama‡, Tomoyasu Nakano‡,
Shinnosuke Takamichi†, Hiroshi Saruwatari†, Masataka Goto‡
SIGMUS Summer Symposium 2018 in Hiroshima Institute of Technology
† The University of Tokyo
‡ National Institute of Advanced Industrial Science and Technology
(AIST)
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 1/31
2. Harmonization
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 2/31
Harmonization = Adding chords to a given song
Chorale harmonization
E.g.:
◦ HARMONET [Hild+ 1991]
◦ DeepBach [Hadjeres+ 2017]
Melody harmonization
E.g.:
◦ [Gang+ 1998]
◦ MySong [Simon+ 2008]
Output
Output
Input
Input
Task addressed by our study
Input
Output
3. Machine Learning-based Harmonization
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Machine Learning
Model
(Hidden Markov Model,
Neural Network, etc.)
Training
Melody
Past chords
Tempo
Etc.
Input Data
Chords
Output Data
Trained Model
New Input Song Harmonized Song
Chord Prediction
3/31
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4. Machine Learning-based Harmonization
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Machine Learning
Model
(Hidden Markov Model,
Neural Network, etc.)
Training
Input Data
Chords
Output Data
Main focus in past
harmonization research
Melody
Past chords
Tempo
Etc.
4/31
Vary data
representations
Models learn different dependencies
between input & output
5. Chord Representations Variations
What is a chord and how to represent it?
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 5/31
Many possible representations
Merits and demerits depend on problem to solve
à Stacking of Major 3rd and Minor 3rd ?
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à
Minor 3rd Major 3rd
à Simple label identifying the chord ?
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Amin<latexit sha1_base64="YGmlq8VX1xDuFmYigCtwbV2+v4A=">AAAB9HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi2GPFi8cKthXaUDbbTbt0dxN3J8US+ju8eFDEqz/Gm//GbZuDtj4YeLw3w8y8MBHcoOd9O4W19Y3NreJ2aWd3b/+gfHjUMnGqKWvSWMT6ISSGCa5YEzkK9pBoRmQoWDsc3cz89phpw2N1j5OEBZIMFI84JWiloIvsCbXMriVX01654lW9OdxV4uekAjkavfJXtx/TVDKFVBBjOr6XYJARjZwKNi11U8MSQkdkwDqWKiKZCbL50VP3zCp9N4q1LYXuXP09kRFpzESGtlMSHJplbyb+53VSjGpBxlWSIlN0sShKhYuxO0vA7XPNKIqJJYRqbm916ZBoQtHmVLIh+Msvr5LWRdX3qv7dZaVey+Mowgmcwjn4cAV1uIUGNIHCIzzDK7w5Y+fFeXc+Fq0FJ585hj9wPn8AW0mSbw==</latexit><latexit sha1_base64="YGmlq8VX1xDuFmYigCtwbV2+v4A=">AAAB9HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi2GPFi8cKthXaUDbbTbt0dxN3J8US+ju8eFDEqz/Gm//GbZuDtj4YeLw3w8y8MBHcoOd9O4W19Y3NreJ2aWd3b/+gfHjUMnGqKWvSWMT6ISSGCa5YEzkK9pBoRmQoWDsc3cz89phpw2N1j5OEBZIMFI84JWiloIvsCbXMriVX01654lW9OdxV4uekAjkavfJXtx/TVDKFVBBjOr6XYJARjZwKNi11U8MSQkdkwDqWKiKZCbL50VP3zCp9N4q1LYXuXP09kRFpzESGtlMSHJplbyb+53VSjGpBxlWSIlN0sShKhYuxO0vA7XPNKIqJJYRqbm916ZBoQtHmVLIh+Msvr5LWRdX3qv7dZaVey+Mowgmcwjn4cAV1uIUGNIHCIzzDK7w5Y+fFeXc+Fq0FJ585hj9wPn8AW0mSbw==</latexit><latexit sha1_base64="YGmlq8VX1xDuFmYigCtwbV2+v4A=">AAAB9HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi2GPFi8cKthXaUDbbTbt0dxN3J8US+ju8eFDEqz/Gm//GbZuDtj4YeLw3w8y8MBHcoOd9O4W19Y3NreJ2aWd3b/+gfHjUMnGqKWvSWMT6ISSGCa5YEzkK9pBoRmQoWDsc3cz89phpw2N1j5OEBZIMFI84JWiloIvsCbXMriVX01654lW9OdxV4uekAjkavfJXtx/TVDKFVBBjOr6XYJARjZwKNi11U8MSQkdkwDqWKiKZCbL50VP3zCp9N4q1LYXuXP09kRFpzESGtlMSHJplbyb+53VSjGpBxlWSIlN0sShKhYuxO0vA7XPNKIqJJYRqbm916ZBoQtHmVLIh+Msvr5LWRdX3qv7dZaVey+Mowgmcwjn4cAV1uIUGNIHCIzzDK7w5Y+fFeXc+Fq0FJ585hj9wPn8AW0mSbw==</latexit><latexit sha1_base64="YGmlq8VX1xDuFmYigCtwbV2+v4A=">AAAB9HicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi2GPFi8cKthXaUDbbTbt0dxN3J8US+ju8eFDEqz/Gm//GbZuDtj4YeLw3w8y8MBHcoOd9O4W19Y3NreJ2aWd3b/+gfHjUMnGqKWvSWMT6ISSGCa5YEzkK9pBoRmQoWDsc3cz89phpw2N1j5OEBZIMFI84JWiloIvsCbXMriVX01654lW9OdxV4uekAjkavfJXtx/TVDKFVBBjOr6XYJARjZwKNi11U8MSQkdkwDqWKiKZCbL50VP3zCp9N4q1LYXuXP09kRFpzESGtlMSHJplbyb+53VSjGpBxlWSIlN0sShKhYuxO0vA7XPNKIqJJYRqbm916ZBoQtHmVLIh+Msvr5LWRdX3qv7dZaVey+Mowgmcwjn4cAV1uIUGNIHCIzzDK7w5Y+fFeXc+Fq0FJ585hj9wPn8AW0mSbw==</latexit>
à
à Set of pitches played simultaneously ?
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à
A C E
6. Harmonization with Tension Notes
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 6/31
Motivation: Extend melody harmonization with models handling
tension notes
à Harmonize jazz and derivate contemporary genres
triad tensions
root 3rd 5th 7th 9th 11th 13th
Common in datasets
Rare in datasets
compared to triads
à Problem: data imbalance
7. Chord Complexity & Representations
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 7/31
Label Representation
Weakness
◦ Simple labels outnumber complex
labels (data imbalance)
◦ E.g. vs
Strength
◦ No risk of unconventional chord,
only chords existing in data
Pitch Representation
Strength
◦ Exploit chord redundancies
◦ E.g.
Weakness
◦ Too much degree of freedom
allow very unlikely chords
◦ E.g.
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Cmaj79]
1113<latexit sha1_base64="Dna0zRlGfKx8wxYcEofbVbS+VCM=">AAACE3icbVA9SwNBEN3z2/gVtbQ5TASxCLd+4EcVSGOpYBIhF8PeZmLW7N4du3NiOO4/2PhXbCwUsbWx89+4iSk0+mDg8d4MM/OCWAqDnvfpTExOTc/Mzs3nFhaXllfyq2s1EyWaQ5VHMtKXATMgRQhVFCjhMtbAVCChHvQqA79+C9qIKLzAfgxNxa5D0RGcoZVa+R0f4Q61SiuK3RweF69802U6LlLqd03MOKRe6UCpjO5lrXzBK3lDuH8JHZECGeGslf/w2xFPFITIJTOmQb0YmynTKLiELOcnBuyKHruGhqUhU2Ca6fCnzN2yStvtRNpWiO5Q/TmRMmVMXwW2UzHsmnFvIP7nNRLsHDVTEcYJQsi/F3US6WLkDgJy20IDR9m3hHEt7K0ut5EwjjbGnA2Bjr/8l9R2S9Qr0fP9QvlkFMcc2SCbZJtQckjK5JSckSrh5J48kmfy4jw4T86r8/bdOuGMZtbJLzjvX5CWnUU=</latexit><latexit sha1_base64="Dna0zRlGfKx8wxYcEofbVbS+VCM=">AAACE3icbVA9SwNBEN3z2/gVtbQ5TASxCLd+4EcVSGOpYBIhF8PeZmLW7N4du3NiOO4/2PhXbCwUsbWx89+4iSk0+mDg8d4MM/OCWAqDnvfpTExOTc/Mzs3nFhaXllfyq2s1EyWaQ5VHMtKXATMgRQhVFCjhMtbAVCChHvQqA79+C9qIKLzAfgxNxa5D0RGcoZVa+R0f4Q61SiuK3RweF69802U6LlLqd03MOKRe6UCpjO5lrXzBK3lDuH8JHZECGeGslf/w2xFPFITIJTOmQb0YmynTKLiELOcnBuyKHruGhqUhU2Ca6fCnzN2yStvtRNpWiO5Q/TmRMmVMXwW2UzHsmnFvIP7nNRLsHDVTEcYJQsi/F3US6WLkDgJy20IDR9m3hHEt7K0ut5EwjjbGnA2Bjr/8l9R2S9Qr0fP9QvlkFMcc2SCbZJtQckjK5JSckSrh5J48kmfy4jw4T86r8/bdOuGMZtbJLzjvX5CWnUU=</latexit><latexit sha1_base64="Dna0zRlGfKx8wxYcEofbVbS+VCM=">AAACE3icbVA9SwNBEN3z2/gVtbQ5TASxCLd+4EcVSGOpYBIhF8PeZmLW7N4du3NiOO4/2PhXbCwUsbWx89+4iSk0+mDg8d4MM/OCWAqDnvfpTExOTc/Mzs3nFhaXllfyq2s1EyWaQ5VHMtKXATMgRQhVFCjhMtbAVCChHvQqA79+C9qIKLzAfgxNxa5D0RGcoZVa+R0f4Q61SiuK3RweF69802U6LlLqd03MOKRe6UCpjO5lrXzBK3lDuH8JHZECGeGslf/w2xFPFITIJTOmQb0YmynTKLiELOcnBuyKHruGhqUhU2Ca6fCnzN2yStvtRNpWiO5Q/TmRMmVMXwW2UzHsmnFvIP7nNRLsHDVTEcYJQsi/F3US6WLkDgJy20IDR9m3hHEt7K0ut5EwjjbGnA2Bjr/8l9R2S9Qr0fP9QvlkFMcc2SCbZJtQckjK5JSckSrh5J48kmfy4jw4T86r8/bdOuGMZtbJLzjvX5CWnUU=</latexit><latexit sha1_base64="Dna0zRlGfKx8wxYcEofbVbS+VCM=">AAACE3icbVA9SwNBEN3z2/gVtbQ5TASxCLd+4EcVSGOpYBIhF8PeZmLW7N4du3NiOO4/2PhXbCwUsbWx89+4iSk0+mDg8d4MM/OCWAqDnvfpTExOTc/Mzs3nFhaXllfyq2s1EyWaQ5VHMtKXATMgRQhVFCjhMtbAVCChHvQqA79+C9qIKLzAfgxNxa5D0RGcoZVa+R0f4Q61SiuK3RweF69802U6LlLqd03MOKRe6UCpjO5lrXzBK3lDuH8JHZECGeGslf/w2xFPFITIJTOmQb0YmynTKLiELOcnBuyKHruGhqUhU2Ca6fCnzN2yStvtRNpWiO5Q/TmRMmVMXwW2UzHsmnFvIP7nNRLsHDVTEcYJQsi/F3US6WLkDgJy20IDR9m3hHEt7K0ut5EwjjbGnA2Bjr/8l9R2S9Qr0fP9QvlkFMcc2SCbZJtQckjK5JSckSrh5J48kmfy4jw4T86r8/bdOuGMZtbJLzjvX5CWnUU=</latexit>
à What chord representation is suitable to build harmonization
models for contemporary genres?
still learnable
vs
8. Research Summary
Results:
Pitch-class representation
◦ Simpler model with constant network parameter number
◦ Less false-positives i.e. less dissonant notes
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 8/31
+
-
o
sus
Triads data suffix classes
0
50000
100000
150000
200000
Numberofsamples
+
+7
+j7
-
-6
-7
-j7
6
7
j7
m7b5
o
o7
sus
sus7
Sevenths data suffix classes
0
25000
50000
75000
100000
125000
150000
Numberofsamples
E[maj7
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F7
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B[maj7
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Cm7
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[ ]
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Experiments:
Four chord representations
◦ Trained on recurrent neural nets (RNN)
Two datasets
◦ Of different chord complexity
10. 1. Chord Labels
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 10/31
Input
Conventional representation
◦ One label per chord
E.g.:
à Can only output chords existing in original dataset
Many inter-chord redundancies
Prediction
Output
Little flexibility
11. 2. Root & Suffix Labels
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 11/31
à Allows chords not in dataset by combining root with
any other existing suffixes
Split chord into root + suffix
◦ Treat both as labels
E.g.:
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“Root”
“Suffix”
Prediction
Input Output
Flexibility ⇧Redundancy ⇩
12. 3. Root Labels + Suffix Intervals
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 12/31
Introduce suffix intervals information
◦ Keep root as labels
E.g.:
4
Semitone
intervals
from root
7
11
Root as reference
C
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10
7
3
B
7
4
10
E
7
11
4
A
à Allows virtually any chord by combining root with
any suffix interval
Prediction
Input Output
7
9
4
A
Redundancy ⇩ Flexibility ⇧
13. 4. Pitch Classes
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 13/31
Constituting
pitches
C E G B
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Gb
D
A
B
D
Ab
B
E E
Db
A
Ab
Chords as constituting pitches
◦ No label or interval information
E.g.:
à Allows virtually any chords in any pitch configuration
(chord inversions, etc.)
Prediction
Input Output
E
Db
A
Gb
Maximum flexibilityMinimum redundancy