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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
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
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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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
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 ?
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
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 ?
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
A C E
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
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
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
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 9/31
Chord Representations
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
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 ⇩
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 ⇧
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
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 14/31
Neural Network Models
Task Definition
Predict chord from: current melody & past chord sequence
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Answer:
Past chord sequence
Current melody
Melody sequence
Chord sequence
RNN
RNN
Chord prediction
15/31
Only chord representation changes across models
Model 1: Chords Labels
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
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F7
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GRU
GRU
+ FC
GRU [Cho+ 2014] = Gated Recurrent Unit Layer, FC = Fully-connected layer
Conventional label representation (Baseline)
16/31
Chord labels as
one-hot vectors
Model 2: Root Label + Suffix Label
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
E[
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GRU
GRU
GRU
+
FC
FC
root
17/31
Root & suffix labels
as one-hot vectors
suffix
Expected to learn root-suffix relationships since trained at the
same time in the model
Model 3: Root Label + Suffix Intervals
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Binary vector
• 1 = semitone
• 0 = no semitone
18/31
Root (blue) will always be present
Model 4: Pitch Classes
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 19/31
Binary vector
• 1 = pitch
• 0 = no pitch
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 20/31
Datasets
Dataset Overview
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Weimar Jazz Database - 456 Jazz solos [Abeßer+ 2013]
◦ Song selection:
◦ Keep 4/4 time signature
◦ More than 2 chords involved
◦ Data augmentation:
◦ Transpose songs to 11 remaining tones (original size * 12)
◦ Melody:
◦ Bring to octave, i.e. 12 pitches
◦ Chords:
◦ 2 datasets of different chord complexity
21/31
Chords Datasets
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 22/31
Triads dataset à commonly used & simple
◦ (12 roots * 5 suffixes = 60 chords)
Sevenths dataset à slight complexity increase
◦ (12 roots * 16 suffixes = 192 chords)
root triad 6th or 7th tensions bass or inversion
Triads data
Sevenths data Discard
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/G[<latexit sha1_base64="zRrAquZ34rsr+hINDjElXgUtRkU=">AAAB+3icbVBNS8NAEN3Ur1q/Yj16CbaCp5qIoHgqeNBjBfsBTSmb7aZdursJuxNpCfkrXjwo4tU/4s1/47bNQVsfDDzem2FmXhBzpsF1v63C2vrG5lZxu7Szu7d/YB+WWzpKFKFNEvFIdQKsKWeSNoEBp51YUSwCTtvB+Hbmt5+o0iySjzCNaU/goWQhIxiM1LfLPtAJKJGe31X9kGOoZn274tbcOZxV4uWkgnI0+vaXP4hIIqgEwrHWXc+NoZdiBYxwmpX8RNMYkzEe0q6hEguqe+n89sw5NcrACSNlSoIzV39PpFhoPRWB6RQYRnrZm4n/ed0EwuteymScAJVksShMuAORMwvCGTBFCfCpIZgoZm51yAgrTMDEVTIheMsvr5LWRc1za97DZaV+k8dRRMfoBJ0hD12hOrpHDdREBE3QM3pFb1ZmvVjv1seitWDlM0foD6zPH4bOlBA=</latexit><latexit sha1_base64="zRrAquZ34rsr+hINDjElXgUtRkU=">AAAB+3icbVBNS8NAEN3Ur1q/Yj16CbaCp5qIoHgqeNBjBfsBTSmb7aZdursJuxNpCfkrXjwo4tU/4s1/47bNQVsfDDzem2FmXhBzpsF1v63C2vrG5lZxu7Szu7d/YB+WWzpKFKFNEvFIdQKsKWeSNoEBp51YUSwCTtvB+Hbmt5+o0iySjzCNaU/goWQhIxiM1LfLPtAJKJGe31X9kGOoZn274tbcOZxV4uWkgnI0+vaXP4hIIqgEwrHWXc+NoZdiBYxwmpX8RNMYkzEe0q6hEguqe+n89sw5NcrACSNlSoIzV39PpFhoPRWB6RQYRnrZm4n/ed0EwuteymScAJVksShMuAORMwvCGTBFCfCpIZgoZm51yAgrTMDEVTIheMsvr5LWRc1za97DZaV+k8dRRMfoBJ0hD12hOrpHDdREBE3QM3pFb1ZmvVjv1seitWDlM0foD6zPH4bOlBA=</latexit><latexit sha1_base64="zRrAquZ34rsr+hINDjElXgUtRkU=">AAAB+3icbVBNS8NAEN3Ur1q/Yj16CbaCp5qIoHgqeNBjBfsBTSmb7aZdursJuxNpCfkrXjwo4tU/4s1/47bNQVsfDDzem2FmXhBzpsF1v63C2vrG5lZxu7Szu7d/YB+WWzpKFKFNEvFIdQKsKWeSNoEBp51YUSwCTtvB+Hbmt5+o0iySjzCNaU/goWQhIxiM1LfLPtAJKJGe31X9kGOoZn274tbcOZxV4uWkgnI0+vaXP4hIIqgEwrHWXc+NoZdiBYxwmpX8RNMYkzEe0q6hEguqe+n89sw5NcrACSNlSoIzV39PpFhoPRWB6RQYRnrZm4n/ed0EwuteymScAJVksShMuAORMwvCGTBFCfCpIZgoZm51yAgrTMDEVTIheMsvr5LWRc1za97DZaV+k8dRRMfoBJ0hD12hOrpHDdREBE3QM3pFb1ZmvVjv1seitWDlM0foD6zPH4bOlBA=</latexit><latexit sha1_base64="zRrAquZ34rsr+hINDjElXgUtRkU=">AAAB+3icbVBNS8NAEN3Ur1q/Yj16CbaCp5qIoHgqeNBjBfsBTSmb7aZdursJuxNpCfkrXjwo4tU/4s1/47bNQVsfDDzem2FmXhBzpsF1v63C2vrG5lZxu7Szu7d/YB+WWzpKFKFNEvFIdQKsKWeSNoEBp51YUSwCTtvB+Hbmt5+o0iySjzCNaU/goWQhIxiM1LfLPtAJKJGe31X9kGOoZn274tbcOZxV4uWkgnI0+vaXP4hIIqgEwrHWXc+NoZdiBYxwmpX8RNMYkzEe0q6hEguqe+n89sw5NcrACSNlSoIzV39PpFhoPRWB6RQYRnrZm4n/ed0EwuteymScAJVksShMuAORMwvCGTBFCfCpIZgoZm51yAgrTMDEVTIheMsvr5LWRc1za97DZaV+k8dRRMfoBJ0hD12hOrpHDdREBE3QM3pFb1ZmvVjv1seitWDlM0foD6zPH4bOlBA=</latexit>
Truncate labels to triads or sevenths:
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 23/31
Experiments and Evaluation
Experimental Setup
Settings:
◦ Epochs: 50 (keep best performance)
◦ Batch-size: 32
◦ GRUs: 128 hidden units
◦ Optimizer: ADAM [Kingma+ 2013]
◦ Data: 80%-10%-10% split
◦ Evaluation: Prediction accuracy & Cohen’s Kappa score [Cohen 1960]
◦ Input chord sequence length: 7 chords
Notes:
◦ Shallow models i.e. reduce influence of network depth
◦ No model fine-tuning to reach optimal performance
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 24/31
Model Comparison on Triads Data
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 25/31
Results:
◦ Model 2 & Model 3 à lower performance than Model 1 (Baseline)
◦ Model 4 à slightly worse than Model 1
à Convert all results to pitch-class (model 4) representation
0.8865
0.8451 0.8465
0.8803
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
Model 1
(Baseline)
Model 2
(Root+Suffix)
Model 3
(Root + Intervals)
Model 4
(Pitch Classes)
Prediction Accuracy
Model Comparison on Sevenths Data
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Results:
◦ Performance drop on both models
◦ Model 1 performed better than Model 4
26/31
0.8865
0.88030.881
0.8622
0.85
0.855
0.86
0.865
0.87
0.875
0.88
0.885
0.89
Model 1 (Baseline) Model 4 (Pitch Classes)
Prediction Accuracy
Triads Sevenths
-1.81%
Discussion: Number of Parameters
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Model 1 à parameters increase from Triads to Sevenths
◦ Triads: 12 roots * 5 suffixes = 60 chord labels
◦ Sevenths: 12 roots * 16 suffixes = 192 chord labels
Model 4 à maintain decent performance with same parameters
27/31
145,215
112,524
229,827
112,524
0
50,000
100,000
150,000
200,000
250,000
Model 1 (Baseline) Model 4 (Pitch Classes)
Neural Network Parameters
Triads Sevenths
Discussion: False-Positives
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Confusion matrices:
◦ Model 1: equal amount of false-positives vs false negatives
◦ Model 4: false-negatives > false-positives
◦ False-positives = dissonant pitches
Model 1
Model 4
28/31
Demo: Afternoon in Paris (by J. Lewis)
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 29/31
Original
Model 1
(Baseline)
Model 4
(Pitch-classes)
# correct notes:
# correct notes:
à Focus on inter-model characteristics, rather than general quality
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 30/31
Conclusion
Conclusion and Future Work
Pitch-class representation à more flexible and reasonable
method
◦ Less DNN parameters required
◦ Less false-positive pitch prediction
Future work:
◦ Extend study with tensions data
◦ Fine-tune models for optimal performance
◦ See if we can apply to other harmonization techniques (e.g. chord
inversions, pitch superposition, etc.)
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 31/31
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 32/31
Appendix
Triads Data
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
+
-
o
sus
Triads data suffix classes
0
50000
100000
150000
200000
Numberofsamples
5 chord classes
major
augmented
minor
diminished
suspended
33/31
+
-
o
sus
Sevenths Data
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
+
+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
16 chord classes
major
augmented
augmented 7th
augmented major 7th
minor
minor 6th
minor 7th
minor major 7th
6th
7th
major 7th
minor 7th flat 5
diminished
diminished 7th
suspended
suspended 7th
34/31
+
+7
+j7
-
-6
-7
-j7
6
7
j7
m7b5
o
o7
sus
sus7
Optimal Chord Sequence Length
Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018
Past chord sequence
Optimal length = ?
35/31

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SIGMUS 夏シンポ2018: ニューラルネットワークによる自動和声付けのための和音表現方法の検討

  • 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 Gmaj<latexit sha1_base64="srGQ6X5mCWTcxP2khSNA0u2qnjU=">AAAB9HicbVDLSgNBEJyNrxhfUY9eFoPgKewGQY8BD3qMYB6QLGF20knGzMyuM73BsOQ7vHhQxKsf482/cZLsQRMLGoqqbrq7wlhwg5737eTW1jc2t/LbhZ3dvf2D4uFRw0SJZlBnkYh0K6QGBFdQR44CWrEGKkMBzXB0PfObY9CGR+oeJzEEkg4U73NG0UpBB+EJtUxvJH2Ydoslr+zN4a4SPyMlkqHWLX51ehFLJChkghrT9r0Yg5Rq5EzAtNBJDMSUjegA2pYqKsEE6fzoqXtmlZ7bj7Qthe5c/T2RUmnMRIa2U1IcmmVvJv7ntRPsXwUpV3GCoNhiUT8RLkbuLAG3xzUwFBNLKNPc3uqyIdWUoc2pYEPwl19eJY1K2ffK/t1FqVrJ4siTE3JKzolPLkmV3JIaqRNGHskzeSVvzth5cd6dj0VrzslmjskfOJ8/UGeSYw==</latexit><latexit 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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 ? 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 Minor 3rd Major 3rd à Simple label identifying the chord ? “Amin”<latexit sha1_base64="9PRN1U0su2znyimUDEsWYud65i4=">AAAB+XicbVBNSwMxEM36WevXqkcvoUXwVHZFsMeKF48V7Ae0S5tNs21okl2S2WJZ+k+8eFDEq//Em//GtN2Dtj4YeLw3w8y8MBHcgOd9OxubW9s7u4W94v7B4dGxe3LaNHGqKWvQWMS6HRLDBFesARwEayeaERkK1grHd3O/NWHa8Fg9wjRhgSRDxSNOCVip57pdYE+gZdbv30quSrOeW/Yq3gJ4nfg5KaMc9Z771R3ENJVMARXEmI7vJRBkRAOngs2K3dSwhNAxGbKOpYpIZoJscfkMX1hlgKNY21KAF+rviYxIY6YytJ2SwMisenPxP6+TQlQNMq6SFJiiy0VRKjDEeB4DHnDNKIipJYRqbm/FdEQ0oWDDKtoQ/NWX10nzquJ7Ff/hulyr5nEU0DkqoUvkoxtUQ/eojhqIogl6Rq/ozcmcF+fd+Vi2bjj5zBn6A+fzB6m1k6A=</latexit><latexit sha1_base64="9PRN1U0su2znyimUDEsWYud65i4=">AAAB+XicbVBNSwMxEM36WevXqkcvoUXwVHZFsMeKF48V7Ae0S5tNs21okl2S2WJZ+k+8eFDEq//Em//GtN2Dtj4YeLw3w8y8MBHcgOd9OxubW9s7u4W94v7B4dGxe3LaNHGqKWvQWMS6HRLDBFesARwEayeaERkK1grHd3O/NWHa8Fg9wjRhgSRDxSNOCVip57pdYE+gZdbv30quSrOeW/Yq3gJ4nfg5KaMc9Z771R3ENJVMARXEmI7vJRBkRAOngs2K3dSwhNAxGbKOpYpIZoJscfkMX1hlgKNY21KAF+rviYxIY6YytJ2SwMisenPxP6+TQlQNMq6SFJiiy0VRKjDEeB4DHnDNKIipJYRqbm/FdEQ0oWDDKtoQ/NWX10nzquJ7Ff/hulyr5nEU0DkqoUvkoxtUQ/eojhqIogl6Rq/ozcmcF+fd+Vi2bjj5zBn6A+fzB6m1k6A=</latexit><latexit sha1_base64="9PRN1U0su2znyimUDEsWYud65i4=">AAAB+XicbVBNSwMxEM36WevXqkcvoUXwVHZFsMeKF48V7Ae0S5tNs21okl2S2WJZ+k+8eFDEq//Em//GtN2Dtj4YeLw3w8y8MBHcgOd9OxubW9s7u4W94v7B4dGxe3LaNHGqKWvQWMS6HRLDBFesARwEayeaERkK1grHd3O/NWHa8Fg9wjRhgSRDxSNOCVip57pdYE+gZdbv30quSrOeW/Yq3gJ4nfg5KaMc9Z771R3ENJVMARXEmI7vJRBkRAOngs2K3dSwhNAxGbKOpYpIZoJscfkMX1hlgKNY21KAF+rviYxIY6YytJ2SwMisenPxP6+TQlQNMq6SFJiiy0VRKjDEeB4DHnDNKIipJYRqbm/FdEQ0oWDDKtoQ/NWX10nzquJ7Ff/hulyr5nEU0DkqoUvkoxtUQ/eojhqIogl6Rq/ozcmcF+fd+Vi2bjj5zBn6A+fzB6m1k6A=</latexit><latexit sha1_base64="9PRN1U0su2znyimUDEsWYud65i4=">AAAB+XicbVBNSwMxEM36WevXqkcvoUXwVHZFsMeKF48V7Ae0S5tNs21okl2S2WJZ+k+8eFDEq//Em//GtN2Dtj4YeLw3w8y8MBHcgOd9OxubW9s7u4W94v7B4dGxe3LaNHGqKWvQWMS6HRLDBFesARwEayeaERkK1grHd3O/NWHa8Fg9wjRhgSRDxSNOCVip57pdYE+gZdbv30quSrOeW/Yq3gJ4nfg5KaMc9Z771R3ENJVMARXEmI7vJRBkRAOngs2K3dSwhNAxGbKOpYpIZoJscfkMX1hlgKNY21KAF+rviYxIY6YytJ2SwMisenPxP6+TQlQNMq6SFJiiy0VRKjDEeB4DHnDNKIipJYRqbm/FdEQ0oWDDKtoQ/NWX10nzquJ7Ff/hulyr5nEU0DkqoUvkoxtUQ/eojhqIogl6Rq/ozcmcF+fd+Vi2bjj5zBn6A+fzB6m1k6A=</latexit> 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 ? 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 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. Cmaj7<latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit><latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit><latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit><latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit> 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 <latexit sha1_base64="T/IHIPRqxYL4tJaKLJitsphkiCA=">AAACAHicbVBNS8NAEJ3Ur1q/oh48eFksgqeSiFCPBRE8VrAf0MSy2W7atbtJ2N0IJeTiX/HiQRGv/gxv/hs3bQ/a+mDg8d4MM/OChDOlHefbKq2srq1vlDcrW9s7u3v2/kFbxakktEViHstugBXlLKItzTSn3URSLAJOO8H4qvA7j1QqFkd3epJQX+BhxEJGsDZS3z7yBNYjKbLr+8wLOdZI4Id6nvftqlNzpkDLxJ2TKszR7Ntf3iAmqaCRJhwr1XOdRPsZlpoRTvOKlyqaYDLGQ9ozNMKCKj+bPpCjU6MMUBhLU5FGU/X3RIaFUhMRmM7iXLXoFeJ/Xi/V4aWfsShJNY3IbFGYcqRjVKSBBkxSovnEEEwkM7ciMsISE20yq5gQ3MWXl0n7vOY6Nff2otpw5nGU4RhO4AxcqEMDbqAJLSCQwzO8wpv1ZL1Y79bHrLVkzWcO4Q+szx/p55aJ</latexit><latexit 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Experiments: Four chord representations ◦ Trained on recurrent neural nets (RNN) Two datasets ◦ Of different chord complexity
  • 9. Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 9/31 Chord Representations
  • 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.: Cmaj7<latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit><latexit 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  • 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 Cmaj7<latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit><latexit 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  • 13. 4. Pitch Classes Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 13/31 Constituting pitches C E G B Cmaj7<latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit><latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit><latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit><latexit sha1_base64="qjIEF530p3AqxTnxbVZVK5+ENFc=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBA8hV0RIp4CuXiMYB6QxDA76U3GzOwuM71qWPIfXjwo4tV/8ebfOEn2oIkFDUVVN91dfiyFQdf9dlZW19Y3NnNb+e2d3b39wsFhw0SJ5lDnkYx0y2cGpAihjgIltGINTPkSmv6oOvWbD6CNiMJbHMfQVWwQikBwhla66yA8oVZpVbH78qRXKLoldwa6TLyMFEmGWq/w1elHPFEQIpfMmLbnxthNmUbBJUzyncRAzPiIDaBtacgUmG46u3pCT63Sp0GkbYVIZ+rviZQpY8bKt52K4dAselPxP6+dYHDZTUUYJwghny8KEkkxotMIaF9o4CjHljCuhb2V8iHTjKMNKm9D8BZfXiaN85Lnlrybi2LlKosjR47JCTkjHimTCrkmNVInnGjyTF7Jm/PovDjvzse8dcXJZo7IHzifP8o0kqg=</latexit> 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
  • 14. Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 14/31 Neural Network Models
  • 15. Task Definition Predict chord from: current melody & past chord sequence Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 Answer: Past chord sequence Current melody Melody sequence Chord sequence RNN RNN Chord prediction 15/31 Only chord representation changes across models
  • 16. Model 1: Chords Labels Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 E[maj7 <latexit sha1_base64="T/IHIPRqxYL4tJaKLJitsphkiCA=">AAACAHicbVBNS8NAEJ3Ur1q/oh48eFksgqeSiFCPBRE8VrAf0MSy2W7atbtJ2N0IJeTiX/HiQRGv/gxv/hs3bQ/a+mDg8d4MM/OChDOlHefbKq2srq1vlDcrW9s7u3v2/kFbxakktEViHstugBXlLKItzTSn3URSLAJOO8H4qvA7j1QqFkd3epJQX+BhxEJGsDZS3z7yBNYjKbLr+8wLOdZI4Id6nvftqlNzpkDLxJ2TKszR7Ntf3iAmqaCRJhwr1XOdRPsZlpoRTvOKlyqaYDLGQ9ozNMKCKj+bPpCjU6MMUBhLU5FGU/X3RIaFUhMRmM7iXLXoFeJ/Xi/V4aWfsShJNY3IbFGYcqRjVKSBBkxSovnEEEwkM7ciMsISE20yq5gQ3MWXl0n7vOY6Nff2otpw5nGU4RhO4AxcqEMDbqAJLSCQwzO8wpv1ZL1Y79bHrLVkzWcO4Q+szx/p55aJ</latexit><latexit 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  • 17. Model 2: Root Label + Suffix Label Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 E[ <latexit sha1_base64="mQP5BET8mnlzevrgA2nV1eVOPJ4=">AAAB+3icbVDLSsNAFJ3UV62vWJduBovgqiQi6LIggssK9gFNLJPppB06mYSZG7GE/IobF4q49Ufc+TdO2iy09cDA4Zx7uWdOkAiuwXG+rcra+sbmVnW7trO7t39gH9a7Ok4VZR0ai1j1A6KZ4JJ1gINg/UQxEgWC9YLpdeH3HpnSPJb3MEuYH5Gx5CGnBIw0tOteRGCiouzmIfNCQSDPh3bDaTpz4FXilqSBSrSH9pc3imkaMQlUEK0HrpOAnxEFnAqW17xUs4TQKRmzgaGSREz72Tx7jk+NMsJhrMyTgOfq742MRFrPosBMFkn1sleI/3mDFMIrP+MySYFJujgUpgJDjIsi8IgrRkHMDCFUcZMV0wlRhIKpq2ZKcJe/vEq6503Xabp3F42WU9ZRRcfoBJ0hF12iFrpFbdRBFD2hZ/SK3qzcerHerY/FaMUqd47QH1ifP6yblMg=</latexit><latexit 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  • 18. Model 3: Root Label + Suffix Intervals Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 Binary vector • 1 = semitone • 0 = no semitone 18/31 Root (blue) will always be present
  • 19. Model 4: Pitch Classes Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 19/31 Binary vector • 1 = pitch • 0 = no pitch
  • 20. Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 20/31 Datasets
  • 21. Dataset Overview Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 Weimar Jazz Database - 456 Jazz solos [Abeßer+ 2013] ◦ Song selection: ◦ Keep 4/4 time signature ◦ More than 2 chords involved ◦ Data augmentation: ◦ Transpose songs to 11 remaining tones (original size * 12) ◦ Melody: ◦ Bring to octave, i.e. 12 pitches ◦ Chords: ◦ 2 datasets of different chord complexity 21/31
  • 22. 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  • 23. Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 23/31 Experiments and Evaluation
  • 24. Experimental Setup Settings: ◦ Epochs: 50 (keep best performance) ◦ Batch-size: 32 ◦ GRUs: 128 hidden units ◦ Optimizer: ADAM [Kingma+ 2013] ◦ Data: 80%-10%-10% split ◦ Evaluation: Prediction accuracy & Cohen’s Kappa score [Cohen 1960] ◦ Input chord sequence length: 7 chords Notes: ◦ Shallow models i.e. reduce influence of network depth ◦ No model fine-tuning to reach optimal performance Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 24/31
  • 25. Model Comparison on Triads Data Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 25/31 Results: ◦ Model 2 & Model 3 à lower performance than Model 1 (Baseline) ◦ Model 4 à slightly worse than Model 1 à Convert all results to pitch-class (model 4) representation 0.8865 0.8451 0.8465 0.8803 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 Model 1 (Baseline) Model 2 (Root+Suffix) Model 3 (Root + Intervals) Model 4 (Pitch Classes) Prediction Accuracy
  • 26. Model Comparison on Sevenths Data Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 Results: ◦ Performance drop on both models ◦ Model 1 performed better than Model 4 26/31 0.8865 0.88030.881 0.8622 0.85 0.855 0.86 0.865 0.87 0.875 0.88 0.885 0.89 Model 1 (Baseline) Model 4 (Pitch Classes) Prediction Accuracy Triads Sevenths -1.81%
  • 27. Discussion: Number of Parameters Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 Model 1 à parameters increase from Triads to Sevenths ◦ Triads: 12 roots * 5 suffixes = 60 chord labels ◦ Sevenths: 12 roots * 16 suffixes = 192 chord labels Model 4 à maintain decent performance with same parameters 27/31 145,215 112,524 229,827 112,524 0 50,000 100,000 150,000 200,000 250,000 Model 1 (Baseline) Model 4 (Pitch Classes) Neural Network Parameters Triads Sevenths
  • 28. Discussion: False-Positives Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 Confusion matrices: ◦ Model 1: equal amount of false-positives vs false negatives ◦ Model 4: false-negatives > false-positives ◦ False-positives = dissonant pitches Model 1 Model 4 28/31
  • 29. Demo: Afternoon in Paris (by J. Lewis) Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 29/31 Original Model 1 (Baseline) Model 4 (Pitch-classes) # correct notes: # correct notes: à Focus on inter-model characteristics, rather than general quality
  • 30. Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 30/31 Conclusion
  • 31. Conclusion and Future Work Pitch-class representation à more flexible and reasonable method ◦ Less DNN parameters required ◦ Less false-positive pitch prediction Future work: ◦ Extend study with tensions data ◦ Fine-tune models for optimal performance ◦ See if we can apply to other harmonization techniques (e.g. chord inversions, pitch superposition, etc.) Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 31/31
  • 32. Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 32/31 Appendix
  • 33. Triads Data Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 + - o sus Triads data suffix classes 0 50000 100000 150000 200000 Numberofsamples 5 chord classes major augmented minor diminished suspended 33/31 + - o sus
  • 34. Sevenths Data Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 + +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 16 chord classes major augmented augmented 7th augmented major 7th minor minor 6th minor 7th minor major 7th 6th 7th major 7th minor 7th flat 5 diminished diminished 7th suspended suspended 7th 34/31 + +7 +j7 - -6 -7 -j7 6 7 j7 m7b5 o o7 sus sus7
  • 35. Optimal Chord Sequence Length Aug 21st 2018 SIGMUS SUMMER SYMPOSIUM 2018 Past chord sequence Optimal length = ? 35/31