classification of triadic chord inverstions using kohonen self-organizing maps
DESCRIPTION
Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps. Luis Felipe de Oliviera, Luis Guilherme Pereira Lima, Andre Luiz Goncalves de Oliveria, Rael Bertarelli Gimenes Toffolo. Schönberg’s Hypothesis. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/1.jpg)
Classification of Triadic Chord Inverstions Using Kohonen
Self-Organizing MapsLuis Felipe de Oliviera, Luis
Guilherme Pereira Lima, Andre Luiz Goncalves de Oliveria, Rael
Bertarelli Gimenes Toffolo
![Page 2: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/2.jpg)
Schönberg’s Hypothesis
“The second inversion, as he argues, has an ambiguity constitution, being it related to its root position chord and to a chord a fifth above. This ambiguity has been lead to specific harmonic rules in the attempt to characterize the function of this chord.”
![Page 3: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/3.jpg)
Inversion
• A chord's inversion describes the relationship of its bass to the other tones in the chord. For instance, a C major triad contains the tones C, E and G; its inversion is determined by which of these tones is used as the bottom note in the chord.
![Page 4: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/4.jpg)
Inversion cont’d
• The term inversion is often used to categorically refer to the different possibilities, although it may also be restricted to only those chords where the bass note is not also the root of the chord (see root position below). In texts that make this restriction, the term position may be used instead to refer to all of the possibilities as a category.
• http://en.wikipedia.org/wiki/Inversion_(music)
![Page 5: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/5.jpg)
Harmonic Partials
![Page 6: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/6.jpg)
Kohenen SOM Details
• Input Pattern: 252 Chords (21 for each of the 12 tonalities
• SOM Network 50 X 50 (2500 units)• Neighborhood Radius: starting with 30,
ending at 1.• Learning rate of .1 and neighborhood
learning rate of .037
![Page 7: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/7.jpg)
Running
1500 iterations, error goes to nothing.
![Page 8: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/8.jpg)
Topological Map
![Page 9: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/9.jpg)
3D topology
![Page 10: Classification of Triadic Chord Inverstions Using Kohonen Self-Organizing Maps](https://reader035.vdocument.in/reader035/viewer/2022062309/5681448f550346895db12abe/html5/thumbnails/10.jpg)
SOM Chord Topology