“Index” in “Connectionist Representations of Tonal Music”
Index
activation function, 42–45, 57, 71–72, 116, 222, 254, 256
Gaussian, 44, 57–58, 65, 85–86, 190, 195, 222
logistic, 42–43, 71, 106, 112, 220, 226–227
algorithmic level, 261–262, 267
artificial neural network(s): activation function, 42–43
classifying musical patterns, previous work, 54–55
definition of, 4–5
description of function, 29–30
examples of use to identify musical patterns, 30–35
multilayer perceptrons, kind of, 69–70
simple perceptrons, kind of, 56–67
backpropagation of error, 70–71
Bonini’s paradox, 38–40
chord inversions, 214, 236, 269
chord progressions, 7, 88, 209–210, 232–233, 248–249, 253
circle(s) of fifths, 21
circle(s) of major seconds, 136–137, 142, 177, 179, 258, 265–266
circle(s) of major sevenths, 133
circle(s) of major sixths, 138, 141
circle(s) of major thirds, 139, 141, 186, 233, 244–247, 266
circle(s) of minor seconds, 24, 51–53, 60, 65, 79, 98, 132–135, 141, 171, 263
circle(s) of minor sevenths, 137
circle(s) of minor sixths, 139, 141
circle(s) of minor thirds, 137, 152, 166, 182, 184
circle(s) of perfect fifths, 82, 133–135, 141, 230, 233–234, 244
circle(s) of perfect fourths, 133–134
circle(s) of tritones, 125, 166, 172, 177, 179, 184
circles of intervals, 130, 141, 144, 156, 159
classical cognitive science, 5, 15–16, 18, 24, 29, 37, 39, 45, 102–103, 251
coarse coding, 6–7, 101–103, 116–117, 199–200, 203, 205, 259–260, 270
cognitivism, 5, 9, 16–18, 25–27, 269–270
Coltrane changes, 7, 209, 232–248
composing, 33–34, 89, 246, 265–267
computational level, 261–262, 267
connectionist cognitive science, 5, 26–29, 37, 39, 45, 48, 102, 251–252, 262, 272
connection weight structure, 175, 191, 200–201
consonance, 10, 12–15, 26, 256, 271
design decisions, 18, 41, 72, 253, 269, 272
enharmonic equivalence, 51
equal temperament, 11–14
equivalence class, 7, 136, 141–142, 157, 166, 258
extended tetrachord, 7, 174–177, 180, 186, 197, 200, 203, 205–206, 259–260
Forte number, 144–145, 170–171, 262, 271
forward engineering, 254–255
frequency, 9–12, 14, 34, 50–51, 145
function approximation, 33
fundamental frequency, 14, 34, 50
Gaussian. See activation function, Gaussian
“gee whiz” connectionism, 39
generalized delta rule, 71, 73, 94, 123, 147, 174
gradient descent learning, 57
harmony, 6, 9–10, 33–34, 111, 119, 128, 209, 269
Helmholtz, Hermann, 14–17, 35, 38
hidden unit space, 74–75, 80–90, 95–98, 148–149, 159–163, 165–166, 175, 257–258, 260, 264
implementational level, 261, 271
integration device, 43–44, 221–224
interference, 14
internal structure, 4–7, 37–49, 72, 169, 222, 251–255, 271–272
interval class vector, 86
interval cycle(s), 119, 124, 127–134, 136–138, 140–141, 166–167, 206
jazz, 7, 88, 134, 170, 209–210, 213, 232–233, 246, 254
jittered density plot, 175–178, 180–181, 183–189, 191, 193–201, 204
key-finding, 6, 91–100, 103–115, 117–118, 253–254
Krumhansl, Carol, 18–22, 40–41, 91–92, 102–105, 116–117, 228, 230, 253, 268–270
Krumhansl-Schmuckler algorithm, 104–105, 107, 110, 115
logistic function, 42, 222, 226
mathematics, 4, 9, 11, 16, 26, 53, 57
mechanical philosophy, 9–10, 15, 26
missing fundamental, 34
mode, 6, 19, 67, 72–76, 85–87, 92–96, 99–101, 115–116, 255, 257, 262, 264
multidimensional scaling, 21, 60, 82–83
musical aesthetics, 13–15, 26, 35, 38
musical cognition, 25–27, 35, 37–41, 207, 249–250, 253, 260–261, 267, 269–272
musical cognitivism, 17, 25–27, 45, 270
musical intervals, 9–12, 19, 50, 86–87, 124–125, 127, 129, 133, 144–145, 166–167, 186, 209, 255–256, 258
musical set theory, 144, 262–263, 271
music perception, 5, 14–15, 35, 91, 104
network interpretation, 41–42, 45, 112, 128, 223, 241, 244, 256, 260, 270
networks of value units, 42, 44, 73, 94, 123, 127, 147, 174, 220, 248
neuron doctrine, 99
octave equivalence, 18, 41, 50–51, 124, 126–127, 142, 215–216, 263
partials, 14
pattern recognition, 32–33, 46, 54, 67, 272
physiology, 14–15
pitch encoding, 122, 214–216, 218, 220–222, 236–238
probe tone method, 19, 229, 268, 271
Pythagorean comma, 10–11
Pythagorean ratios, 11–12
Pythagorean tuning, 10–11
readiness-to-hand, 212
reverse engineering, 249, 254–255
Romanticism, 15, 26, 36–38, 47, 252–253
roughness, 14–15
scale(s): mode, 67, 72–76, 80, 85–86, 89, 94, 99–100, 115, 142, 248, 255, 257, 264
tonic, 41, 49, 54–63, 66–67, 72–74, 81, 94, 99, 113, 115–116, 248, 254–255, 260, 262, 264
set theory, 46, 86, 144–145, 171, 262–263, 271
Shepard tone, 23
strange circle(s), 7, 119, 128, 141–142, 147, 166–167, 169, 184, 206, 209, 255, 258–259, 262–263, 265–267, 270
supervised learning, 32, 39–41, 46, 48, 57, 70–71, 253
synthetic psychology, 47, 49, 254–256
tempered scale, 10–12
tonal hierarchy, 18–22, 25, 33, 91–92, 104, 117, 228–230, 269–270
tonality, 7–8, 19, 33–34, 52, 104, 119, 141, 209, 256, 261, 271
triad, 6–7, 87–89, 119–128, 143–144, 169–770, 257–259, 268
trigger features, 99
tritone balance, 78–80, 85, 89, 126, 152, 195, 197, 201, 257–258, 263
tritone equivalence, 125–127, 151, 155, 159, 257–258, 263
tritone paradox, 22–25
unconscious inference, 17–18
unsupervised learning, 39–40
value unit, 42–46, 72–73, 77, 95–97, 160–163, 175–176, 220, 222, 238–241, 248, 256, 259, 264
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