Data and Sounds from psychoacoustic experiments
"The dependency of timbre of musical on fundamental frequency "

Experiments made by:

Jeremy Marozeau , Alain de Cheveigné , Stephen McAdams and Suzanne Winsberg.

Musical Perception and Cognition Team at Ircam

download here the submited version of the article

Summary: Goal, Stimuli, Results: Exp. I, Exp. II, Exp. III

Goal:

The dependency of the timbre of musical sounds on their fundamental frequency (F0) was examined through three timbre dissimilarity experiments. In the first experiment (Exp. I), subjects judged timbre dissimilarity between pairs of stimuli produced by a set of twelve musical instruments with equal F0, duration and loudness. There were three sessions, each at a different F0 (Exp. Ia at B2, 247 Hz; Exp. Ib at C#3, 277 Hz, and Exp. Ic at Bb3, 466 Hz). In the second experiment (Exp II) the same stimuli were rearranged in pairs always having the same difference in F0. There were two sessions, each involving a different magnitude of F0 difference (Exp. IIa : B2 with C#3, Exp. IIb B2 with Bb3), and subjects were instructed to ignore the difference in pitch. In the third experiment, a subset of the same instruments were paired both with and without an F0 difference, and all pairs were presented within the same session. There were two sessions, each involving the same different magnitude of F0 difference, as in Experiment II (Exp. IIIa : B2 with C#3, Exp. IIIb B2 with Bb3). Experiment 1 produced dissimilarity matrices that were similar at different F0 s, suggesting that the relative positions of instruments within timbre space varied little with changes in F0. Experiment 2 produced dissimilarity matrices that were symmetrical, suggesting further that absolute displacements within timbre space are also small, at least compared to between-instrument dissimilarities. Patterns of dissimilarity were similar with or without an F0 difference, showing that subjects could ignore a constant difference in pitch when making timbre dissimilarity judgments. Experiment 3 extended this result to the case where the stimulus set included pairs both with and without an F0 difference, showing that subjects could ignore a variable difference in pitch. Dissimilarity scores were also subjected to multidimensional scaling, and produced solutions (timbre spaces) that varied little across conditions and experiments. Taken together, the results suggest that the perception of timbre is relatively independent from pitch at least with pitch difference smaller than an octave, and can be abstracted across differences in fundamental frequency.

Stimuli:

Ten natural and two synthetic instruments were used. Each instrument was played at three notes: B2 (247 Hz), C#3 (277 Hz) and Bb3 (466 Hz), chosen to explore the effects of a small difference (two semitones) and a moderate difference (eleven semitones) of F0. Natural instrument samples were extracted from the Studio On Line (SOL) database of Ircam : a guitar (B2 was played on the E string, C#3 on the A string, and Bb3 on the D string), a harp, a violin pizzicato (the B2 and the C#3 notes were played on the G string, the Bb3 on the D string), a bowed violin (strings were the same as for the violin pizzicato), a bowed double bass (all notes were played on the G string), an oboe, a clarinet, a flute, a horn in F, a trumpet in C. In the following, these instruments will be abbreviated as Gu, Hr, Vp, Vl, Ba, Ob, Cl, Fl, Ho, Tr, respectively. In addition to these natural instruments, two synthetic instruments were built with the help of the analysis/synthesis programs ADDITIVE. A natural saxophone note (B2, mezzo forte) was analyzed to estimate the time-varying spectral envelope of the harmonic partials (the residual inharmonic part was discarded). Based on this envelope three sounds were produced, at B2, C#3 and Bb3. This instrument was named 'SA'. A second instrument was created by stretching the same spectrotemporal envelope along the frequency axis by a ratio of 1.89, corresponding to the F0 ratio between B2 and Bb3. This was used to synthesize three sounds at B2, C#3 and Bb3. This instrument was named 'SB'. The spectrum of SB at Bb3 is a dilated version of the spectrum of SA at B2 (partials of same rank have the same amplitude). Thus, the stimulus set contains two stimuli that share the same spectrotemporal envelope in terms of rank across F0, as well as several that share the same envelope in terms of frequency. All stimuli were clipped to the same duration of 1.5 s by applying a 200 ms cosinusoidal offset ramp after 1.3 s. Amplitudes were adjusted to obtain equal subjective loudness when the stimuli were presented at approximately 60 dB SPL. Stimuli were sampled at a rate of 44100 Hz, and presented diotically over Sennheiser 520 II headphones.

Click here to download all the stimuli

Results:

Exp. I:

Stimuli compared pairwise with the same F0.
One F0 per matrix, 24 subjects, 12 stimuli (66 pairs)
-> matrix 12 X 66, one subject per line, pairs are set as follow:
Instrument Gu Hr Vp Vl Bs SA SB Ob Cl Fl Ho Tr
Guitar . . . . . . . . . . . .
Harp 1 . . . . . . . . . . .
Violin Pizz. 2 3 . . . . . . . . . .
Violin Bowed 4 5 6 . . . . . . . . .
Bass 7 8 9 10 . . . . . . . .
Synth A 11 12 13 14 15 . . . . . . .
Synth B 16 17 18 19 20 21 . . . . . .
Oboe 22 23 24 25 26 27 28 . . . . .
Clarinet 29 30 31 32 33 34 35 36 . . . .
Flute 37 38 39 40 41 42 43 44 45 . . .
Horn 46 47 48 49 50 51 52 53 54 55 . .
Trumpet 56 57 58 59 60 61 62 63 64 65 66 .

download :


MDS solution:

A two dimensional space with specificities, (two classes of subject) was found with the help Clascal Software

Space Exp. 1a
Space Exp. 1a
Space Exp. 1b
space Exp. 1b
Space Exp. 1c
space Exp. 1c


The data are written in a matrix 12 X 3 set as follow:

Instrument Dimension 1 Dimension 2 Specificities
Guitar . . .
Harp . . .
Violin Pizz. . . .
Violin Bowed . . .
Bass . . .
Synth A . . .
Synth B . . .
Oboe . . .
Clarinet . . .
Flute . . .
Horn . . .
Trumpet . . .

download :

Exp. II:

Stimuli compared pairwise with the same difference of F0.
Two F0s per matrix, 24 subjects, 12 stimuli (144 pairs)
-> matrix 12 X 144, one subject per line, pairs are set as follow:
F0_2 \ F0_1 Gu Hr Vp Vl Bs SA SB Ob Cl Fl Ho Tr
Guitar 1 2 3 4 5 6 7 8 9 10 11 12
Harp 13 14 15 16 17 18 19 20 21 22 23 24
Violin Pizz. 25 26 27 28 29 30 31 32 33 34 35 36
Violin Bowed 37 38 39 40 41 42 43 44 45 46 47 48
Bass 49 50 51 52 53 54 55 56 57 58 59 60
Synth A 61 62 63 64 65 66 67 68 69 70 71 72
Synth B 73 74 75 76 77 78 79 80 81 82 83 84
Oboe 85 86 87 88 89 90 91 92 93 94 95 96
Clarinet 97 98 99 100 101 102 103 104 105 106 107 108
Flute 109 110 111 112 113 114 115 116 117 118 119 120
Horn 121 122 123 124 125 126 127 128 129 130 131 132
Trumpet 133 134 135 136 137 138 139 140 141 142 143 144

download :

Exp. III:

Stimuli compared pairwise with or without a difference of F0.
Two F0s per matrix, 22 subjects for Exp. IIIa, 18 for Exp. IIIb, 18 stimuli (156 pairs) -> matrix 22 (or 18) X 153, one subject per line, pairs are set as follow:

Instrument Gu 1 Hr 1 Vp 1 Vl 1 SA 1 Ob 1 Cl 1 Ho 1 Tr 1 Gu 2 Hr 2 Vp 2 Vl 2 SA 2 Ob 2 Cl 2 Ho 2 Tr 2
Guitar 1 . . . . . . . . . . . . . . . . . .
Harp 1 1 . . . . . . . . . . . . . . . . .
Violin P. 1 2 3 . . . . . . . . . . . . . . . .
Violin B. 1 4 5 6 . . . . . . . . . . . . . . .
Synth A 1 7 8 9 10 . . . . . . . . . . . . . .
Oboe 1 11 12 13 14 15 . . . . . . . . . . . . .
Clarinet 1 16 17 18 19 20 21 . . . . . . . . . . . .
Horn 1 22 23 24 25 26 27 28 . . . . . . . . . . .
Trumpet 1 29 30 31 32 33 34 35 36 . . . . . . . . . .
Guitar 2 37 38 39 40 41 42 43 44 45 . . . . . . . . .
Harp 2 46 47 48 49 50 51 52 53 54 55 . . . . . . . .
Violin P. 2 56 57 58 59 60 61 62 63 64 65 66 . . . . . . .
Violin B. 2 67 68 69 70 71 72 73 74 75 76 77 78 . . . . . .
Synth A 2 79 80 81 82 83 84 85 86 87 88 89 90 91 . . . . .
Oboe 2 92 93 94 95 96 97 98 99 100 101 102 103 104 105 . . . .
Clarinet 2 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 . . .
Horn 2 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 . .
Trumpet 2 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 .

download :

MDS solution

A four-dimensional space without specificities, (one class of subject) was found for the Exp. IIIa,
and a four dimensional space without specificities, (one class of subject) was found for the Exp. IIIb.
The point represents the position of the instrument at the low F0 (B2), the end of line represents the position of the same instrument at high F0 (C#3 for Exp. IIIa, Bb3 for Exp. IIIb).
Space Exp. IIIa dim1 versus dim2 sp3a_12.jpg
Space Exp. IIIa dim3 versus dim4 sp3a_34.jpg
Space Exp. IIIb dim1 versus dim2 sp3b_12.jpg
Space Exp. IIIb dim3 versus dim4 sp3b_34.jpg

download :

Matrix space are in the size 18 X 3 (for Exp. IIIa) and 18 X 4 (for Exp IIIb). There is one instrument per row (the order are the same as the above matrix), and one dimension per column.