Christoph
Reuter1, Isabella Czedik-Eysenberg1,4, Dijana Popovic2, Esther Rois-Merz3, Fatima
Gerendas Obiols1,3,
Marik Roos1, Sarah Ambros1, Jörg Jewanski1, Felix Klooss2, Michael Oehler4,
Anja-Xiaoxing Cui1
1Musicological
Department, University of Vienna, 2MediaLab, University of Vienna,
3Audienz, Hearing Examination, Vienna, 4Musicological
Department, Osnabrück University
■
=
reduced hearing at 2-4 kHz ■ =
better hearing at 2-4 kHz
envelope
1 (e1)
envelope
2 (e2)
envelope
3 (e3)
envelope
4 (e4)
C->F#
0.71
F#->C
0.31
C#->G
0.78
G->C#
0.30
D->G#
0.79
G#->D
0.22
D#->A
0.63
A->D#
0.31
E->A#
0.67
A#->E
0.46
F->B
0.44
B->F
0.56
C->F#
0.32
F#->C
0.74
C#->G
0.32
G->C#
0.78
D->G#
0.32
G#->D
0.71
D#->A
0.32
A->D#
0.71
E->A#
0.47
A#->E
0.61
F->B
0.64
B->F
0.25
C->F#
0.87
F#->C
0.23
C#->G
0.89
G->C#
0.29
D->G#
0.88
G#->D
0.36
D#->A
0.73
A->D#
0.47
E->A#
0.50
A#->E
0.56
F->B
0.21
B->F
0.78
C->F#
0.62
F#->C
0.60
C#->G
0.59
G->C#
0.63
D->G#
0.64
G#->D
0.60
D#->A
0.61
A->D#
0.51
E->A#
0.58
A#->E
0.59
F->B
0.68
B->F
0.51
Perceived
interval direction for stimuli with e1,
e2, e3,
and e4 envelopes Selected envelope: e1
Select an
envelope (e1,
e2,
e3,
ore4),
move the mouse over the curves and listen if the interval rises or falls
Interval
direction for stimuli with e4 envelopes
perceived by worse and better
hearers
Click on
the graph, move the mouse over the curves and listen if the interval
rises or falls
Is
there an explanation for the tritone paradox?
Shepard tones
are sounds composed only of sine waves at octave intervals whose
amplitudes become smaller and smaller toward the limits of our hearing range.
Because of this construction, Shepard tones are heard as infinitely ascending
or descending. Listen to a typical Shepard scale here:
Volume:
The tritone
paradox describes the acoustic phenomenon that two Shepard notes
spaced an augmented fourth apart (tritone, exactly in the middle of
an octave) can no longer be clearly identified as rising or
falling.
However, when
the direction of randomly played (Shepard) tritone intervals is to
be estimated and the results are arranged according to pitch classes, a clear
pitch class boundary can be found usually at or near the tritone C/F#,
above which subjects consistently recognize a (Shepard) tritone interval as
ascending or descending
The stimuli
officially used most often for Shepard tritone experiments are each composed
of only six partials and run under four envelopes while their
peaks are one tritone apart from each other (e1-e4 with peaks at 300,
450, 600 and 900 Hz).
However, partials of the highest envelope (e4) are particularly present
at the outer ear's resonant frequency at 2-4 kHz, where we hear specifically
well. Consequently, the stimuli of the highest envelope may bias the
average across envelopes.
Select arbitrary
tritone intervals from the tables below and hear for yourself whether
you perceive the respective interval as ascending or descending. >0.5 = tritone is perceived as ascending by most participants, <0.5 = tritonus is perceived as descending by most participants.
On the right
side you can select the different hearing thresholds of the participants.
