| Reading Materials for Final |
| Reading Materials |
all materials will be on reserve in CCRMA's library located on the 2nd floor of the Knoll
| January 21 |
January 21 |
Critical Bands and Cochlear Place, Donald Greenwood
read abstract and introduction
Greenwood, D.D. (1990) "A Cochlear Frequency-Position Function for
Several Species -29 Years Later," J. of Acoustical Society of America
87, 2592-2605 [An updated review of the frequency-position function
as indicated by the title]
read abstract and introduction
Greenwood, D.D. (1991) "Critical bandwidth and consonance: In
relation to cochlear frequency-position coordinates." Hear. Res. 54,
164-208 [Includes report of the origin of Zwicker, et al. critical
bandwidth function and compares its fit of the early critical band
data to the fit of Greenwood's CB function]
Frequency Analysis and Masking, Brian Moore
read to page 47
Cochlear Structure and Function, Graeme Yates
Some might think that a critical consideration of the Mel Scale
(Stevens and Volkmann, 1940) constitutes beating a dead (or at least
moribund) horse. But that horse is still leaning against the stable
wall and is mounted occasionally by persons uninformed of its
condition. Moreover, there is still some interest in the scale's
Stevens (and later Zwicker) had hypothesized that equal pitch
differences corresponded to equal distances in the cochlea (and to
equal fractions or multiples of critical bandwidth) but not to equal
frequency ratios - a contrasted hypothesis [hence musical intervals
would not correspond to equal pitch differences, which bothered some
musicians]. However, data commissioned by Stevens in 1956 (Greenwood,
1997a,b), indicates (a) bias in the Mel Scale of 1940 and (b) a
correspondence of the 'new' (1956) equal pitch differences to both
equal cochlear distances and (nearly as well) to equal frequency
This is an agreement that is inevitable if the cochlea is
approximately logarithmic between 400 and 7000 Hz (as it appears to
be) AND IF either hypothesis (equal-distance or equal-ratio) is
correct. Both rise equivocally, or fall, together unless an
equisected interval is large enough and extends into the apical
These points and others related (a) to possible ways to discriminate
the hypotheses, (b) to differences between musical and non-musical
subjects in judging 'equivalence', and (c) to musical intervals
converted to cochlear distances will be illustrated.
Some might also think that the Bark Scale reflects the cochlear map
and that it is based on early critical band data. However, the
'classical' critical-band curve's SHAPE was actually based mainly on
frequency DL data (Shower and Biddulph, 1933) - and not on critical
band data (Feldtkeller and Zwicker, 1953; Gässler, 1954).
Two empirical and hypothetical frequency-position functions
(Steinberg, 1937; Stevens and Davis, 1936) were used by Feldtkeller
and Zwicker to extract graphically two derivative curves. They then
drew a visual mean (Mittelwert) derivative curve between the two
original curves. That Mittelwert derivative was later used (after
flattening below 300 Hz) as the critical band CURVE, after having
been ordinate-shifted into an approximate agreement with just the
central portion of some early critical band DATA (Zwicker et al.,
1957), who presented the CURVE also as a TABLE. [Unfortunately, the
CURVE and TABLE markedly disagree in shape with the path of the DATA
(Zwicker, 1952, 1954; Gassler, 1954) below 500 Hz and above 3 kHz.]
In 1958-9 Greenwood used the Zwicker et al critical bandwidth TABLE
of 1957 to construct a hypothetical frequency-position scale - in
effect an integral of the critical band TABLE (revising above 3 kHz)
- on which to plot and compare masked audiograms (Greenwood, 1960,
61a,b). Using the same CURVE and TABLE, Zwicker (1961) constructed an
essentially identical (below 3 kHz) frequency-position scale, which
he named the Bark Scale.
In Greenwood (1961b) an alternative critical band function was also
suggested in mathematical form, which fits the critical band DATA
quite well above 400 Hz (and much better than the critical band CURVE
of 1957, 61, or 80 - cf Greenwood, 1991). It also fits two-tone
consonance data from about 100 Hz to 3 kHz (Mayer, 1894; Plomp and
Steeneken, 1965; and Plomp and Steeneken, 1968, Greenwood, 1991).
The integral of the mathematical CB function also yields a putative
frequency-position function, which well fits cochlear maps of several
species (Greenwood, 1961b, 1974, 1990, 1996). It also permits
calculation of distances subtended by tones - to be used, for
example, to plot two-tone consonance, musical ratios, 3-dB
Modulation TF bandwidths, Q-10s, etc. vs cochlear distance.
Timbre evaluation based on auditory information processing , Miriam N. Valenzuela
read all, this is an excellent starting point for
introduction into the timbre literature
Handel, S. (1995) "Timbre Perception and Auditory Object Recognition"
In B.C.J. Moore (Ed.), Hearing. New York: Academic Press.
read all, this is to my mind the
best paper I have read on timbre identification. Summarizes
and obviates the need to wade through the many articles that
have been written on automatic timbre identification.
Martin, Keith and Kim Youngmoo (1998) "Musical Instrument Identification:
A Pattern Recognition Approach" Presented at 136th Meeting of ASA,
read to page 93, This is a retrospective article which
summarizes work that has been done on
the multidimensional perceptual representation of timbre.
Explains Multi dimensional scaling (MDS) a statistical
techinique which has proved to have much power in allowing
us to conceptualize timbre space.
McAdams, Stephen (1999) "Perspectives on the Contribution of Timbre to Musical S tructure" Computer Music Journal Fall 1999,
The sense of hearing plays an important role in acoustic
investigations of musical instruments. Therefore the processing of a
musical sound signal through the auditory system must be considered
properly. A method will be presented with which the signal parameters
that are relevant to hearing can be extracted out of the audio
signal. With this method a distinct reduction of the data necessary
for the reproduction of instrument sounds by additive synthesis can
be achieved with hardly any change in the perceptual quality of the
Assuming that judgments about the sound quality of musical
instruments are based on audible dissimilarities, experiments were
conducted to determine the perceptual attributes listeners use to
judge dissimilarities between different piano tones. The
psychoacoustic results show that two major attributes contribute with
over 90% to the explanation of the perceived dissimilarities: the
psychoacoustic "sharpness" and a second attribute that was described
with the scale "open-closed". The model developed for calculating
audible dissimilarities between piano tones shows a good agreement
between psychoacoustically measured and calculated dissimilarities
The influence of the two attributes on sound quality judgments was
verified by listening tests with appropriately modified piano sounds.
The results show that calculating the sound quality of musical
instruments on the basis of their sound signals requires a signal
processing that is related to auditory perception. A model to
estimate the sound quality of piano tones was developed and will be
discussed along with the results obtained in psychophysical
Christopher Plack and Robert Carlyon (1995) "Loudness Perception and Intensity Coding" In B.C.J. Moore, Hearing, New York: Academic Press.
C.J. Darwin and R.P. Carlyon (1995) "Auditory Grouping" In B.C.J. Moore, Hearing, New York: Academic Press.
Graeme Yates (1995) "Cochlear Structure and Fucntion" In B.C.J. Moore, Hearing, New York: Academic Press.
Brian C.J. Moore (1995) "Frequency Analysis and Masking" In B.C.J. Moore, Hearing, New York: Academic Press.
Adrianus J.M. Houtsma (1995) "Pitch Perception" In B.C.J. Moore, Hearing, New York: Academic Press.