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 28
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]
read all 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 
motivating hypothesis.

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 
(non-logarithmic) cochlea.

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.
January 28

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, 85-102
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 
(correlation 0.90).

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. 85-102
C.J. Darwin and R.P. Carlyon (1995) "Auditory Grouping" In B.C.J. Moore, Hearing, New York: Academic Press. 123-156
Graeme Yates (1995) "Cochlear Structure and Fucntion" In B.C.J. Moore, Hearing, New York: Academic Press. 41-71
Brian C.J. Moore (1995) "Frequency Analysis and Masking" In B.C.J. Moore, Hearing, New York: Academic Press. 161-200
Adrianus J.M. Houtsma (1995) "Pitch Perception" In B.C.J. Moore, Hearing, New York: Academic Press. 267-291
Stephen Handel (1995) "Timbre Perception and Auditory Object Identification" In B.C.J. Moore, Hearing, New York: Academic Press. 425-463
Parag Chordia