Pitch shift from change in loudness

With reference to the MMD thread of 2003.12.12.04 and following, the
attached samples illustrate one way to see how loudness affects pitch.
The examples are taken from a psychoacoustics demo CD I prepared
a few years ago for my electroacoustics students.

Intensity level and sound pressure level are physical measures that
tell how 'strong' a sound is, the 'volume' of it, most often on a
standardized decibel (dB) scale.  Idiosyncrasies of hearing physiology
combined with physical phenomena like resonance in the ear canal make
up for a complicated relation between intensity and the perceptual
measure of loudness level, measured in Phone.  This relation is
generally described by the famous Fletcher-Munson curves.  The affix
'level' implies these are logarithmic measures.

Furthermore there is a perceptual quantity of comparative loudness,
measured in Sone, a linear measure.  Twice the number of Sone, twice
as loud perceptually.  It is noteworthy that this over most of the
hearing range this corresponds to about 9 Phone and 9 dB - to make your
hi-fi twice as loud you have to increase its power by a factor of 8,
not only 4.

Frequency is a physical measure that tells the number of cycles per
second in a periodic signal.  Frequency can usually be measured in Hz
with high accuracy, using appropriate instruments.  For a contrast,
pitch is a psychological measure, how you perceive frequency.  This is
not so easy to find out because human individuals differ a lot, and
also do not have very tangible pointers or digital displays.  Instead
you have to use indirect methods, and also take an average of results
obtained from many persons.

This is also complicated by the fact that you perceive pitch two
different ways, in what we may roughly call a musical context as
opposed to a non-musical one.  The prototype example of a non-musical
tone is a sinusoid, a signal having one specific frequency component.
The present illustrations are of this type, representing some 'lab'
conditions.  A prominent finding is that by varying loudness you can
cheat the perception of pitch corresponding to a semitone of more.

But a continuous musical note generally is complex, it has a
fundamental plus several harmonics sounding simultaneously.  Musical
pitch is established in octaves (frequency ranges with factors 1:2),
each divided into 12 semitone intervals with names from A through #G.
For microscopic work one semitone interval can further be divided into
a range of 100 cents.  With such complex sounds the ear is remarkably
sensitive, you usually can perceive deviations to the order of a few
cents.

The following three illustrations are at frequencies 100, 200, and 400
Hz respectively.  Each has six pairs of tones.  In each pair there is
first 1 second of a weak tone, then 1 second of a strong tone, 30
decibel higher level.  The pairs are interlaced with 0.5 second of
silence.  Ideally they should be reproduced at about 56 and 86 dB sound
level respectively, the latter pretty loud, so probably you should
listen to them over headphones, rather than small computer
loudspeakers.

  100 Hz
  200 Hz
  400 Hz

In one sample of six pairs, the weak first tone in a pair is always
exactly the same.  But the following strong tone is successively rising
in frequency, by 0, 20, 40, 60, 80, and 100 cents respectively.
Listening to the first pair you will probably perceive that the strong
tone in the first pair has a lower pitch than the leading weak one.
But somewhere along the sequence the weak and the strong one should
have the same pitch.  The ordinal number of this pair determines your
perceptual pitch shift at a 30 dB level change, in terms of cents.

A special remark is that winds and strings in an orchestra tend to rise
their pitch a few cents at loud passages.

Johan Liljencrants
Stockholm, Sweden
johan(at)fonema(dot)se

 [ Thanks, Johan.  I'll place this article and the MP3 sound files
 [ at the MMD Tech site in the section of reference data (at bottom
 [ of the index page) at http://mmd.foxtail.com/Tech/
 [
 [ Professor Liljencrants teaches speech communication and
 [ electroacoustics at the Royal Institute of Technology, Stockholm,
 [ Sweden.  Born in 1936 in Uppsala, his first training was in
 [ electronic engineering and he worked in industry for 10 years.
 [ He holds a Doctorate in Technology and has published many scientific
 [ articles on topics from loudspeaker enclosures to sound production
 [ in the human throat.  See his home page at
 [ http://w1.879.telia.com/~u87902212/
 [
 [ Johan is a skilled handiworker, too, and enjoys several hobbies
 [ including pipe organ building.  He is moderator of the MMD Pipes
 [ Forum, an e-mail (list-server) technical discussion group concerned
 [ with the theory and practice of small player pipe organs.  Send an
 [ e-mail note to Jody <rollreq@foxtail.com> if you wish to participate
 [ in the discussion group.  -- Robbie