Re: harmonic vs. inharmonic sounds

[Kevin Austin <kevin.austin@xxxxxxxxxxxx>]

I think you are dealing with two different issues. The metric one is
about periodicity, which can be measured; the psychometric one is
about the 'perception' of a missing fundamental.

With your example, assume that the (missing) fundamental is 50Hz, and
the partials are: 200, 300, 400, 500. This would mean that the
components are:
  f4, f6, f8, f10  (they are neither adjacent nor odd numbers *)
Working backwards, the next lower part of the sequence is f2. Adding
f1, the components with 50Hz become:
   (1, 2,) 4, 6, 8
f1 (50Hz) is a 'subharmonic' partial, as would be 25Hz. With 25Hz as
the fundamental, the partials are:
   (1, 2, 3, 4, 5, 6, 7,) 8, 12, 16, 20, 24

The (other part of the) question is: how does the hearing mechanism
translate a sequence of partials? Which will the mind go for:
   (1,) 2, 3, 4, 5
   (1, 2,) 4, 6, 8
   (1, 2, 3, 4, 5, 6, 7,) 8, 12, 16, 20, 24

[There is a form of intelligence test that asks to give the next
elements of a sequence, such as 6, 5, 4, 3, ..., ...  . Do this with
24, 20, 16, 12, 8, ..., ???]

The demonstration I use in class about "missing" features is to walk
behind the small upright piano and announce that I have cut off the
lower part of my body. (Many students faint when hearing this.)

Those who do not believe me, I ask them if my legs reach the floor,
and how can they tell since it might be possible that my legs shrunk
when I went behind the piano, but in their experience (the
psychometric / memory side), they have not seen my legs "shrink". In
the absence of direct information, they go for "the best fit".

* In my (acoustical) experience, when I hear sounds that have missing
lower partials, the components have either been adjacent:
as in the sound of the cello whose body does not support the low C fundamental,
or, odd numbered partials:
as in the sound of the bass clarinet, whose lowest notes contain a
very very weak fundamental and is mostly odd-numbered partials up to
about the seventh partial.

Or at least that's my practical take on the matter.

Best

Kevin



> Hello list - I feel really silly asking this, but I can't seem to dig up
> a straight answer to this question.=20
>
> When I present complex sounds to my Physics of Speech class, I
> present different classifications: periodic vs. aperiodic, harmonic
> vs. inharmonic, continuous vs. transient, etc. One of the tasks the
> students will have in homework is to determine whether a given sound
> is harmonic or inharmonic. I tell them a sound containing energy at
> 200, 300, 400, 500, and 600 Hz is harmonic because all of those are
> integer multiples of the same fundamental (which happens to be
> missing).
>
> I have two questions:
>
> 1) Is this actually correct?=20
> 2) If so, it seems to me there must be some constraint on which
> harmonics of the fundamental are there. In the example I gave above,
> I've had students say "Couldn't the fundamental be 50 Hz? Or 25 Hz? Or
> even 1 Hz?" Is there a rule I can give them?=20
>
> ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~=20
> Sarah Hargus Ferguson, Ph.D., CCC-A
> Assistant Professor
> Department of Speech-Language-Hearing: Sciences and Disorders=20
> University of Kansas=20
> Dole Center=20
> 1000 Sunnyside Ave., Room 3001=20
> Lawrence, KS  66045
> office: (785)864-1116
> Speech Acoustics and Perception Lab: (785)864-0610=20
> http://www.ku.edu/~splh/ipcd/Faculty/FergusonBio.html
>
> ------------------------------

--
Associate-Professor Kevin Austin (Music) / (EuCuE)
Department of Music (Electroacoustic Studies)
Faculty of Fine Arts, Concordia University
7141, rue Sherbrooke o
Montreal, QC,  CANADA  H4B 1R6