Subject: Re: harmonic vs. inharmonic sounds From: Kevin Austin <kevin.austin@xxxxxxxx> Date: Sat, 10 Mar 2007 07:57:45 -0500 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>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