If for 'harmonic' its mean 'consonat' or 'pleasant', in my opinion, it is better to 'label' a waveform in these terms by using only the perceptual experiments (the classical Plompt and Levet, 1961; Kameoka and Kuriyagawa, 1969; references in Tramo et. al., 2001, many papers form Terhardt referenced in his webpage, et.), and not the waveform characteristics. This may seem trivial, but these papers already provide a perceptual quantification of consonance which does not straightforward can be explained as the differences in 'spectral harmonicity' or in other more sophisticated time series complexity measure of the waveform (for example the roughness of the sounds could be related closely to the waveform complexity, but according to the experiments the consonant sensation is no just the roughness).
Sarah, I do not know if there is a standard definition of what an inharmonic sound is. I do not think so, but I may be wrong. Anyway, I am going to give you my own definition of an inharmonic sound in case it helps. I define an inharmonic sound as a SOUND FOR WHICH THEIR COMPONENTS ARE "FAR" FROM BEING MULTIPLES OF THE PITCH. I found an excellent example of this type of sounds in Patel. A. et al: "Human pitch perception is reflected in the timing of stimulus-related cortical activity", in Nature Neuroscience 4, 839 - 844. They test humans pitch perception of a stimulus built from the 13th, 19th, and 25th harmonics of a fundamental of 50 Hz (i.e., 650, 950, and 1250 Hz). Most people perceive a pitch close to 334 Hz (+-6Hz) for this stimuli. Since the ratio of the components with respect to the pitch are "far" from being integer numbers (1.95, 2.84, 3.74), according to my definition, this is an inharmonic sound. In my case, I perceive a pitch of around 315 Hz, not 334 Hz, but the ratios are also "far" from being integers (2.06, 3.02, 3.97). Something I need to define is what "far" means. For example, is a signal with components 300, 600, and 901 Hz inharmonic? Given that we perceive a signal with components 300, 600, and 900 as having a pitch of 300 Hz, and we cannot tell the difference between the two stimuli, both should be considered as harmonic, and therefore the component at 901 Hz is not "far" from 900 Hz. However, I think that instead of hard-labeling signals as harmonic or inharmonic, we should define a continuous measure of inharmonicity. For example, we should say that setting the third component to 901 Hz makes the inharmonicity of the sound so low that it is practically harmonic, however, setting the component to 910 Hz starts to make it perceptually more inharmonic. However, those levels of inharmonicity are small compared to the inharmonicity of the sound with components at 650, 950, and 1250. Arturo > Hello list - I feel really silly asking this, but I can't seem to dig up > a straight answer to this question. > > 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? > 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? > > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ > Sarah Hargus Ferguson, Ph.D., CCC-A > Assistant Professor > Department of Speech-Language-Hearing: Sciences and Disorders > University of Kansas > Dole Center > 1000 Sunnyside Ave., Room 3001 > Lawrence, KS 66045 > office: (785)864-1116 > Speech Acoustics and Perception Lab: (785)864-0610 > http://www.ku.edu/~splh/ipcd/Faculty/FergusonBio.html > > > -- __________________________________________________ Arturo Camacho PhD Candidate Computer and Information Science and Engineering University of Florida E-mail: acamacho@xxxxxxxxxxxx Web page: www.cise.ufl.edu/~acamacho __________________________________________________