Subject: Re: AUDITORY Digest - 21 Jan 2005 to 22 Jan 2005 (#2005-14) From: Jont Allen <Jontalle(at)UIUC.EDU> Date: Sun, 23 Jan 2005 05:47:56 -0600In the article below (you'll have difficult time getting it I suspect) I measured B for new and "old" guitar strings. The hypothesis was that as the string ages, B would change. What I found was that the damping of the high partials changed and that was the real source of the aging effect. A second conclusion was that the size of B is perceptually very important. [A tiny value of B (numbers are in the paper, and I suspect in many other places as well) leads to a huge perceptual effect.] A third conclusion was that there are two sets of modes, and the beating of these harmonics from the two sets of modes, was as important as the inharmonisity (sp?) effect (the effect of B). These mode sets make the measurement of B a nontrivial exercise in a real string sound. The "vertical" and "horizontal" modes are most likely (this was the assumption of the model I developed in the paper, at least) due to the difference in the boundary condition at the bridge. Thus in the paper, the impedance was represented as a matrix, with the two modes separated by the bridge matrix boundary condition. A forth conclusion was that there was another effect I didd not nail down. There is a fast wave that arrives much before the normal wave on the string, which is easily seen in the impulse response. I have no idea how important this fast wave is perceptually, but I cant rule it out as important, other than to say the following. With Mindy Garber (my student many years later) we did time domain simulations of piano strings, and we used three strings in parallel, with vertical and horzizontal waves (for a total of 6 modes at each partial, all beating against each other), at we found excellent agreement with real sounds. They were really natural sounds. As far as I know, Mindy never published this result. She went off to Stanford and started working for Charles Steel, and I never (well almost never) saw here again. author = {Allen, J. B.}, title = {On the aging of steel guitar strings}, journal = {Catgut Acoustical Society Newsletter}, year = {1976} PS: If I get more than 10 requests for this, I'll scan a copy and make it available on my web site. If you wish to make one of these requests, send it to the following email address. Please dont spam my regular email address: jba-catgut76(at)auditorymodels.org Jont Allen (jba "at" auditorymodels.org) Automatic digest processor wrote: > There are 2 messages totalling 151 lines in this issue. > > Topics of the day: > > 1. Definition and Measurement of Harmonicity (2) > > ---------------------------------------------------------------------- > > Date: Sat, 22 Jan 2005 11:06:36 -0500 > From: Judy Brown <brown(at)MEDIA.MIT.EDU> > Subject: Definition and Measurement of Harmonicity > > I have a paper measuring this ratio plus calculation on other instruments. > > Brown, J.C.(1994). ``Measurement of harmonic ratios of sounds > produced by musical instruments,'' J. Acoust. Soc. Am. 95, 2889. > > > >>At 05:23 15/01/2005, Reinhart Frosch wrote: >> >>>The inharmonicity of piano strings is treated in >>>section 12.3 of the book "The Physics of Musical >>>Instruments", by Fletcher and Rossing (Springer, >>>2nd ed. 1998). >>> >>>The basic equation for the frequency of the k-th >>>partial tone is: >>> >>>f[k] = f[1i] * k * (1 + k^2 * B)^0.5 ; >>> >>>here, f[1i] is the fundamental frequency of an >>>idealized string that has the same length, mass >>>and tension as the real string but is infinitely >>>flexible (i.e., has no stiffness). >>> >>>B = 0 corresponds to a string without stiffness >>>and thus to a harmonic complex tone; >>>B is an "inharmonicity coefficient". > > > etc > > > > -- > =*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* > Judy Brown |http://www.media.mit.edu/~brown > jbrown (at) wellesley.edu|http://www.wellesley.edu/Physics/brown/jbrown.html > brown (at) media.mit.edu |E15 483, MIT, Cambridge, MA 02139 > |584 Science Cnt, Wellesley College, 02481 > =*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* > > ------------------------------ > > Date: Sun, 23 Jan 2005 10:44:35 +1100 > From: Harvey Holmes <H.Holmes(at)UNSW.EDU.AU> > Subject: Re: Definition and Measurement of Harmonicity > > Jim, Reinhart, Chris and Others, > > I think Jim's comment below (under the new thread: Inharmonicity definition > and measurement) is probably what Chris intended, and my contribution was > attempting to show ways of doing this, with measures of degree of > harmonicity that could be derived from the signal itself without reference > to a physical production mechanism (e.g. vibrating strings), interesting > though the production mechanism may be in its own right. > > I mentioned two basic harmonicity measures (with variations, including > another one below), but there are many other conceivable measures, such as > those in the survey by W.J. Hess that I quoted, plus a great many > contributions in the speech coding literature of the last 10 or 15 years. > > However, I think the term "tonality" should be used with care, since this > and several similar words (below) have a number of different but related > meanings, largely depending on who is using them. You can check this by > doing Google searches and looking at how the words are used. In addition, > most of these meanings relate to psychoacoustic perception, which is much > more than just harmonicity. > > In the first place, "tonality" means something else entirely in music > theory. In addition, it is often also used to mean the same as > "tonalness", which is a purely perceptual concept, referring to the > sensation of pitch of a sound complex. Pitch perception is much more > complex than the question of the degree of harmonicity. For example, pitch > can be heard in sounds that are far from being harmonic, as explained in > the articles by E. Terhardt on pitch that are available on > http://www.mmk.ei.tum.de/persons/ter.html or by R. Meddis and M.J. Hewitt > (JASA, 89 (6), June 1991). There have been attempts to predict tonalness > based on various theories, such as Terhardt's virtual pitch concept or the > Meddis and Hewitt temporal approach (q.v.). I haven't seen them, but I > believe that there are even standards about this: ASA 118-1995 and DIN > 45681 (the latter still in draft form a few years ago, but may be final by > now). > > Another similar concept with a similar name is "tonality measure", which is > used when deriving auditory masking thresholds (also a perceptual concept) > for use in audio coding algorithms such as MPEG. This refers to the degree > to which the individual sine wave components stand out above the noise > floor. Masking models often treat "tonal components" differently from > others when calculating the auditory masking threshold. > > Also, in some speech coding work these or similar terms may also refer to > the degree to which individual partials of a tonal complex can be "heard > out" individually (usually only the lower partials), still another > perceptual concept, and similar to (but different from) the masking concept > above. If partials can be heard out, they are sometimes coded differently > from those that can't be heard individually. > > The fact that these terms (tonality etc.) are often used to mean different > things by different authors is alone a good reason to avoid them unless > they are clearly defined when used. > > I therefore think that degree or measure of harmonicity (or similar) is a > better term when referring to the degree to which a signal is > harmonic. This is a relatively straightforward physical concept (though > with many possible ways of defining or estimating it), and is much simpler > than the concepts underlying the other terms (tonality, tonalness, virtual > pitch etc.), which are mostly perceptual in nature and have shifting > meanings depending on who uses them. > > > ******************** > While still on this topic, another variation of my first harmonicity > measure H1 is obtained with a different definition of ACF: > > RB(k) = SUM (x(n) * x(n+k)), > > where the sum is taken over all n in the range [0, N-1], with values of > x(n) outside this range being set to zero. (This definition is the one > used by the Matlab function xcorr.m. It applies a window to the signal, > and, apart from a constant scale factor, gives a biassed estimate if > certain statistical assumptions are made, unlike the previous > definition.) The resulting harmonicity measure is then > > H11 = MAX (RB(k)) / RB(0), > > where the maximum is taken over k in the range [1, MAX], where MAX should > be larger than any likely period of the harmonic component. > > (Incidentally, I should also have written [1, MAX] instead of [1, N-1] for > this range earlier, since both R(k) and RB(k) are unreliable for large lags > k, though for different reasons.) > > Harvey Holmes > > At 09:45 22/01/2005, Jim Beauchamp wrote: > >>----- >>That said, it turns out that this is not really what Chris >>was interested in. He is interested in something called "tonality", >>which is something that has been mentioned in the audio >>literature many times, but I have not seen a simple definition. >>But basically if a signal is composed of harmonic or quasi-harmonic >>sinusoids, it is "tonal". The other extreme is a noisy, random >>signal. And, of course, signals can be combinations of both. >> >>Jim Beauchamp > > > ------------------------------ > > End of AUDITORY Digest - 21 Jan 2005 to 22 Jan 2005 (#2005-14) > ************************************************************** >