Subject: Re: question about overtones From: beaucham <beaucham(at)MANFRED.MUSIC.UIUC.EDU> Date: Thu, 17 Nov 2005 03:08:49 -0600Tom, The amplitudes of "overtones" or harmonics based on a fundamental frequency are in principle completely arbitrary. Analysis of a periodic signal waveform into a set of harmonic amplitudes and phases is discussed in many books including the fifth chapter entitled "Fourier Series" of W. M. Hartmann, Signals, Sounds, and Sensation (Springer, 1998). Now, if you are talking about musical instrument or vocal waveforms this is a different story. In these cases, the harmonic amplitudes are limited by the acoustics of the instrument in question. An old book which contained graphs of many instrument harmonic amplitude series (called "spectra") is H. F. Olson, Music, Physics, and Engineering (Dover, 1952, 1967). The graphs are mostly in Olson's Chapter six entitled "Characteristics of Musical Instruments". These spectra should be taken as typical but not all-inclusive because instrument spectra depend on many factors such as instrument, player, fundamental frequency, performance, room acoustics, and microphone placement. These days you can find out the spectrum of an instrument by having a player blow a tone into a computer and have the spectrum displayed on the screen using a real-time analysis program. Several programs of this type have been suggested on this list in the past. Unfortunately, it seems that noone has yet published a complete corpus of musical instrument spectra. Back in the 90's Gregory Sandell hosted a website called SHARC which contained a pretty complete set of data of this type. Unfortunately it seems that that site is dormant. However, using the Univ. of Iowa samples (http://theremin.music.uiowa.edu/MIS.html) and a program such as SNDAN (http://ems.music.uiuc.edu/beaucham/software/sndan/) you can easily make your own data. The percept most closely associated with the spectrum is called timbre. Numerous studies have been published on aspects of timbre in the Journal of the Acoustical Society and other journals and some of these are discussed in various acoustics books. Jim James W. Beauchamp Professor Emeritus of Music and Electrical & Computer Engineering University of Illinois at Urbana-Champaign 2136 Music Bldg. MC-056 1114 W. Nevada, Urbana, IL 61801 USA email: jwbeauch(at)uiuc.edu (also: beaucham(at)manfred.music.uiuc.edu) phone: +1-217-344-3307 (also: 217-244-1207 and 217-333-3691) fax: +1-217-344-3723 (also: 217-244-4585) WWW: http://ems.music.uiuc.edu/beaucham Original message: > From: Tom Lee <edgar109(at)YAHOO.COM> > Date: Wed, 16 Nov 2005 16:58:35 -0800 > To: AUDITORY(at)LISTS.MCGILL.CA > Subject: question about overtones > > Dear list, > > Does anyone have information about the amplitude > relation between a tone and its overtones? What I mean > is, if I have some frequency and I want to generate > its natural overtone series, how loud do I make the > overtones in relation to the fundamental? Thanks in advance! > > -Tom