source file: mills2.txt Date: Mon, 1 Jul 1996 09:52:03 -0700 Subject: Re: Post from McLaren From: PAULE Gary wrote: >Paul E. said: >> Didn't I qualify this to say that apparant >> subharmonics can result when a note is itself a harmonic, i.e., all notes on >> brass instruments? You're right though, I haven't done any actual fourier >> analysis of musical instruments. > Uhmmm... Perhaps mean "undertones" rather than subharmonics? If the "note >is itself a harmonic", then the statement is inherently true by definition, >since harmonics of subharmonics are subharmonics of harmonics. Not really. You could conceive of a "perfectly" performed brass tone, where, say, the odd modes of vibration were completely absent. Then you would have a harmonic (a note an octave above the fundamental pitch of the instrument) without subharmonic content. However, there is no such thing as a "perfectly" performed brass tone, and this applies to winds as well. However, string instruments typically perform in their fundamental mode of vibration; did you find subharmonics in string timbres as well, after controlling for Nyquist effects? In the case of brass and wind instruments, clearly the expected effect according to my argument is undertones, not necessarily subharmonics. These undertones would form an overtone series above the fundamental mode of vibration of the instrument, and not a subharmonic series below the note being played. There is also a technique of playing brass instruments (or singing) so that a buzzy note results which is a subharmonic of the intended note, but is not an overtone of the fundamental mode of vibration. I believe Benade describes this phenomenon in his book on acoustics. A brass instrument with a fundamental frequency of 100 can produce buzzy notes at 125, 133.3, 150, 250, 266.7, 375. But again, the final product is a harmonic series (above the "subharmonic"), not a subharmonic series. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 1 Jul 1996 23:20 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id OAA19959; Mon, 1 Jul 1996 14:20:08 -0700 Date: Mon, 1 Jul 1996 14:20:08 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu