source file: mills3.txt Date: Wed, 31 Dec 1997 22:33:09 +0100 Subject: Stretching, beating, dissonance, and perfect JI From: "Paul H. Erlich" }Also, regarding Gregg Gibson's assertion that the octave should be stretched }a few cents, wouldn't this be a problem for guitar players (and steel }guitarists) who are accustomed to sounding harmonics to get an octave above }the note they are fingering (or barring)? Guitarists commonly sound the 5th harmonic, even though it is 13.7 cents off 12TET. The 2nd harmonic being 2.7 cents off will not be a problem. }I also suspect that there would }be a lot of beats happening around double- and triple-octave pairs. If the }bass player plays an A, and my A three octaves higher adds 10 cents to the }equation, I wouldn't expect it to sound good. An 8:1 off by 10 cents would be no worse than a 5:1 off by 14 cents, and we accept the latter. Certainly a 7:1 off by 31 cents is much worse, and yet the harmonic seventh has been used as a consonance even in 12TET. Gamelan orchestras purposely detune octaves by far more than 2.7 cents; although their instruments have inharmonic partials, they can tune pure octaves using second-order beating and difference tones, and yet they choose highly distorted (usually stretched) octaves. They even tune their unisons so that they produce beating. Beating is not the same as dissonance. Beating occurs when two pure tones are so close in pitch that they are perceived as one tone of changing amplitude. Roughness, one contributor to dissonance, occurs when the two pure tones are partially resolved from one another but are less than the critical bandwidth apart. Beating may be incidental to roughness, but changes in amplitude are not what constitutes dissonance (or else we would consider a tremolo effect dissonant). For an interval in perfect just intontation, whatever phase difference was present at the beginning of the sound would persist for the duration of the sound. Let's say two instruments are producing tones, both of which have an equally loud partial at 1000Hz. For someone standing in a particular location with respect to the two instruments, there is some delay time between the beginning times of the two instruments for which the 1000Hz components will interefere constructively, resulting in four times the energy at that frequency than what one instrument alone would produce. For a delay time just 1/2000 of a second longer, you get destructive interference, or no energy at that frequency. Obviously no human instrumentalist can control their onset time to within 1/2000 of a second relative to the onset time of another instrument. So you end up with a random number between zero and four to describe the energy of the 1000Hz component -- probably not the musical effect you were looking for. Even an individual performer playing both instruments can't do it -- try tuning two synth keys to the same note and notice how repeatedly playing both keys "simultaneously" leads to random fluctuations in the loudness. Now if the onset times are controlled really accurately by MIDI, and let's say a 90-degree phase shift is chosen so that the energy at 1000Hz is twice that from one instrument, then you're doing okay, right? But for someone standing in a different location in the room, though, the differece in the path lengths from the two instruments, and thus the phase, will be different. There are nodes of destructive interference and antinodes of constructive interference in the room no matter what the original phase shift was. So some members of the audience may be receiving no energy at 1000Hz, while others may be receiving four times what they would from one instrument. Again, probably not the effect you were looking for. If both instruments are electronic, and their signals are mixed into one speaker, there will be no spatial nodes or antinodes. So finally you can control the musical effect. But other than monophonic electronic MIDI-sequenced music, perfect JI can lead to big problems. In the real world, thankfully, acoustic instruments are slightly out-of-tune with each other, so that whatever the onset delay and whatever the position in the room, one gets a signal that frequencies common to both tones have an average energy twice that of one instrument. There will not be noticeable, let alone startling, differences in the musical effect depending on minute variations in the onset delay or position in the room. SMTPOriginator: tuning@eartha.mills.edu From: "Brian M. Ames" Subject: Semiconductor analog to phonons PostedDate: 01-01-98 08:42:01 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 01-01-98 08:39:33-01-01-98 08:39:34,01-01-98 08:38:55-01-01-98 08:38:56 DeliveredDate: 01-01-98 08:38:56 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125657F.002A1202; Thu, 1 Jan 1998 08:41:27 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17731; Thu, 1 Jan 1998 08:42:01 +0100 Date: Thu, 1 Jan 1998 08:42:01 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA18203 Received: (qmail 2417 invoked from network); 31 Dec 1997 23:41:58 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 31 Dec 1997 23:41:58 -0800 Message-Id: <199801010740.CAA01958@junior.apk.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu