source file: mills3.txt Date: Fri, 24 Oct 1997 20:59:23 +0200 Subject: reply to Carl Lumma From: "Paul H. Erlich" >Mr. Erlich can rest assured that I have nothing but the >highest respect for his work. >>His was one of my favorite cuts on the tape >>swap and has got me wanting more. > >Why thank you. I almost improvised it, and when I analyzed it later, I was >pretty amazed at how coherent it looked. It has nothing to do with what I >originally chose 22 for, but sometimes the wrong reasons can lead to the >right actions. > >He also may or may not wish to know that one of the first tunings I'm going >to map to my generalized keyboard (when I get it) will be 22 equal. Great! What is this generalized keyboard you're getting? I had a hell of a time stretching my hands to play that piece. > >>>Today is my last day as a full-time employee of an investment company. I >>>already spend almost all my free time playing music... > >>So how is that working out? Are you able to resist the temptation of >>playing with your 12 tone friends enough to go home and be microtonal? > >Not yet, but I have at least one friend who's getting good at 22-tone kbd. > >>To paraphrase: If you've got two frequencies represented by a ratio in >>lowest terms whose decimal value is between 1 and 2, then the period of the >>composite waveform of these two frequencies is the product of the two >>numbers in the ratio. I believe this makes a more useful definition of >>Consonance than any other I've ever heard. If somebody's got one they think >>I havn't heard, please share. > >Of course. This definition doesn't even make sense if the frequencies are at >an irrational interval, as in any equal temperament. Some good definitions of >consonance are to be found in Journal of the Acoustical Society of America >articles by Plomp and Levelt, Kameoka and Kuriagawa, and Terhardt. > >>This definition is independent of what a person may or may not hear, and it >>is independent of how they might like or dislike what they hear. For those >>of you who do not view these as assets, don't use this definition. > >As a musican, I am ultimately concerned only with what people can actually >hear. The rest is pure intellectualization (or mythology). Yes, it can _feel_ >like you can feel music with your whole body, or with an extended body the >size of the universe, but once you shut off your ears the whole effect >disappears (I'm baiting Neil). > >>The ear has a limit of resolution, just like anything else. That the one >>example given by Mr. Erlich is beyond the ear's resolution does not mean >>that this definition has no practical application. Clorox is poison but >>lots of folk find it useful to chlorinate their water. I think the >>practical usefulness of the definition is obvious. > >I'm with you so far. > >>While I can't hear the difference between a 3/2 and a 300001/200001, I can >>hear the difference between a 19/16 and a [19723/16585.] >>I'm listening to it >>right now. But I've been told that an error of 2 cents is not significant >>when comparing tempered intervals to just ones. > >Just because you can hear it doesn't mean it's an important musical >difference. Let's talk about beating, since you brought it up. Let's assume >the lower note is A440. Both 19/16 and 19723/16585 have significant beating >between the 6th harmonic of the lower note and the 5th harmonic of the higher >note. The rates of beating are 27.5 Hz and 23.744 Hz, respectively. Between >the 13th harmonic of the lower note and the 11th harmonic of the higher note, >the rates of beating are 27.5 Hz and 35.762 Hz, respectively. Finally, if the >19th harmonic is actually audible, the rates of beating between the 19th >harmonic of the lower note and the 16th of the upper note are 0 and 12.018 >Hz, respectively. This, alone in the cloud of beating of other harmonics, is >the only significant difference. > >But why use 19723/16585 to represent the fourth root of two? It's only an >approximation! Had we used 44/37 instead, our beat rates would be 23.784, >35.676, and 11.892. Is there any audible difference between 44/37 and >19723/16585 and the fourth root of two? Does the relative >complexity/existence of the ratios for these three intervals mean anything >for how they sound? > >>Working within the practical limits of human hearing, the perception of >>subtle mis-tuning is very sensitive to the timbres used, the voicing of the >>intervals, how high the identities are, and how they are used in combination >>with other intervals. > >And most of all, how long the sound lasts! > >>If your timbres have a high degree of inharmonicity, you'll loose >>resolution. Don't use bowed strings for high resolution work. > >Bowed strings are not inharmonic. > >>If your >>interval is down in the lowest octave of the piano, don't expect to hear a >>10 cent difference. You're much less likely to notice a 3/2 2 cents off >>than a 11/7 mistuned by 2 cents. You can't hear the difference between a >>3/2 and 700 cents in a melody, but in an otherwise just triad, it sticks out >>like a sore thumb. > >>So my original point was: When comparing an equal-step tuning to a just >>tuning on a broad, theoretical level, define Consonance on a broad >>theoretical level. > >Such as: a few simple-integer ratios, plus a band of allowable mistuning >around each of them? That's the type of thinking behind my posts, and to >which you seemed to object so strongly. What are your arguments against it? > >>My other original point was: Equal step tunings have nothing to apologize >>for. I don't view them as imitating just tunings. They're a different >>breed of cat. The kind of music that makes sense in an equal temperament >>doesn't make sense in JI and vice versa. It's like apples and oranges. > >And don't forget meantone (the pear?). But I think JI is simply an ideal >tuning for harmonic consonance, and the harmonic consonance of any other >tuning depends solely on how closely it approximates JI. For melodic (let >alone modulatory or fingering) considerations, JI is not ideal. SMTPOriginator: tuning@eartha.mills.edu From: "David Worrall" Subject: Re: more consonance and dissonance PostedDate: 25-10-97 03:19:14 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: 25-10-97 03:18:19-25-10-97 03:18:19,25-10-97 02:18:57-25-10-97 02:18:57 DeliveredDate: 25-10-97 02:18:57 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 C125653B.0007299D; Sat, 25 Oct 1997 03:18:14 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA26997; Sat, 25 Oct 1997 03:19:14 +0200 Date: Sat, 25 Oct 1997 03:19:14 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA26988 Received: (qmail 25560 invoked from network); 24 Oct 1997 18:19:10 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 24 Oct 1997 18:19:10 -0700 Message-Id: <9710251118.ZM20906@simba> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu