reply to Carl Lumma

>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
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