Erlich's Issues

>>>http://www.catalog.com/starrlab/uzone.htm
>>
>>This site contains no price or ordering info. Can someone help?

You've got to e-mail 'em. The keyboard is in development, as can be noticed
by the fact that the "picture" of it is CG.

They told me that there will be 5 pre-release versions of the thing, and
that all of them have sold at $3500. They aim to officially release it in
January, with an estimated cost of $5000. I am going out to California in
December to participate in the development of my own version of this keyboard.

>I've posted at length on definitions of consonance and dissonance (as
>well as discussions of melody and modulation) in previous Tuning
>Digests.

I would appreciate it if you could forward them to me. If not, it would
help a great deal to know which digests to look in.

>The issue is complicated but that is no reason to retreat to a
>simpler, less useful definition. Your definition makes no sense, because
>you'll never come up with an answer for irrational intervals.

Thanks for the encouragement. I have already admitted that my definition is
for Just Intervals only. I'm not the one trying to compare tempered
intervals to Just ones. I recommended against this.

As far as retreating is concerned, retreating from where? For measuring the
consonance of irrational intervals, the only thing I've heard from you is
cents deviation from Just intervals. And I haven't heard any definition
from you for measuring the consonance of Just Intervals.

In fact, despite my requests, I have not heard anyone give any definitions
of consonance whatever regarding this thread. I've heard plenty of where to
find definitions, which dead scientists the definitions I may find agree
with, and what categories the definitions can and can't fit into.

>How do you propose to "measure [the mistuning of an equal temperament] in cents
>deviation _and_ consonance* deviation" when you can't define the consonance
of >an irrational interval?

Maybe something like the difference between the products of the numbers in
the Just Ratio and the products of the numbers in the simplest rational
approximation of the tempered interval that is within the ear's limit of
resolution.

This isn't good, but it's better than cents deviation alone.

>Presumably, you want to use rational approximations, but how do you decide
>whether to use 25/21, 44/37, 1785/1501, 10754/9043, or 19723/16585?

All of these are more dissonant than the 19/16 by my definition. I think
all but the first could probably be used to approximate 300 cents. I would
choose between them based on the purpose I needed them for. For music, any
ratio closer to the irrational than the ear's resolution can serve.

>You seem to like the latter, but if you really go to that level of
accuracy, >you face a very large danger that some of your so-called JI
perfect fifths will >turn out to be closer to 30001/20001, in which case
you'll have to call the
>equal-tempered minor third more consonant that the just perfect fifth!

You make a good point, but it is slight of hand: You selectively ignore the
resolution of the ear in order to accuse me that I have done so. I already
claim to define dissonance without using the experience of the ear.

But I have not ever used my definition in a musical example without
factoring in the limits of hearing. Theoretically, the 30001/20001 is more
dissonant than the 3/2, but I'm sure I can't hear the difference. I can
hear the difference between 25/21 and 19/16, 25/21 and 19723/16585, and
19/16 and 19723/16585.

>The only definition I care about is one with a psychoacoustic
>correlative. Otherwise we're not talking about music, we're talking
>about abstract marks on a piece of paper or computer screen. My
>calculation of beat rates was an attempt to show that the one
>psychoacoustic correlate you did mention does not lead to a first-order
>qualitative difference between 19/16 and 2^(1/4).

But it does. Go figure. I am working on an analysis of the "clouds of
beating harmonics" in our example. I am in way over my head, but I know
that there's a lot more going on in there than what you mentioned.

>You can't always believe what the "Physics for Dummies" books tell you;
>in fact, it was only shortly before receiving my B.S. in Physics from
>Yale that many of my own misconceptions about acoustics were dispelled.

It must be something else, then, that causes additive patches to sound more
like violins when you detune the harmonics.

>>>This purity is not always desirable.

Nothing is always desirable.

>>Differences of tuning as small as 1 cent do affect the sound
>>of the chord. I'm unable to try smaller intervals at present.
>
>Real musicians playing acoustic instruments don't have this level of control.

While it may work, to me there's something conceptually wrong about saying
one interval might as well be another on an instrument if the difference
between the intervals is less than the instrument's accuracy. It encourages
sloppy instrument building. New instruments can be designed for new types
of music.

But there's nothing conceptually wrong, as far as I can see, with saying
that two intervals whose difference is less than the ear's accuracy are
musically the same. This is the only way Canright's "all intervals" can be
"just".

>>>The idea that dissonance increases with prime limit is erroneous.

Dissonance does increase with prime limit. Maybe a better indicator is odd
limit. Probably the best is the product of the numbers in the ratio.

>>I bought a copy of Partch's book while in San Francisco (I last read it
many >>years ago) and on virtually every page there is evidence, often
strong, >>emphatic evidence, that his definition of "limit" was the odd, not
prime, >>definition. All the Partch "experts" using the prime definition
frustrate me >>to no end as they clearly have not listened as much as Partch
and yet fail to >>understand the ideas he derived from years of listening.
And for those using >>the prime limit definition to describe the resources
of a tuning system rather >>than consonance/dissonance issues, what
information is contained in the >>knowledge of the highest prime one is
using that is more important than >>knowing any of the other primes one is
or is not using?

This is a very interesting topic. Partch based his tunings on what he
called "primary tonalities". That is, he stopped stacking like intervals
fairly early. Guys like Doty prefer to model tuning by getting all the odd
identities they can as "secondary tonalities" (9 is two 3's) before moving
up to the next limit.

Both methods have pros and cons. Partch's method is more in touch with the
harmonic series, but he wound up having to add in "secondary tonalities"
rather arbitrarily. Doty's method seems cleaner, until you realize that the
stacking could go on indefinitely at any limit, and you've got to pick
arbitrary stopping points for each.

I tend to prefer the Partch method. I think that by adding more dimensions
to the tonality diamond I can rid my model of a need for "secondary
tonalities". While this idea is not yet ready for publication, I can share
my rules for understanding tunings based on the harmonic series...

1. No tuning can use the entire series, they must "start" and "stop"
somewhere.
2. Each new prime member you include provides intervals you couldn't
get before.
3. The even-number identities are all duple copies of lower odd-number
identities.
4. Each higher odd-number identity gives you primary tonalities that
were secondary tonalities at the lower identity, that is, stand alone
intervals now appear that were compound intervals at a lower odd-number.
5. When the start and stop notes of a mode bare ratio 1:2, then that
mode is a duple wide.
6. A given duple of the series contains twice the number of notes as
the duple just below it: it contains all the notes in that previous mode
and a new note between each of the old ones.

Carl


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Subject: Re: Consonance
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