Just Intervals?

[Robin Hufford]

Bradley,
>" The ratio of an interval, if smaller than an octave, taken
ascending,  when multiplied by the ratio of the interval that is the
musical  inversion of the first, also taken ascending,  must equal two.
Hummm . . . I don't think that this is an applicable assumption. What
you say turns out to be true, but does that really factor in to what
constitutes the justness on an interval? Besides, all the intervals that
I put down are also true for these parameters."

This is demonstrably true.  It has no relevance to the degree of
justness of an interval, except that it only applied to just
intervals.   I used it merely to validate the correct ratio for the
Major and Minor seventh.  In fact, and here I repeat, the  list which
you posted last week has errors in it for these. I would check this out
if you intend to base further work on your list.

." the fundamental nature of just intervals; they are the paradigm of
the tempered intervals we are accustomed to.
I don't think that I understand this statement clearly. But I did not
mean to imply that tempered intervals can start to sound 'just' simply
because we are accustomed to them."

I am saying that tempered intervals are just intervals that are out of
tune.  When we hear a tempered third its effect is of a third whether
tempered or not.  The third is simply out of tune, we are able to
tolerate it because it harkens back essentially to the sense of the just
third.

]>" Listening to choral music, great orchestral performances and string
music and, in particular, string quartets, I don't sense the unpleasant
aspect of the tempered values; it is obvious to me that their tuning of
harmonic values, if not completely just,  is substantially closer than
tempered values.
I have been arguing about this with Susan for a while, and my opinion
sides with that statement exactly. The only thing that I would add is
that we also temper intervals occasionally to help increase tension (and
also just play out-of-tune), but what we are shooting for is just."

     I agree with this personally, but as I said in an earlier post,
tastes differ, and, in my case, my reaction to just intervals can vary
from time to time, although, in general, I prefer much  intervals closer
to those of just intonation in a harmonic context.   In Susan's defense
this variability may well apply to her.  Additionally, I think there is
a complicated arguement to made that cellists, simply as a result of the
part-writing for the instruments, may find it necessary to play closer
to ET values
than the violas and violins.  Similarly, I think, were this true, it
would apply also, and possibly in greater degree, to the doublebasses.
Also there is something to be said for Susan's arguments, if I
understand them, for the consideration of tuning alterations to achieve
small intervals in stepwise progressions.

> " I believe that people in general are conditioned on an unconscious
level by the vast amount of music they hear, the great bulk of which is
in equal temperament, so that, when asked to make sounds or sing a pitch
level, the sounds so generated will be centered around the  frequencies
generated by Equal Temperament at A-440 to a significant degree such
that this cannot possibly be random.
That is a good thesis statement, but it is not true. Go to any very high
level music school/conservatory and listen to some an ear training
class. Even though the musicians are very highly trained on their
specific instrument, I have never heard anyone even come close to
centering around EQT. Even some of the pianist that have perfect pitch
have a difficult time. I am not saying that it is impossible, but I am
saying that it does not happen without specific training. There are some
string players that specialize in duo work; they must train very hard to
approximate EQT."

Well, I do believe it is true, as this has been the case in my
experience.  I have been in many, high school band rooms and am aware of
the poor intonation there; I am aware of the intonation in various music
schools, particularly from my own experience as a music major at North
Texas State many years ago; I am aware of the intonation problems of the
orchestras I have tuned for, I am aware of the intonation of individuals
completely lacking a formal education in music and from these things,
and others, I stand by my statement that individuals are involuntarily
conditioned to pitch and intervals in the way I have described it.  This
may pique the vanity of the hard-working,  well trained string player
but it, from my perspective, is nevertheless true.
Regards, Robin Hufford
"Bradley M. Snook" wrote:

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