RE: [tuning] Re: Adaptive tuning

Patrick Mullen wrote,

>I've been going through the posts on the
>tuning list and have seen yours, as well as the discussion about
>consonance vs. concordance. To me, it's so much hoo hah. After
>looking up the two terms in various dictionaries at work, some music,
>some not, I have come to the conclusion that they are essentially two
>senses of the same term, therefore I can't say that I agree with Paul
>Erlich on his distinction (or Blackwood, though I have yet to read
>his book cover-to-cover). If we're going to make such a distinction,
>then it seems to me that we also have to come up with a term that
>will separate mathematical consonance from subjective consonance. A
>4:5:6:7 chord is mathematically consonant, since each interval within
>it exists in symetry with the others, with difference tones that are
>octave transpositions of tones already present in the chord. A
>4:5:6:7 could sound dissonant is if it was voiced too low, in which
>case the difference tones could be low enough to be perceived as
>beats instead of logical bass tones, but it would still be
>mathematically consonant. On the other hand, there seem to be those
>who say that tunings other than just are consonant (or is it
>concordant?). Interesting. I see no mathematical basis for this
>viewpoint. Maybe I've misinterpreted? Of course there are plenty of
>"dissonant" constructs that sound great, but they're still dissonant.
>As a player, my ears tell me what is consonant, and they usually
>agree with the mathematical model.

Patrick, some aspects of music psychology are more amenable to mathematical
modeling than others, and some have been explained my so many contrasting
mathematical models that they can't all be right. Anyway, Patrick, I think
you have misinterpreted somewhat, in that, while I claim the dominant
seventh chord is dissonant within the language of Western common practice,
i.e., triadic diatonic music (even when the chord is tuned 4:5:6:7), I claim
that the chord can be used as a consonance in other styles (and this is all
based on my personal musical experience, not conjectures on paper). I
suggest you read my paper (http://www-math.cudenver.edu/~jstarret/22ALL.pdf)
where I give a mathematical enough (I hope) explanation of how consonance
works in a tonal system, both our familiar one, and a proposed new one which
would use 7-limit tetrads as the basic harmonies. Essentially, one must
remember a chord in music is not an isolated entity, but is generally built
from whatever scale the melody is built from (in contrapuntal music, this is
unavoidable), and it is the combination of concordance and scalar properties
of the chord that gives it its musical meaning and direction. As Toch points
out, even a perfect octave can function as a dissonance if it is foreign to
the prevailing scale of the moment.

>I'll grant that tuners of fixed pitch instruments have had to go to
>great mathematical lengths to find workable tunings for these
>instruments to play in more than one key, but players of variable
>pitched instruments and vocalists have always been free of such
>constraints (unless we have to play with keyboards!). Remember, the
>keyboard tuners and theoreticians were the ones who wrote down what
>they did. No one else thought to do that, or needed to, for that
>matter. Good, simple, garden variety intonation just _is_.

I'd say the players of variable pitch instruments and vocalists have had to,
generally by ear and without the aid of any mathematics, solve a much more
difficult problem than that solved by keyboard tuners and the vast majority
of historical theoreticians. Namely, they've had to come up with some
adaptive tuning scheme, like the ones John deLaubenfels's computer program
solve. Since "adaptive tuning" was the subject line of your message, I
presume you have some idea of what I'm talking about?

>Time to digress: Having said all this about how just intervals are so
>cool, I have to admit that there are instances where 12tET or other
>tunings do sound good. I am a jazz player too, and there are many
>jazz chords that don't work well in the just scale, 7-limit or not.
>In fact, 12tET has spawned harmonic extensions that sound really cool
>in 12tET, but not so good when tuned to just intervals. As if such a
>thing could even be done with some chords. Try tuning the beats out
>of a G13#11! But it sounds very nice in 12tET.

I've made those points before -- another example being a 6/9 chord, which
sounds best in meantone, OK in 12-tET, and not too hot in JI.

Paul H. Erlich wrote,

> Essentially, one must remember a chord in music is not an isolated
entity, but is generally built from whatever scale the melody is built
from (in contrapuntal music, this is unavoidable), and it is the
combination of concordance and scalar properties of the chord that
gives it its musical meaning and direction. As Toch points out, even a
perfect octave can function as a dissonance if it is foreign to the
prevailing scale of the moment.

This is really a very nice description Paul... the Toch point really
cuts right to the heart of the matter! (Though it also broadens the
contextual scope of the consonance versus concordance distinction far
beyond its usual usage; i.e., as by Blackwood, Margo, you, et al, and
I could see how that could perhaps dissipate the impact its usual
intended meaning to some.)

> I've made those points before -- another example being a 6/9 chord,
which sounds best in meantone, OK in 12-tET, and not too hot in JI.

Ah, but there have been folks here in the past -- notably Gerald
Eskelin and John Link -- who did attempt to empirically sing out the
beats (so to speak, as this wasn't exactly what they were doing, but
rather looking for the best aural way to approach, or "lock in" some
of the more complex jazz extensions in an a cappella context) in
chords like a G13#11.

Dan

Dan Stearns wrote,

>> I've made those points before -- another example being a 6/9 chord,
>>which sounds best in meantone, OK in 12-tET, and not too hot in JI.

>Ah, but there have been folks here in the past -- notably Gerald
>Eskelin and John Link -- who did attempt to empirically sing out the
>beats (so to speak, as this wasn't exactly what they were doing, but
>rather looking for the best aural way to approach, or "lock in" some
>of the more complex jazz extensions in an a cappella context) in
>chords like a G13#11.

Gerald Eskelin pretty much conceded at the end of his adventures here that
what he perceived as "locking in" did not necessarily correspond to
eliminating beats -- as in the case of the "high third", which he "locked
in" at a value somewhere between the 12-tET and Pythagorean major thirds.

Patrick wrote,

>That may be, but as I said in my original post, the point of the
>excercise is to examine the mathematical tyranny imposed by strict
>adaptive tuning, not its aesthetic quality.

In the way we've been using the terms, "strict" and "adaptive" tuning are
opposites. You must mean strict JI, since adaptive JI would allow lots of
sub-commatic shifts to cancel the net drift.

Dan Stearns wrote,

>Hello Patrick, and welcome to the list. I Just wanted to pass on a
>brief point that I once came across (and that I've already posted to
>the list before regarding this; especially in the context of the
>tuning of the dominant seventh chord)... I remember reading in Joseph
>Yasser's 1930s "A Theory of Evolving Tonality," a bit where he
>specifically mentions that the a cappella music of the Russian
>church -- free from the influence of equal temperament -- avoids the
>4:5:6:7 dominant seventh... that the seven tone diatonic scale itself
>(so constructed), 'necessitates' a more 'tense' intonation... and that
>the overall context (i.e., the need to establish resolution here),
>even in this variable pitch, a cappella context, overrides whatever
>the most aurally expedient isolated tuning of this chord itself might
>be... While I can't pretend to vouch for the accuracy of the account,
>I thought I'd pass it on as I found it interesting in the context of
>this discussion.

I'd like to join you in welcoming Patrick to the list, and would like to
vouch for your comments. Though one clearly hears 4:5:6:7 chords in
Barbershop music, music such as that of the Bulgarian Women's Choir has a
very different aesthetic, and often sounds to me like it uses minor sevenths
that result from stacking a 6:5 minor third on top of a 3:2 perfect fifth .
. . and I heartily agree with the assessment you/Yasser make above,
notwithstading my feelings about Yasser's other ideas . . . and I'm sure
Margo would agree too and might be able to offer some augmentative remarks .
. .