RE: Buzz Feiten's tuning

Neil wrote,

>>In the June 98 issue of Guitar Player, on p86, there's a huge ad for
>>guitars using the new Buzz Feiten system for intonation. What makes me >a
>>bit ill is 2 things: one, as far as I can tell, after playing guitar for
>>33 years, if the guitar keeps the same 12 note/octave eq temp
>>arrangement,

Gary wrote,

> I guess I'll ask the obvious question: What aspects of intonation does
>the Buzz Feiten system address if not microtonality? Is its purpose
>greater accuracy to 12TET (in the spirit of moveable bridges and such)?

Yes. As much as I agree with Neil that it would be more valuable to
start educating guitarists on microtonality than obsessing over getting
perfect 12tET, it is the latter that Feiten's system is geared toward.
In addition to the usual bridge adjustments, Feiten proposes some
string-specific nut adjustments. I remember Steve Vai saying he is
getting Feiten's system installed on all his guitars, as he was never
before able to play chords anywhere on the fingerboard and have them all
sound in tune. When playing along with keyboards, etc, it is 12tET that
defines whether one is in tune or out of tune, and deficiencies in 12tET
itself are not really an issue to most musicians, who have never spent
time listening to purer intervals.

>Dave, I know you
>just joined this forum, but I think your name was mentioned before in
>that you (or someone named Ralph David Hill?)...

They are one in the same. A loooonnng time ago, Dave put together a
wire-wrapped Z80-based single-board computer and with it did a wonderful
lecture demo tape series called "Introduction to Nontraditional Harmony",
which I think is a great, historical introduction to JI.




>To me, [prime limits] sounds preposterous, as there seems to be no
>mechanism or reason for the auditory system to be performing prime
>factorizations.

I personally am pretty much a fence-sitter on the prime vs. odd
question, but perhaps it's worth asking: Do you perceive that there's any
mechanism in our auditory system for detecting powers of two (i.e.,
octaves)? If so, then why not powers of three or five?

On Thu, 30 Apr 1998, Paul H. Erlich wrote:
> Ken, you appear to agree with me that the "limit" is best defined as the
> largest odd, not prime, factor, in the ratios, when the intention is to
> characterize the complexity of an interval's sound. Dave, I know you
> just joined this forum, but I think your name was mentioned before in
> that you (or someone named Ralph David Hill?) also believed that it is
> the odd, not prime, limit, that best characterizes an interval's effect
> (and affect?). [snip]
>
> Shall
> we have a go at preparing an article or Web page to defend our position?

'Scuse me for butting in, but it was an open letter. I certainly agree.
I'm not sure what I can contribute to such an effort, but I'm on your
side at least.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

I've thought about the matter of prime integers vs odd integers re the
contribution of successively higher ones to musical harmony, and it seems to
me that intervals based on the successively higher odd integers each
contribute something unique in the way of a musical sound effect on a
listener, so that the effect of a 9/8 musical interval, say, is, from a
psychological listening point of view essentially different than a 3/2 musical
interval. While there is the octave equivalence effect for intervals
differing by a factor of 2 or 2 to the nth power, so that a 10/4 interval is
psychologically harmonically more or less the same as a 5/4 interval, there
isn't such an equivalence effect for intervals related by factors other than
2.

I can see that from the point of view of building up a musical system, once
one included 3-ratio intervals in the system, one would want to use combined
intervals, adding one such interval to another - e.g. creating a ninth by
adding two fifths, etc. But from the psychological perspective, I believe the
ninth really has a different character than the fifths from which it is
constructed by addition.

>While there is the octave equivalence effect for intervals
>differing by a factor of 2 or 2 to the nth power, so that a 10/4 interval is
>psychologically harmonically more or less the same as a 5/4 interval, there
>isn't such an equivalence effect for intervals related by factors other than
>2.

I think that those who favor a prime-based limit scheme would agree with
that, but say that you're listening for the wrong thing.

They would agree that any arbitrary power of 2 produces an effect of
equivalence, but that equivalence is not what arbitrary powers of 3
produce. They'd say that three produces that feeling of steely coldness we
hear in 3:2 and 4:3 (for example), and you can stack up as many threes as
you'd like without changing that effect much.

They'd then further say that any arbitrary power of 5 produces a
sensation of sweetness, any power of 7 produces that classic septimal zap,
and so forth. But there would not be a feeling of octave-like equivalence
between, say, 3:2 and 9:8, because equivalence is a property of powers of
2.

Again, I personally am a bit ambilvalent on the topic, but that's what I
suspect the counterargument would be.

Dave Hill wrote,

>>While there is the octave equivalence effect for intervals
>>differing by a factor of 2 or 2 to the nth power, so that a 10/4 interval is
>>psychologically harmonically more or less the same as a 5/4 interval, there
>>isn't such an equivalence effect for intervals related by factors other than
>>2.

Gary wrote,

>I think that those who favor a prime-based limit scheme would agree with
>that, but say that you're listening for the wrong thing.

>They would agree that any arbitrary power of 2 produces an effect of
>equivalence, but that equivalence is not what arbitrary powers of 3
>produce. They'd say that three produces that feeling of steely coldness we
>hear in 3:2 and 4:3 (for example), and you can stack up as many threes as
>you'd like without changing that effect much.

>They'd then further say that any arbitrary power of 5 produces a
>sensation of sweetness, any power of 7 produces that classic septimal zap,
>and so forth. But there would not be a feeling of octave-like equivalence
>between, say, 3:2 and 9:8, because equivalence is a property of powers of
>2.

If you're doing the stacking and maintaining the intermediary tones in
the chord, then I would agree with them. Otherwise I would disagree. But
there's more.

"An arbitrary power of two produces an effect of equivalence." This must
of course include the case where the power is zero, and the equivalence
is greatest. The equivalence evidently falls off as the power increases.

But what about steely coldness? Is it there when the power is zero? Does
a unison contain all potential interval qualities, to a greater degree
than the intervals themselves? It would seem hard to argue that way.

The equivalence Dave was referring to was not a property of intervals
themselves, but a similarity relation between different intevals. If
there was a specific quality associated with given prime factors, than
that quality might result in a similarity between different intervals
with the same prime factors albeit to different powers. But it seems
hard to formulate a consistent theory along those lines.

What about intervals like 3/5? Does this have both steely coldness and
sweetness? You can't say it has steely coldness and anti-sweetness
because a 5/3 sounds the same as a 3/5. So does 15/1 (or 15/8) have the
same qualities as 5/3, since the factors are still 5 and 3? It seems
hard to maintain that 5/3 has a greater affective similarity to 15/8 (or
15/1) than to any other interval. But that is exactly where such an
association of primes with qualities leads.

No more time now, but I think any such prime-quality theory could be
shown to be either logically inconsistent or severly at variance with
observation.

>What about intervals like 3/5? Does this have both steely coldness and
>sweetness? You can't say it has steely coldness and anti-sweetness
>because a 5/3 sounds the same as a 3/5.

I don't think that anybody would claim there to be any concern over
which number you is the denominator and which is the numerator.

As for having both a steely cold 3 and a sweet 5 in a ratio, I think the
prime-limit proponent's answer would be that the larger prime always wins -
demands more attention.

But again, I'm kind of a fence-sitter on the question of the basis of
limits. A while back I would have towed the prime line, but now I'm not so
sure.