RE: Microtonal Jazz

Don Ellis wrote a book on his experiences as a quarter-tone jazz trumpeter.
He derived his scale in a very silly way: those of Partch's 43 which were
within 5 cents of an integer number of equal-tempered quartertones away from
the 1/1 made it into his scale. I've heard that he was a great trumpeter,
though.


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How arbitrary are cents? Surprisingly, not very.

Firstly, they are at the threshold of human hearing for pitch
differentiation.

Secondly, allow total intellectualization of all pitch "points" on the
line of frequency to be immediately apprehended.

History has done away with Savarts which are larger than cents
in favor a system which, thankfully, anchors on good old 12-tone ET (e.g.
100 cents is a semitone, 200 cents is a whole tone, etc.) Dare we admit
that this is of value?

Amazingly, most musicians do not realize that the ear does not hear
logarithmically. It learns by rote. For example, sing alound a 7/4 and
then try to find the logarithmic midpoint that bisects the interval.
Knowing this interval is made up of 969 cents, one can calculate a center.

If music is reduced to mathematics, why not cents?

Most important - players constantly reference new pitches to constants
(like open strings, harmonics, etc.) in order to find exotics.
Microtonal notations that represents moving relationships that lose their
constants, make it difficult to come up with the necessary hand positions
to produce the appropriate sounds. It must relate.

No, Gary, you don't need to mix your tunings in a single piece. But a
player on an AFMM series will surely be alternating tunings from piece to
piece on a single program.

Re: polymicrotonal compositions: perhaps just as their are conservatives
and liberals, there will be those that want to stay safe and those that
want to go outside. I want to stay safe by composing intervals that I
can "hear." However a listener cares not what the laws of interaction
are for the soup of pitches, only that they express something that
transcends their experience.

Johnny Reinhard
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com


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>History has done away with Savarts which are larger than cents
>in favor a system which, thankfully, anchors on good old 12-tone ET (e.g.
>100 cents is a semitone, 200 cents is a whole tone, etc.) Dare we admit
>that this is of value?

Denying this would be cutting oneself from 99.99% of Western teaching and
performance practices.

>Amazingly, most musicians do not realize that the ear does not hear
>logarithmically. It learns by rote.

There seems to be plenty of psychoacoustical evidence that refutes the first
claim. We do indeed hear pitch logarithmically, where pitch is defined as
the "virtual pitch" that is assigned to any harmonic or near-harmonic set of
partials. However, due to beats and combination tones, we can detect much
finer deviations from an arithmetic or harmonic series in a chord than
deviations from a geometric (logarithmic) series in either a chord or a
melody. This leads talented performers to essentially mutate the 12-tone
grid to achieve 5-limit just intonation in sustained harmonies. It also
leads people to think of just intonation as representing the way we actually
hear, but it just ain't so.

>For example, sing alound a 7/4 and
>then try to find the logarithmic midpoint that bisects the interval.
>Knowing this interval is made up of 969 cents, one can calculate a center.

Knowing that it is 9 2/3 semitones (you can't hear a 2-cent discrepancy
under performance conditions), one can calculate a center even more easily:
4 5/6 semitones (beats won't help you tune this one!). Sixths of semitones
can be taught systematically, through 11-limit JI harmonies and Arabic and
Byzantine scales, while cents imply a lot of guesswork. (I'm thinking of how
to best educate, and notate music for, tomorrow's musicians, not necessarily
Johnny's highly-skilled ensemble).

I suppose if Johnny wins out, I would recommend restricting the allowed
deviations to 17, 33, and 50 cents when first beginning a course of
microtonal education, so that certain points of reference can be
established. It's just that having to attach numbers like 17 and 33 to these
sounds seems like an unnecessary burden. For the extreme purists among the
JI advocates, I would say that really good performers of 11-limit vocal and
string music will intuitively mutate the 72-tone grid (by no more than 4
cents) in sustained harmonies to achieve absolute perfection; more accurate
notation would not be of any help to those with inferior ears.


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Paul, it is not possible to sing the midpoint of a 7/4 without first
learning it by rote, by memory, from a tuning machine. This logarithmic
division of a "usually"
unfamiliar interval is impossible to divide "on the cuff" into 2 equal
halves (of 484.5
cents each). If you insist that you can do it, and I was to trust your
veracity, you would be the first person in the world that has ever been
able to achieve the feat. Can you sing easily a scale of 5ET? 7ET?
Yes, IF you learn it by rote.

Mathematical machinations to the contrary, cents deviations from a 12ET
grid is for all musicians, not only AFMMers.

Johnny Reinhard
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com


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>Cents notation uses all the symbols of 24ET: this means that a 969 would
>be notated as a B natural with a "-41" above the notehead (assuming C as
>the fundamental).

If I saw that, I would think 1059 cents, not 969.

>Paul, it is not possible to sing the midpoint of a 7/4 without first
>learning it by rote, by memory, from a tuning machine. This logarithmic
>division of a "usually"
>unfamiliar interval is impossible to divide "on the cuff" into 2 equal
>halves (of 484.5
>cents each). If you insist that you can do it, and I was to trust your
>veracity, you would be the first person in the world that has ever been
>able to achieve the feat.

I did not claim that I could do this! I certainly couldn't do it very
accurately. I did mention that the accuracy of logarthmic pitch-distance
perception was far more crude than the accuracy that can be acheived by
tuning to eliminate beats. I just claimed if one had systematically learned
72-tet, one could do it very easily. I've given myself comprehensive
ear-training in 22-tet and 31-tet, not 72-tet. I would further claim that
one could hear the difference in the melodic intervals without a tuning
machine. It is quite possible to distinguish, by ear, major scales which
divide the major third in half, from those that divide it into unequal parts
like 5:4 (logarithmically), without listening to any harmonies.

>Can you sing easily a scale of 5ET? 7ET?
>Yes, IF you learn it by rote.

The musicians of Thailand, without the benefit of oscilloscopes, etc.,
achieve 7et very nearly. This was probably achieved through a
trial-and-error method, and subsequently learned by rote. But the fact that
it was acheived in the first place is evidence of logarithmic hearing. One
can distinguish 5ET from other pentatonic scales, not necessarily in a
musical context, but by listening to the melodic intervals one by one and
noting any differences.

>Mathematical machinations to the contrary, cents deviations from a 12ET
>grid is for all musicians, not only AFMMers.

Dismissing arguments based on practicality, feasibility, and acoustics as
"mathematical machinations" does not contribute to intelligent dialogue.
Apparantly members of Franz Richter Herf's institute and those who have
performed Ezra Sims' music do not fall under the heading of "all musicians."


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American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com

On Mon, 4 Nov 1996, PAULE wrote:

>
> >Cents notation uses all the symbols of 24ET: this means that a 969 would
> >be notated as a B natural with a "-31" above the notehead (assuming C as
> >the fundamental).
>
> If I saw that, I would think 1059 cents, not 969.

You are correct here. Two booboos in one: a Bb -31 is the correct notation.

>
> >Paul, it is not possible to sing the midpoint of a 7/4 without first
> >learning it by rote, by memory, from a tuning machine. This logarithmic
> >division of a "usually"
> >unfamiliar interval is impossible to divide "on the cuff" into 2 equal
> >halves (of 484.5
> >cents each). If you insist that you can do it, and I was to trust your
> >veracity, you would be the first person in the world that has ever been
> >able to achieve the feat.

> I did not claim that I could do this! I certainly couldn't do it very
> accurately. I did mention that the accuracy of logarthmic pitch-distance
> perception was far more crude than the accuracy that can be acheived by
> tuning to eliminate beats. I just claimed if one had systematically learned
> 72-tet, one could do it very easily.

This is what I mean by "rote." You learned in advance of applying your
ear. If you had not, you would join the human race in being unable to
split the unfamiliar 7/4 in half.

> >Can you sing easily a scale of 5ET? 7ET?
> >Yes, IF you learn it by rote.
>
> The musicians of Thailand, without the benefit of oscilloscopes, etc.,
> achieve 7et very nearly. This was probably achieved through a
> trial-and-error method, and subsequently learned by rote. But the fact that
> it was acheived in the first place is evidence of logarithmic hearing. One
> can distinguish 5ET from other pentatonic scales, not necessarily in a
> musical context, but by listening to the melodic intervals one by one and
> noting any differences.

Actually, I am fluid in playing and singing both 7ET and 5ET, but I
learned them. One could not simply initiate these scales on the spot.
One can "learn" the placements of anything (12ET proves that). One
cannot do so unaided by previous preparation.

> >Mathematical machinations to the contrary, cents deviations from a 12ET
> >grid is for all musicians, not only AFMMers.
>
> Dismissing arguments based on practicality, feasibility, and acoustics as
> "mathematical machinations" does not contribute to intelligent dialogue.
> Apparantly members of Franz Richter Herf's institute and those who have
> performed Ezra Sims' music do not fall under the heading of "all musicians."

Please don't misunderstand me. I only want to underscore that AFMM
musicians may be more devoted and more virtuosic than some, but they
merely paid their dues, learning one tuning after another. They are
drawn from the pool of all trained conservatory players. There is less
of a difference in skill than in attitude, based upon my experiences.

Johnny Reinhard

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And if we don't hear logarithmically, how can Aristoxenus have come up with
the idea of equal temperament long before either logarithms or frequency
counters existed?


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On Tue, 5 Nov 1996, PAULE wrote:

>
> And if we don't hear logarithmically, how can Aristoxenus have come up with
> the idea of equal temperament long before either logarithms or frequency
> counters existed?
>

Through intellect, not ears.

Johnny Reinhard


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