Infinite (de)Gradation

Hello,

Being fairly new to the list, and from reading a few "woes" from composers in finding performers, I have been wondering at where "the point of diminishing returns" lies in developing and using alternate tuning systems.

I seem to remember reading a comment attributed to JS Bach that the average (or was it "competent") musician should be able to "hear/decern" 100 pitches in an octave. That comes out to a scale of 12-cents per step.

But, from reading comments of present-day performers balking at 72-tone scales, which comes out to be 16 2/3 cents per step, I wonder if Bach was being too demanding?

John Chalmers wrote about a scale with 612-edo, that comes to about 1.96 cents per step. This seems to be more a theoretical scale than one someone would write a full-blow work in (I could be [and probably am] wrong here, I just haven't heard one yet). At what point does the "infinite" scale of pitches start to sound like unrelated noise.

The scale that I have been working with has steps as small as 14.367 cents (I'm working with Harry Partch's 43 tone scale), and I have often wondered how musically useful (at least at this point in my explorations) some of these smaller intervals are for me.

One of the things that I find most intriguing about exploring different tuning systems is that each one seems to present a different palette or "sonic universe". This alone justifies these explorations. But on the other hand, how much can we demand of a "professional" musician in playing in these "alternate sonic universes", and then how much can we expect from our "audience" in their appreciation of these "alternate universes" (that is if the musicians are playing in the right universe in the first place)?

Is there some "standard" that some of the schools who teach Microtonal skills that each "graduate" is expected to be able to demonstrate? Are they expected to be able to identify various "tuning systems" just by listening to their scales? I went to school more than 20 years ago, and there were no classes in "alternate tuning", and the ear-training was not that demanding, just teaching the ability to hear the 12-et intervals.

This does not even begin to touch on the added problems with notational systems, which a whole thing unto itself.

While it is expected that musicians be able to perform these works, how much will the "listening" audience appreciate (let alone understand, or even care about) what they are hearing?

Mike

hi Michael,

> From: "Michael J McGonagle" <fndsnd@rcnchicago.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, October 11, 2002 12:10 PM
> Subject: [tuning] Infinite (de)Gradation
>

> Hello,
>
> Being fairly new to the list, and from reading a few "woes" from
> composers in finding performers, I have been wondering at where "the
> point of diminishing returns" lies in developing and using alternate
> tuning systems.
>
> I seem to remember reading a comment attributed to JS Bach that the
> average (or was it "competent") musician should be able to "hear/decern"
> 100 pitches in an octave. That comes out to a scale of 12-cents per step.

hmmm... that's really interesting to me just now, because i
just found out that 200edo (6 cents per step) gives a nice easy
approximation to Werckmeister III tuning, and that was Bach's
preferred tuning according to Johnny Reinhard.

> John Chalmers wrote about a scale with 612-edo, that comes to about 1.96
> cents per step. This seems to be more a theoretical scale than one
> someone would write a full-blow work in (I could be [and probably am]
> wrong here, I just haven't heard one yet). At what point does the
> "infinite" scale of pitches start to sound like unrelated noise.

to my mind, it's not very likely that anyone would use 612edo
as a *scale*. its usefulness is in measuring the comparisons
of other scales with much lower cardinalities, similar to the
way cents (1200edo) are used as a standard.

i just found that 612edo gives excellent integer approximations
to both 12edo and Werckmeister III, which makes it very easy
to compare those two tunings without having to bother with
decimal points or fractional remainders.

> Is there some "standard" that some of the schools who teach Microtonal
> skills that each "graduate" is expected to be able to demonstrate? Are
> they expected to be able to identify various "tuning systems" just by
> listening to their scales? I went to school more than 20 years ago, and
> there were no classes in "alternate tuning", and the ear-training was
> not that demanding, just teaching the ability to hear the 12-et intervals.

AFAIK, not much about microtonality is being taught in schools,
altho the situation now is certainly better than when you and
i were both in school (around the same time).

last year, many of us here did more-or-less agree on 72edo as
a useful tuning standard, especially for notation, but ...

> This does not even begin to touch on the added problems with notational
> systems, which a whole thing unto itself.

there's been a huge amount of stuff posted both here and on tuning-math
regarding microtonal notation. and unfortunately we could not even
agree last year on a good 72edo notation, me touting my "HEWM" notation
/tuning/files/dict/hewm.htm
and everyone else who had a preference preferring another variety based
more closely than mine on Ezra Sims's 72edo notation.

> While it is expected that musicians be able to perform these works, how
> much will the "listening" audience appreciate (let alone understand, or
> even care about) what they are hearing?

you might be interested in taking a look at my ideas on "finity"
and "bridging":
/tuning/files/dict/finity.htm
/tuning/files/dict/bridging.htm
/tuning/files/dict/xenbridg.htm

and also the related subject of "periodicity blocks":
/tuning/files/dict/pblock.htm
(especially paul erlich's excellent tutorial)

there's been some argument (between paul and i) about exactly
what "xenharmonic bridge" means, and how it's different from
"unison vector". unfortunately we never finished that argument
and many of my ideas on it are still not clear ... consider
everything about finity and bridging a "work in progress".

-monz
"all roads lead to n^0"

--- In tuning@y..., Michael J McGonagle <fndsnd@r...> wrote:

> I seem to remember reading a comment attributed to JS Bach that the
> average (or was it "competent") musician should be able to "hear/decern"
> 100 pitches in an octave. That comes out to a scale of 12-cents per step.

99 pitches per octave is a good system. :)

> John Chalmers wrote about a scale with 612-edo, that comes to about 1.96
> cents per step. This seems to be more a theoretical scale than one
> someone would write a full-blow work in (I could be [and probably am]
> wrong here, I just haven't heard one yet).

I've actually written stuff in 612; of course I cheated and used a computer.

At what point does the
> "infinite" scale of pitches start to sound like unrelated noise.

Never. A pitch isn't noise.

--- In tuning@y..., Michael J McGonagle <fndsnd@r...> wrote:

/tuning/topicId_39499.html#39499

> Hello,
>
> Being fairly new to the list, and from reading a few "woes" from
> composers in finding performers, I have been wondering at
where "the point of diminishing returns" lies in developing and using
alternate tuning systems.
>
> I seem to remember reading a comment attributed to JS Bach that the
> average (or was it "competent") musician should be able
to "hear/decern" 100 pitches in an octave. That comes out to a scale
of 12-cents per step.
>
> But, from reading comments of present-day performers balking at 72-
tone scales, which comes out to be 16 2/3 cents per step, I wonder if
Bach was being too demanding?
>

***Well, let's be realistic. *Most* young performers nowadays play
quartertones. That's partially because quartertones are so
established in the contemporary repertory. That's one reason that
music composition software manufacturers like *Sibelius* pretty much
*have* to include quartertone options. So we're at 50 cents, there...

Now, the "smaller" divisions, like the 1/6th tone at 33 cents or the
1/12th tone at 17 cents are *new* to many performers. So, sure, they
are going to balk... Or at least the less adventurous ones.

Surely, though, that doesn't mean that 17 cents doesn't make a
difference!

> John Chalmers wrote about a scale with 612-edo, that comes to about
1.96
> cents per step. This seems to be more a theoretical scale than one
> someone would write a full-blow work in (I could be [and probably
am]
> wrong here, I just haven't heard one yet). At what point does the
> "infinite" scale of pitches start to sound like unrelated noise.
>

***Well, keep in mind, too that scales like Partch's 43 give
particular *glissando*-type effects that would be impossible to get
any other way. So, surely, his divisions are not too small.

> The scale that I have been working with has steps as small as
14.367 cents (I'm working with Harry Partch's 43 tone scale), and I
have often wondered how musically useful (at least at this point in
my explorations) some of these smaller intervals are for me.
>

***My guess is that they *will* be, depending on how you use them.
My point in some recent posts, though, is that there *is* a certain
bone fide performer resistance, and we have to plow through that, one
way or another!!

> One of the things that I find most intriguing about exploring
different tuning systems is that each one seems to present a
different palette or "sonic universe". This alone justifies these
explorations.

***Yes, this is Ivor Darreg's *basic* musical concept (and
transferred to Brian McLaren later)

But on the
> other hand, how much can we demand of a "professional" musician in
> playing in these "alternate sonic universes", and then how much can
we expect from our "audience" in their appreciation of
these "alternate universes" (that is if the musicians are playing in
the right universe in the first place)?
>

***Well, Michael, this is a "work in progress." Partch, as you know,
has been *very* successful with audiences. (Well, Partch became
*very* successful on the overall... :) Part of that, I believe, is
the incorporation of the corporal... or, in other words, the
*theatrical* element. So, you never know what will tickle and
audience's fancy... but it can't be dull, that's for certain! :)

> Is there some "standard" that some of the schools who teach
Microtonal skills that each "graduate" is expected to be able to
demonstrate?

***There are no such courses and there are no such
determined "skills" except, possibly, for the 72-tET training going
on in Boston at the New England conservatory. *They* are expected to
master 1/12th of a whole tone, or the 17 cent interval as the
smallest, as mentioned above...

Are
> they expected to be able to identify various "tuning systems" just
by listening to their scales?

***They just study one. Johnny Reinhard in New York teaches many
instrumentalists many scales, but it's more in the course of learning
*pieces..." Of course, that's the most important part, after all!!

I went to school more than 20 years ago, and
> there were no classes in "alternate tuning", and the ear-training
was not that demanding, just teaching the ability to hear the 12-et
intervals.

***Well, I took some ear training classes at Eastman that drove me up
the wall! But they surely weren't microtonal! :)

>
> This does not even begin to touch on the added problems with
notational systems, which a whole thing unto itself.
>
> While it is expected that musicians be able to perform these works,
how much will the "listening" audience appreciate (let alone
understand, or even care about) what they are hearing?
>
> Mike

***Well, Michael, you are addressing some very important issues
here. You will find that there are several people on this list who
are *primarily* interested in the *theoretical* HOWEVER, there are
some *practical* people here too: I would include Johnny Reinhard,
Jon Szanto and myself in that category, with some others who visit
here from time to time...

So these *practical* issues need to be brought up as a kind of "foil"
to the important theoretical work that goes on here...

So, all of this is very much a "work in progress" and *you*, Michael,
are very much a part of it, just by asking these questions!!!

Joe Pehrson

Michael J McGonagle wrote:

> Hello,
>
> Being fairly new to the list, and from reading a few "woes" from
> composers in finding performers, I have been wondering at where "the
> point of diminishing returns" lies in developing and using alternate
> tuning systems.
>
> I seem to remember reading a comment attributed to JS Bach that the
> average (or was it "competent") musician should be able to "hear/decern"
> 100 pitches in an octave. That comes out to a scale of 12-cents per step.
>
> But, from reading comments of present-day performers balking at 72-tone
> scales, which comes out to be 16 2/3 cents per step, I wonder if Bach
> was being too demanding?
>
> John Chalmers wrote about a scale with 612-edo, that comes to about 1.96
> cents per step. This seems to be more a theoretical scale than one
> someone would write a full-blow work in (I could be [and probably am]
> wrong here, I just haven't heard one yet). At what point does the
> "infinite" scale of pitches start to sound like unrelated noise.
>
> The scale that I have been working with has steps as small as 14.367
> cents (I'm working with Harry Partch's 43 tone scale), and I have often
> wondered how musically useful (at least at this point in my
> explorations) some of these smaller intervals are for me.
>
> One of the things that I find most intriguing about exploring different
> tuning systems is that each one seems to present a different palette or
> "sonic universe". This alone justifies these explorations. But on the
> other hand, how much can we demand of a "professional" musician in
> playing in these "alternate sonic universes", and then how much can we
> expect from our "audience" in their appreciation of these "alternate
> universes" (that is if the musicians are playing in the right universe
> in the first place)?
>
> Is there some "standard" that some of the schools who teach Microtonal
> skills that each "graduate" is expected to be able to demonstrate? Are
> they expected to be able to identify various "tuning systems" just by
> listening to their scales? I went to school more than 20 years ago, and
> there were no classes in "alternate tuning", and the ear-training was
> not that demanding, just teaching the ability to hear the 12-et intervals.
>
> This does not even begin to touch on the added problems with notational
> systems, which a whole thing unto itself.
>
> While it is expected that musicians be able to perform these works, how
> much will the "listening" audience appreciate (let alone understand, or
> even care about) what they are hearing?
>
> Mike
>

Hi Mike and welcome. I assume you speak of the Western tradition. Have you considered the Indian
classical vocal and instrumental tradition to name but one? The masters are capable of great
accuracy at speed, and the audiences certainly appreciate. I'd be optimistic and declare that we
haven't scratched the surface of the potential for microtonal performance in the West. We simply
need to work hard at it.

Kind Regards

In reading the literature on J.S. Bach, the attribution below given to Bach is nowhere to be found. I have never even seen a reference to it before.

best, Johnny Reinhard

In a message dated 10/11/2002 2:10:52 PM Eastern Standard Time, fndsnd@rcnchicago.com writes:

>
> I seem to remember reading a comment attributed to JS Bach that the
> average (or was it "competent") musician should be able to "hear/decern"
> 100 pitches in an octave. That comes out to a scale of
> 12-cents per step.

Afmmjr@aol.com wrote:
> In reading the literature on J.S. Bach, the attribution below given to Bach is nowhere to be found. I have never even seen a reference to it before. > Johnny,

Yes, that is why I said "seem to remember". My memory for things that I heard 20 years ago may not be quite accurate. The point of this was more to find out what sorts of "standards" have been adopted (or ones that are just good guidelines), not to say that Bach espoused what I said below...

Mike

> best, Johnny Reinhard
> > > In a message dated 10/11/2002 2:10:52 PM Eastern Standard Time, fndsnd@rcnchicago.com writes:
> > >>I seem to remember reading a comment attributed to JS Bach that the >>average (or was it "competent") musician should be able to "hear/decern" >>100 pitches in an octave. That comes out to a scale of >>12-cents per step.
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