New tuning site at www.ppexpressivo.wyenet.co.uk

Dear All,I have just put the finishing touches on a new website which hopefully
puts an new slant on the subject of Tunings and Temperaments. I would really
appreciate any comments, notification of problems, encouragement etc. The site
can be found at:http://www.ppexpressivo.wyenet.co.uk
[http://www.ppexpressivo.wyenet.co.uk]Hope you find it interesting.RegardsChris
Tyler

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Bravo! on the webpage design and the tables,

but:

Just tuning is "never used in practice"????

I guess you havn't been around here very long! Nor, apparently, are you
familiar with 20th c. music history! Ever heard of Harry Partch of LaMotte
Young (to mention "just" two)?

Dante

-----Original Message-----
From: Family Tyler [mailto:familytyler@hotmail.com]
Sent: Thursday, March 07, 2002 3:28 PM
To: tuning@yahoogroups.com
Subject: [tuning] New tuning site at www.ppexpressivo.wyenet.co.uk

Dear All,

I have just put the finishing touches on a new website which hopefully
puts an new slant on the subject of Tunings and Temperaments. I would
really appreciate any comments, notification of problems, encouragement etc.
The site can be found at:

http://www.ppexpressivo.wyenet.co.uk

Hope you find it interesting.

Regards
Chris Tyler

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Dear Chris,

I'll second Dante in a couple of ways: first off, very nice both in
design AND implementation - I'm going to check out the tuning widget
later tonight.

But more importantly, you've really put up a problematic
premise: "Natural tuning, sometimes called Just Tuning or Ptolemaic
Tuning is something of an oddity in that it has some attributes which
would commend it as the best possible tuning but its drawbacks are so
great that it is never used in practice."

I happened to have performed many concerts of the music of Harry
Partch on his original instruments, and even helped him prepare the
second edition of his book "Genesis of a Music", which goes into
great detail not only about Just Intonation, but how he delved into
it and made a lifetime of music-making in it, starting in the 1920's.
The Harry Partch Foundation maintains a website which I curate:

http://www.corporeal.com/

and on the links page:

http://www.corporeal.com/links.html

you can see many other peoples writings on Partch, as well as similar
topics. And this is just (no pun intended) one person who has
successfully utilized JI - many, many more, I assure you, including
people that have as recently as this week posted new recordings of JI
music, not to mention people on this list that compose and perform in
JI (in addition to other tunings as well).

It's a big world, and it is easy to miss some stuff. But it is pretty
hard to miss someone like Partch, and many people don't. They might
be scratching their heads about now when they see the bit
about "never used in practice"...

Looking forward to spending a little more time on your site tonight!

Cheers,
Jon

In-Reply-To: <F60MAKyttoRaD689cMh00007ce5@hotmail.com>
Family Tyler wrote:

> <DIV>I have just put the finishing touches on a new website which
> hopefully puts an  new slant on the subject of Tunings and
> Temperaments.  I would really appreciate any comments,
> notification of problems, encouragement etc.  The site can be
> found at:</DIV>
> <DIV> </DIV>
> <DIV><A
> href="http://www.ppexpressivo.wyenet.co.uk">http://www.ppexpressivo.wyen
> et.co.uk</A></DIV>

This is good in intent, but it's the problems I'm going to concentrate on
because they're always easier to discuss. Don't let that put you off!

You say "but musical instruments and almost all modern music is based on
sets of discrete notes". This is a gross over-simplification. You say
you're a cellist -- well, do you *really* think a cello uses a discrete
set of notes?

The "almost universally" popup could be replaced with a link (replacing
the top-level frame) to
<http://www.mmk.ei.tum.de/persons/ter/top/octequiv.html>. I completely
disagree with the last sentence of what you have: "However, these are very
much the exceptions." These kinds of imperfect octaves are the rule, not
the exception.

Having some kind of octave is the rule for music that covers more than an
octave. So the octave phenomenon is the nearest we have to a universal,
but its tuning of 2:1 is certainly not. The link I gave before explains
this.

Your definition of "tuning" is a bit odd. You seem to be saying that
tunings involve integer ratios but temperaments do not. Rather,
temperaments are a subset of tunings and plenty of tunings are neither
temperaments nor involve integer ratios.

Could you add a volume control to The Musical Calculator? I usually have
my system volume set high so I can play MP3s without distortion. This
stuff came through very loud. Oh, you're using Pierre Lewis's Java. I
was thinking it how similar it was :-). I wonder though why I got a
message box about untrusted Active X.

The phrase "1/4 comma Meantone, sometimes called Aaron's Meantone or just
plain Meantone" is a good example of why I try to avoid the word "just" in
tuning discussions where it doesn't refer to just intonation. 1/4 comma
meantone can indeed be referred to as simply "meantone" but "just plain
meantone" suggests a different kettle of ball games.

You say "A further drawback is that the human ear is more sensitive to
poorly tuned 5ths than it is to 3rds ..." without evidence. Find some
evidence, or remove the assertion.

1/11 comma meantone isn't *quite* the same as 12 note equal temperament.

Wow, you know about Ordinaire!

In fact, my general impression of this site is that it's a worthy attempt
to re-invent the wheel. There are quite a few sites out there explaining
the traditional temperaments, including Pierre's that you link to and took
the Java from. I'd be more interested in hearing your personal opinions
on these topics, and the music you've made along the way.

Graham

--- In tuning@y..., graham@m... wrote:

> You say "A further drawback is that the human ear is more sensitive
to
> poorly tuned 5ths than it is to 3rds ..." without evidence. Find
some
> evidence, or remove the assertion.

the vos articles i reproduced here (in part) do seem to provide
strong evidence for this assertion, both for complex and for pure
tones.

but kyle gann asserts the exact opposite, here:

http://home.earthlink.net/~kgann/histune.html

"There are acoustical reasons for this, namely - though I wouldn't
want to go into the math involved - that the notes in a slightly out-
of-tune third, being closer together than those in a fifth, create
faster and more disturbing beats than those in a slightly out-of-tune
fifth. (I can confirm this from experience with my own Steinway
grand, which I keep tuned to an 18th-century tuning.)"

what kyle doesn't mention is that the beats are much louder for the
fifth than for the third.

Thank you, Paul! Good points. I think we can generalize with a fair
degree of safety (cringing defensively) that the octave is the most
critical interval in terms of human tolerance for tuning error, the
perfect fifth next, etc., right on up the harmonic series, but
eliminating factors of two.

I appreciate very much, by the way, your statement to me in your
reply to my post of a few days ago, that my presence here has been
sorely missed. Sorry I haven't responded before now, and also that I
haven't been more active here. I am horribly busy with a lot of
things, not the least of which is preparation of my choir for a
performance in our local community concert series. No local
organization has ever before been invited to perform in this series,
and we feel very honored and grateful.

Cheers and best wishes to all,

Bob

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., graham@m... wrote:
>
> > You say "A further drawback is that the human ear is more
sensitive
> to
> > poorly tuned 5ths than it is to 3rds ..." without evidence. Find
> some
> > evidence, or remove the assertion.
>
> the vos articles i reproduced here (in part) do seem to provide
> strong evidence for this assertion, both for complex and for pure
> tones.
>
> but kyle gann asserts the exact opposite, here:
>
> http://home.earthlink.net/~kgann/histune.html
>
> "There are acoustical reasons for this, namely - though I wouldn't
> want to go into the math involved - that the notes in a slightly
out-
> of-tune third, being closer together than those in a fifth, create
> faster and more disturbing beats than those in a slightly out-of-
tune
> fifth. (I can confirm this from experience with my own Steinway
> grand, which I keep tuned to an 18th-century tuning.)"
>
> what kyle doesn't mention is that the beats are much louder for the
> fifth than for the third.

--- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
> Thank you, Paul! Good points. I think we can generalize with a fair
> degree of safety (cringing defensively) that the octave is the most
> critical interval in terms of human tolerance for tuning error, the
> perfect fifth next, etc., right on up the harmonic series, but
> eliminating factors of two.

Hi Bob, It's lucky you cringed defensively. :-)

I feel that what you say holds until the complexity a*b of a ratio a:b
(in lowest terms) gets up around 35. Then I think tolerance for
mistuning (e.g. in cents) starts to decrease again, but for an
entirely different reason. A complex ratio doesn't become much more
dissonant with mistuning like a simple ratio does, since it is already
fairly dissonant, but it loses its justness, or its identity _as_ that
ratio, with a smaller mistuning the more complex the ratio, until
finally up around a complexity of 100 to 120 (depending on the timbre
and lots of other things) it _has_ no identity distinct from its
nearby mistunings and its justness cannot be found.

The above assumes we're talking about bare dyads. If the more complex
ratios are embedded in larger otonal chords then I think the tolerance
stays about the same as we keep going up.

Just my humble opinion.

In a message dated 3/8/02 11:36:26 PM Eastern Standard Time,
rwendell@cangelic.org writes:

> I think we can generalize with a fair
> degree of safety (cringing defensively) that the octave is the most
> critical interval in terms of human tolerance for tuning error, the
> perfect fifth next, etc., right on up the harmonic series, but
> eliminating factors of two.
>
>

Hi Bob,

In general I agree, as would Andreas Werckmeister. He talks of this in his
book "Musical Temperament." My question is how do we account for the piano
having all its octaves stretched, more than the perfect fifth is shrunk.
Isn't this the case?

Curiously, Johnny Reinhard

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
> > Thank you, Paul! Good points. I think we can generalize with
a fair
> > degree of safety (cringing defensively) that the octave is the
most
> > critical interval in terms of human tolerance for tuning error,
the
> > perfect fifth next, etc., right on up the harmonic series, but
> > eliminating factors of two.
>
> Hi Bob, It's lucky you cringed defensively. :-)
>
> I feel that what you say holds until the complexity a*b of a ratio
a:b
> (in lowest terms) gets up around 35. Then I think tolerance for
> mistuning (e.g. in cents) starts to decrease again, but for an
> entirely different reason. A complex ratio doesn't become much
more
> dissonant with mistuning like a simple ratio does, since it is
already
> fairly dissonant, but it loses its justness, or its identity _as_
that
> ratio, with a smaller mistuning the more complex the ratio, until
> finally up around a complexity of 100 to 120 (depending on the
timbre
> and lots of other things) it _has_ no identity distinct from its
> nearby mistunings and its justness cannot be found.
>
> The above assumes we're talking about bare dyads. If the
more complex
> ratios are embedded in larger otonal chords then I think the
tolerance
> stays about the same as we keep going up.
>
> Just my humble opinion.

i think dave keenan is exactly right. there's no substitute for
actually *listening* to lots of just and mistuned ratios, and dave
has obviously done a great deal of this.

--- In tuning@y..., Afmmjr@a... wrote:
> In a message dated 3/8/02 11:36:26 PM Eastern Standard
Time,
> rwendell@c... writes:
>
>
> > I think we can generalize with a fair
> > degree of safety (cringing defensively) that the octave is the
most
> > critical interval in terms of human tolerance for tuning error,
the
> > perfect fifth next, etc., right on up the harmonic series, but
> > eliminating factors of two.
> >
> >
>
> Hi Bob,
>
> In general I agree, as would Andreas Werckmeister. He talks
of this in his
> book "Musical Temperament." My question is how do we
account for the piano
> having all its octaves stretched, more than the perfect fifth is
shrunk.

bob is dealing with human voices, which have perfectly harmonic
partials, while the piano has stretched partials, so the "target"
(however you define it -- generally an artistic choice) for
eliminating beats is always stretched relative to ji. donald hall's
book _musical acoustics_ has an excellent discussion of piano
tuning, its vagaries and the physical and psychophysical factors
involved.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_35317.html#35435

> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > --- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
> > > Thank you, Paul! Good points. I think we can generalize with
> a fair
> > > degree of safety (cringing defensively) that the octave is the
> most
> > > critical interval in terms of human tolerance for tuning error,
> the
> > > perfect fifth next, etc., right on up the harmonic series, but
> > > eliminating factors of two.
> >
> > Hi Bob, It's lucky you cringed defensively. :-)
> >
> > I feel that what you say holds until the complexity a*b of a
ratio
> a:b
> > (in lowest terms) gets up around 35. Then I think tolerance for
> > mistuning (e.g. in cents) starts to decrease again, but for an
> > entirely different reason. A complex ratio doesn't become much
> more
> > dissonant with mistuning like a simple ratio does, since it is
> already
> > fairly dissonant, but it loses its justness, or its identity _as_
> that
> > ratio, with a smaller mistuning the more complex the ratio, until
> > finally up around a complexity of 100 to 120 (depending on the
> timbre
> > and lots of other things) it _has_ no identity distinct from its
> > nearby mistunings and its justness cannot be found.
> >
> > The above assumes we're talking about bare dyads. If the
> more complex
> > ratios are embedded in larger otonal chords then I think the
> tolerance
> > stays about the same as we keep going up.
> >
> > Just my humble opinion.
>
> i think dave keenan is exactly right. there's no substitute for
> actually *listening* to lots of just and mistuned ratios, and dave
> has obviously done a great deal of this.

***This is terribly interesting, but I'm only *half* getting it.

Bob Wendell is saying that the tolerance for error increases as we go
further up the harmonic series. Dave Keenan says this is true, but
after a certain a*b (num*denom) then again we need to be more
sensitive to error again, yes?

But the reasoning is the "justness" of the larger ratio which becomes
rather an "academic" distinction, yes, since we're in the realm
of "rational" intonation rather than truly "just" intonation.

So, in other words, the necessity for increased specificity is more a
*theoretical* concept than an *auditory* one??

Or am I not understanding this... ??

Thanks!!!

jp

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_35317.html#35435
>
> > --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> > > --- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
> > > > Thank you, Paul! Good points. I think we can generalize
with
> > a fair
> > > > degree of safety (cringing defensively) that the octave is
the
> > most
> > > > critical interval in terms of human tolerance for tuning
error,
> > the
> > > > perfect fifth next, etc., right on up the harmonic series, but
> > > > eliminating factors of two.
> > >
> > > Hi Bob, It's lucky you cringed defensively. :-)
> > >
> > > I feel that what you say holds until the complexity a*b of a
> ratio
> > a:b
> > > (in lowest terms) gets up around 35. Then I think tolerance
for
> > > mistuning (e.g. in cents) starts to decrease again, but for
an
> > > entirely different reason. A complex ratio doesn't become
much
> > more
> > > dissonant with mistuning like a simple ratio does, since it
is
> > already
> > > fairly dissonant, but it loses its justness, or its identity _as_
> > that
> > > ratio, with a smaller mistuning the more complex the ratio,
until
> > > finally up around a complexity of 100 to 120 (depending on
the
> > timbre
> > > and lots of other things) it _has_ no identity distinct from its
> > > nearby mistunings and its justness cannot be found.
> > >
> > > The above assumes we're talking about bare dyads. If the
> > more complex
> > > ratios are embedded in larger otonal chords then I think the
> > tolerance
> > > stays about the same as we keep going up.
> > >
> > > Just my humble opinion.
> >
> > i think dave keenan is exactly right. there's no substitute for
> > actually *listening* to lots of just and mistuned ratios, and
dave
> > has obviously done a great deal of this.
>
>
> ***This is terribly interesting, but I'm only *half* getting it.
>
> Bob Wendell is saying that the tolerance for error increases as
we go
> further up the harmonic series. Dave Keenan says this is true,
but
> after a certain a*b (num*denom) then again we need to be
more
> sensitive to error again, yes?

right, between a*b=35 and a*b=100, or higher.

>
> But the reasoning is the "justness" of the larger ratio which
becomes
> rather an "academic" distinction, yes, since we're in the realm
> of "rational" intonation rather than truly "just" intonation.

no, that comes in with even more complex ratios.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_35317.html#35465

> >
> >
> > ***This is terribly interesting, but I'm only *half* getting it.
> >
> > Bob Wendell is saying that the tolerance for error increases as
> we go further up the harmonic series. Dave Keenan says this is
true, but after a certain a*b (num*denom) then again we need to be
> more sensitive to error again, yes?
>
> right, between a*b=35 and a*b=100, or higher.
>
> >
> > But the reasoning is the "justness" of the larger ratio which
> becomes rather an "academic" distinction, yes, since we're in the
realm of "rational" intonation rather than truly "just" intonation.
>
> no, that comes in with even more complex ratios.

****Hmmm. Well, this is odd then, no? So for these "intermediate-
sized" ratios one has to be *more* accurate?? Whyzzat??

jp

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> ****Hmmm. Well, this is odd then, no? So for these
"intermediate-
> sized" ratios one has to be *more* accurate??

*less* accurate.

> Whyzzat??

because they're simple enough that they can be recognized even
under moderate mistuning, but complex enough that moderate
mistuning won't produce loud, disturbing beating in the louder,
lower partials.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> i think dave keenan is exactly right. there's no substitute for
> actually *listening* to lots of just and mistuned ratios, and dave
> has obviously done a great deal of this.

This is very nice of you to say Paul. But I have to be honest. I
really haven't done a lot of listening to the tuning of harmonies.
I've done some of course. Occasionally setting up a chord on the synth
with unadorned sawtooth waves and moving one of the notes around with
the pitch wheel. But what I have done a lot of, is listening to all
the people on this list. And whenever someone claims they hear
something that doesn't fit my current theories, I first give 'em a
hard time to make sure they aren't fooling themselves or have the
numbers wrongs, but ultimately I try to figure out how _everyone_
could be right, even tho at first they may seem to be contradicting
one another, and even if my ears don't hear it.