RE: Digest Number 375

Please remove me from your mailing list!

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From: tuning@onelist.com [SMTP:tuning@onelist.com]
Sent: Monday, November 01, 1999 4:25 AM
To: tuning@onelist.com
Subject: [tuning] Digest Number 375

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There are 5 messages in this issue.

Topics in today's digest:

1. Re: Re : many topics
From: patrick pagano <ppagano@bellsouth.net>
2. Re: guitar chord sustain
From: John Starrett <jstarret@math.cudenver.edu>
3. Re: Re: MOS = Myhill's Property = Self-similarity?
From: "D.Stearns" <stearns@capecod.net>
4. RE: Infinite sustain
From: "Glen Peterson" <Glen@OrganicDesign.org>
5. Re: RE: Infinite sustain
From: patrick pagano <ppagano@bellsouth.net>

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Message: 1
Date: Sun, 31 Oct 1999 11:02:30 -0800
From: patrick pagano <ppagano@bellsouth.net>
Subject: Re: Re : many topics

> (how
> were McDisney, Scoring Software, and the not-so-free-market
> all related and why?)
>
> Bob

we got into scoring software via midi files as scores and the
inadequacy of
scoring for microtunings etc....i don't know how hitler got in there
either

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Message: 2
Date: Sun, 31 Oct 1999 09:19:01 -0700 (MST)
From: John Starrett <jstarret@math.cudenver.edu>
Subject: Re: guitar chord sustain

Wim-
Check out the Sustainiac. There is a web page at

www.sustainiac.com

John Starrett
http://www-math.cudenver.edu/~jstarret/microtone.html

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Message: 3
Date: Mon, 1 Nov 1999 01:18:12 -0800
From: "D.Stearns" <stearns@capecod.net>
Subject: Re: Re: MOS = Myhill's Property = Self-similarity?

I noticed that a host of old disembodied posts have suddenly
materialized just in time for Halloween...

[me:]
> > s=(-n), just means that the small step
> > size is a negative number,
[Graham Breed:]
> s<0, then.

Well I find that being able to see in a glance the EDOs that don't
work in a particular mapping (where s=(-n)), to also be a useful
convenience... but as you point out, not a musically significant
mapping.

[Graham:]
> Yes, it can be clearly defined at a glance, so no need for all
this
verbiage.

Yes... verbiage... Rereading most any post I've ever done does cause
(even) me to cringe in horror... but no matter how many times I say
to
myself: "self, you've really got to tone it down a bit," I just seem
to come right back and embarrass myself all over again... oh well,
so
it goes I guess...

[Graham:]
>I find the scale tree the clearest way of showing it.

By the scale tree, in this context (i.e., a 7L+3s linear mapping of
an
interval inside a 1/70th of an octave space between a 3/10 and a
2/7),
I would take that to mean (something along the lines of):

3/10 2/7
\ /
5/17
/ \
7/24 8/27
/ \ / \
9/31 10/34 11/37
/ \ / \ / \
11/38 12/41 13/44 14/47
/ \ / \ / \ / \
13/45 14/48 15/51 16/54 17/57

(etc.)

or:

3/10 2/7
5/17
8/27 7/24
11/37 13/44 12/41 9/31

(etc.)

Please let me know if you mean something different.

(thanks,)
Dan

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Message: 4
Date: Sun, 31 Oct 1999 13:40:09 -0500
From: "Glen Peterson" <Glen@OrganicDesign.org>
Subject: RE: Infinite sustain

> From: "Wim Hoogewerf" <wim.hoogewerf@fnac.net>
>
> the list. It's urgent! Does anyone know how to obtain an
> infinite chord
> sustain? The score I'm working on (Gavin Bryars' Bi-Ped) asks for
high
> three-note chords coming out of nothing, lasting for about 30
> seconds with
> some crescendo in the middle and dying out at the end.

Obviously you could get a compressor, and maximize the compression.
Follow
it with a volume pedal. You could use a bow, Jimmy Page style. Or
make a
magnetic feedback system on your guitar...

http://www.fernandesguitars.com/Misc/Index/index_Sus.html

As I understand it, you use an extra pickup, a small amplifier, and
an
electromagnet (could be a pickup with the magnets removed, or a coil
from a
speaker, etc). The pickup captures the tone of the strings, then
you
amplify it, but instead of sending to a speaker, send it to an
electromagnet
underneath the strings thereby exciting the string with more of the
original
vibration and sustaining it. If you add volume and tone pots to the
system,
you can control how much feedback there is (volume), and the ratio
of
fundamental to overtone in the feedback(tone). The pickup that goes
to your
guitar amp can be totally separate from this system. In the
Fernandes
system, I think they use the same pickup.

I bet this would give you the exact effect you are looking for,
without
compromising tone, volume, dynamic range, or responsiveness of the
instrument.

I just tried it using the tiny coil of a cheap old car stereo
speaker. It
sort of worked for the bass string when I cranked the amp up, but
just when
the effect started getting noticeable, the coil started smoking.
:-( Also,
it was very easy to get piercing feedback magnetically through the
pickups -
keep the coil away from the pickup! I probably need some sort of
pole piece
inside the coil to focus the magnetic field. I tried using a hex
nut that
fit in there, but it didn't make much difference. The steel in the
nut did
not seem very magnetic, maybe part aluminum. Also hex nuts are
torroidal,
probably the only shape that wouldn't work for this application.
Any
suggestions would be welcome. I think I have the right idea, but am
grasping at straws for the implementation. Maybe a pickup with the
magnet
removed? Don't feel like smoking any pickups today. I'll wait for
suggestions.

So for the time being, buy a Fernandes.

You will still need to use your volume knob, or a volume pedal to
get the
"coming out of nothing" effect.

---
Glen Peterson
Peterson Stringed Instruments
30 Elm Street North Andover, MA 01845
(978) 975-1527
http://www.organicdesign.org/peterson

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Message: 5
Date: Sun, 31 Oct 1999 21:11:21 -0800
From: patrick pagano <ppagano@bellsouth.net>
Subject: Re: RE: Infinite sustain

if you are talking guitar type stuff i say Ebows on three or four
guitars

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"Tuning" people,
Can anyone tell me the location of an article on the tuning (including
partials) of the original Hubei Marquis Yi bells? I specify "original"
because the bells that toured the U.S. (and are recorded on the Fontana CD
called "The Imperial Bells of China") are facsimiles made in the 20th
century. In my quick spectral analysis of the tuning of a couple of the
bells from the facsimiles, I think that the partials have been tuned as
1:1, 2:1, 3:1, 4:1, and 5:1 (the lowest bell is 172.3, 344.7, 516.5, 689.4,
and 861.2). Were the originals that way?

Marty Hatch

Marty Hatch
Department of Music
Lincoln Hall (now in White Hall 316)
Cornell University
Ithaca, New York 14850, U.S.A.
607-2555049
fax: 607-2542877

>From: martin hatch <mfh2@cornell.edu>
>
>"Tuning" people,
>Can anyone tell me the location of an article on the tuning (including
>partials) of the original Hubei Marquis Yi bells?

I only have the discussion in Fritz Kuttner's _The Archeology of Music in
Ancient China_ where he quotes the measurements done by Ma Chengyuan
("Ancient Chinese Two-Pitch Bronze Bells," _K'ao Ku Hs�eh Pao_ No. 1
(1981), translated and reprinted in _Chinese Music_ vol. 3 #4 (1981-82))
and Jao Tsung-I and Tseng Ksientung _Studies on the Inscriptions of the
Bells and Chimes from the Tomb of Marquis Yi of the Tseng State at
Sui-Hsien_ (Province of Hebei, county of Sui, 1985). The second of these
includes a bibliography of 88 publications on the bells, presumably mostly
in Chinese.

As these authors seem to be only interested in identifying the so-called
sui and ku pitches (presumably the most subjectively prominent partials),
Kuttner does not give the complete spectral details. This is unfortunate
because it prevents discussion on what constitutes the sui and ku pitches
as well as the kind of overall tuning of partials that you seek. I would be
very interested to hear if you find any other information.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

--- In tuning@yahoogroups.com, martin hatch <mfh2@xxxxxxx.xxxx wrote:
> "Tuning" people,
> Can anyone tell me the location of an article on the tuning
(including
> partials) of the original Hubei Marquis Yi bells?

There is now for the first time a thorough analysis of the tuning
system of these bells (incl. pictures and sound sample from the
original bells):

http://w1.570.telia.com/~u57011259/Zengbells.htm

The 65 Zeng bells prove that about 2500 years ago the Chinese had
fifth generation, fifth temperament, a 12-tone system in musical
practice (not just in theory), a norm tone for an orchestral
ensemble, an integration of fifths and thirds in tuning, and a
preference of pure thirds over pure fifths. At this point in history,
China was 2000 years ahead of Europe, not only in bell casting, but
also in musical acoustics.

Martin Braun

Very nice. Tuning D-F just and tempering the fifths inbetween makes
it like 1/3 comma tuning. I now want to check out the bells the
article says may be out of tune (may be the chinese discovered 19
tone equal?).

Gabor

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> --- In tuning@yahoogroups.com, martin hatch <mfh2@xxxxxxx.xxxx
wrote:
> > "Tuning" people,
> > Can anyone tell me the location of an article on the tuning
> (including
> > partials) of the original Hubei Marquis Yi bells?
>
> There is now for the first time a thorough analysis of the tuning
> system of these bells (incl. pictures and sound sample from the
> original bells):
>
> http://w1.570.telia.com/~u57011259/Zengbells.htm
>
> The 65 Zeng bells prove that about 2500 years ago the Chinese had
> fifth generation, fifth temperament, a 12-tone system in musical
> practice (not just in theory), a norm tone for an orchestral
> ensemble, an integration of fifths and thirds in tuning, and a
> preference of pure thirds over pure fifths. At this point in
history,
> China was 2000 years ahead of Europe, not only in bell casting, but
> also in musical acoustics.
>
> Martin Braun

I had checked on these way back in the day. At the time Fritz Kuttner had a
cassette tape of the bells (better chimes), with their 2 or 3 "koo," or pitch
spots. The Chinese at the time had not let any Westerners near them. And
they were found on the floor, out of order. My question is whether the pitch
could hold after all of those years on the floor. Even metal must change its
physical composition enough over two millennia for its exact pitch to be
questionable. No?

best, Johnny

----- Original Message -----
From: <Afmmjr@aol.com>

> I had checked on these way back in the day. At the time Fritz Kuttner had
a
> cassette tape of the bells (better chimes), with their 2 or 3 "koo," or
pitch
> spots. The Chinese at the time had not let any Westerners near them. And
> they were found on the floor, out of order.

Out of order? Maybe they were in a specific order, until
they were found...and that order is lost to time...

* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> Even metal must change its
> physical composition enough over two millennia for its exact
> pitch to be questionable. No?

Yes. Metal changes.

Cheers,
Jon

Only 4 of the 66 tones of the 33 melody bells are relevantly out of
tune.

A 1/3 comma tuning seems possible, because the bell casters knew all
about thirds.

Whether the bell casters knew about 19ET seems impossible to
determine, because the number of "accidentals" outside DEFGAC was
small. But anybody is invited to check this. All the figures you need
are in the data tables:

http://w1.570.telia.com/~u57011259/Bellstab.htm

Martin

--- In tuning@yahoogroups.com, "alternativetuning"
<alternativetuning@y...> wrote:
> Very nice. Tuning D-F just and tempering the fifths inbetween makes
> it like 1/3 comma tuning. I now want to check out the bells the
> article says may be out of tune (may be the chinese discovered 19
> tone equal?).
>
> Gabor

I never read that the position of these bells in the tomb could
affect metal changes, let alone metal changes that could affect
pitch. Metal changes by age alone were so small that they were
irrelevant for pitch, as Lothar von Falkenhausen worked out in minute
detail (see refs.).

Martin

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> .... My question is whether the pitch
> could hold after all of those years on the floor. Even metal must
change its
> physical composition enough over two millennia for its exact pitch
to be
> questionable. No?
>
> best, Johnny

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> --- In tuning@yahoogroups.com, martin hatch <mfh2@xxxxxxx.xxxx
wrote:
> > "Tuning" people,
> > Can anyone tell me the location of an article on the tuning
> (including
> > partials) of the original Hubei Marquis Yi bells?
>
> There is now for the first time a thorough analysis of the tuning
> system of these bells (incl. pictures and sound sample from the
> original bells):
>
> http://w1.570.telia.com/~u57011259/Zengbells.htm

"If struck correctly, both tones are fully independent, each with its
own fundamental and harmonics."

mr. hatch was asking about the partials, but the above seems to be
the only mention of such. do you have any data on the series of
partials for each, or any, of the bell tones? such data would have
some bearing on the tuning issue, since certain tunings sound better
with certain series of partials than others. perhaps the chinese had
a whole other set of instruments with which the tuning actually
evolved, and the application to bells happened only later?

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:

> The 65 Zeng bells prove that about 2500 years ago the Chinese had
> fifth generation, fifth temperament, a 12-tone system in musical
> practice (not just in theory), a norm tone for an orchestral
> ensemble, an integration of fifths and thirds in tuning, and a
> preference of pure thirds over pure fifths. At this point in
history,
> China was 2000 years ahead of Europe, not only in bell casting, but
> also in musical acoustics.

Are we reading the same table of pitches? What I saw was all over the
map, and hardly amounts to a system of any kind. In any case, 2500
years ago the Greeks had highly sophisticated music--if these bells
are a clue, much more sophisticated than in China.

To my knowledge a spectral analysis has not yet been done for any of
these bells. The Chinese do not let them out of the country, and
might not have much interest in the spectra themselves. To be certain
on this issue, you would have to write to Lothar von Falkenhausen and
to Thomas D. Rossing (both easy to google).

Yes, I assume the bell casters had a tuning maths that was derived
from string instruments, like the zither. It seems likely, though,
that the double-tone charater of these types of bells had forced the
Chinese over several centuries to deal with the problems of
integrating thirds and fifths in scales.

Martin

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> .... do you have any data on the series of
> partials for each, or any, of the bell tones? such data would have
> some bearing on the tuning issue, since certain tunings sound
better
> with certain series of partials than others. perhaps the chinese
had
> a whole other set of instruments with which the tuning actually
> evolved, and the application to bells happened only later?

What did you see? The data I used are the best that are available,
and they are completely documented in the tables that I added to the
article.

As far as I know there is no archeology of fixed-pitch instruments
from ancient Greece that could be relevant for tuning issues. Much of
the "sophistication" of the music in ancient Greece seems to be that
of the scholars. Has any of these scholars suggested that the ancient
Greeks had tempered fifths for the sake of improved thirds?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> Are we reading the same table of pitches? What I saw was all over
the
> map, and hardly amounts to a system of any kind. In any case, 2500
> years ago the Greeks had highly sophisticated music--if these bells
> are a clue, much more sophisticated than in China.

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:

> What did you see? The data I used are the best that are available,
> and they are completely documented in the tables that I added to the
> article.

One thing I saw was that I don't seem to completely check with your
arithmetic; however, using your figures, the SD of these presumptive
scale tones varies from 6.9 to 26.9 cents, which means any conlusion
you can draw from averaging is very tentative. Another possible
interpreation is that exact tuning didn't much matter for the music of
the time. Certainly these bells, whether they were that way to start
with or got that way over time, are all over the tuning map.

> As far as I know there is no archeology of fixed-pitch instruments
> from ancient Greece that could be relevant for tuning issues.

No, but we *do* have a few fragments of actual musical scores, along
with a lot of elaborately worked-out musical theory, which paid close
attention to tuning issues. The tiny bit which has come down to us is
damned impressive; you might recall that the Greek theatre of that
time was the best in the world, and music was a part of it.

Much of
> the "sophistication" of the music in ancient Greece seems to be that
> of the scholars. Has any of these scholars suggested that the ancient
> Greeks had tempered fifths for the sake of improved thirds?

(1) That's hardly the sole measure of sophistication

(2) You've not established the Chinese used meantone

>No, but we *do* have a few fragments of actual musical scores, along
>with a lot of elaborately worked-out musical theory,

Theory isn't up for consideration here.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >No, but we *do* have a few fragments of actual musical scores,
along
> >with a lot of elaborately worked-out musical theory,
>
> Theory isn't up for consideration here.

Yes it is, because it lets us reconstruct ancient Greek music, which
as I said was damned impressive. What have we got for the allegedly
meantone Chinese bells?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > Theory isn't up for consideration here.
>
> Yes it is, because it lets us reconstruct ancient Greek music, which
> as I said was damned impressive.

Wrong. Dead wrong. Theory doesn't reconstruct, it guesses. Educated guesses, in the best of theory, but guesses just the same. Unless you can put the fragments together into a seamless whole, you are injecting part of yourself, and other investigators, into the process.

This objection coming from someone - me - who not only believes that the Greeks had a great thing going, but that it has been lost and only touched on by a few. And current culture is going away from even those touches...

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > Theory isn't up for consideration here.
> >
> > Yes it is, because it lets us reconstruct ancient Greek music, which
> > as I said was damned impressive.
>
> Wrong. Dead wrong. Theory doesn't reconstruct, it guesses. Educated
guesses, in the best of theory, but guesses just the same. Unless you
can put the fragments together into a seamless whole, you are
injecting part of yourself, and other investigators, into the process.

People have tried to reconstruct wholes, but as you say that is
speculative. However, you could make the same claim of "dead wrong"
about Bach if you want to push the matter far enough. The sad little
fragments we have left can be found here:

http://www.oeaw.ac.at/kal/agm/index.htm

I think it is a safe bet that the actuality of this music was a great
deal more than what this shows, but this is already enough to show
that dismissive contempt is hardly an apporopriate position to take on
it--least of all from microntonalists.

Meanwhile, do we have a clue about what these Chinese bells were
actually used for? That they can produce two different tones show the
Chinese were up to something interesting, but the tuning evidence
hardly allows one to conclude the something in question was meantone.
It certainly does not support some idiotic anti-Greek bias.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> However, you could make the same claim of "dead wrong"
> about Bach if you want to push the matter far enough.

I am not pushing the matter. You *are*.

> The sad little fragments we have left can be found here:
>
> http://www.oeaw.ac.at/kal/agm/index.htm

Exactly. _Fragments_ Much as I love the thought and feel of what I think this music may be, I think it is pretty slim to say you can "reconstruct" it.

> I think it is a safe bet that the actuality of this music was a great
> deal more than what this shows, but this is already enough to show
> that dismissive contempt is hardly an apporopriate position to take on
> it--least of all from microntonalists.

I speak as a musician, not a microtonalist, thankyouverymuch. Place your bets, Gene, but I think it is silly to play fast and loose with these issues. I'm not doing a comparison with what Martin has to say about the Chinese bells, I'm simply responding to the Greek issue.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> I speak as a musician, not a microtonalist, thankyouverymuch. Place
your bets, Gene, but I think it is silly to play fast and loose with
these issues.

It's not playing fast and loose to see that ancient Greek music must
have been very impressive. If you can't, speaking as a musician, hear
that, clear the wax from your ears and the cobwebs from your brain.
I repeat--contempt for the microtonal past hardly makes sense on list
list.

>> Theory isn't up for consideration here.
>
>Yes it is, because it lets us reconstruct ancient Greek music,

Many would argue this is not the case.

I wonder if John Chalmers has anything to say about Greek
theory vs. practice, and if any original instruments have
been reverse-engineered?

-Carl

>People have tried to reconstruct wholes, but as you say that is
>speculative. However, you could make the same claim of "dead wrong"
>about Bach if you want to push the matter far enough.

Huh? We've got the music, and a direct pedagogy going back to
him, and excellently-preserved samples of the instruments from
the period.

>The sad little fragments we have left can be found here:
>
>http://www.oeaw.ac.at/kal/agm/index.htm

This was posted here years ago.

>I think it is a safe bet that the actuality of this music was a great
>deal more than what this shows, but this is already enough to show
>that dismissive contempt is hardly an apporopriate position to take on
>it--least of all from microntonalists.

Who dismissed it with contempt?

>Meanwhile, do we have a clue about what these Chinese bells were
>actually used for? That they can produce two different tones show the
>Chinese were up to something interesting, but the tuning evidence
>hardly allows one to conclude the something in question was meantone.
>It certainly does not support some idiotic anti-Greek bias.

???

I, for one, don't have any clue about ancient Chinese music. Paul
asked the right question about other instruments.

Perhaps you, Gene, would like to detail where the meantone analysis
went wrong. Which numbers have an SD problem? How were the
fundamentals extracted from the bells?

-Carl

>It's not playing fast and loose to see that ancient Greek music must
>have been very impressive. If you can't, speaking as a musician, hear
>that, clear the wax from your ears and the cobwebs from your brain.
>I repeat--contempt for the microtonal past hardly makes sense on list
>list.

I must have missed the post where Greek music was deprecated. These
mofos had slamin' theater, philosophy, architecture, etc, etc. Why
wouldn't they have slamin' music too?

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Theory isn't up for consideration here.
> >
> >Yes it is, because it lets us reconstruct ancient Greek music,
>
> Many would argue this is not the case.
>
> I wonder if John Chalmers has anything to say about Greek
> theory vs. practice, and if any original instruments have
> been reverse-engineered?

We have the fragments which have come down to us, and we have the
theory, with its emphasis on nuances of intonation. I think it's
preposterous to assume all of that had nothing to do with the reality,
especially considering that what little we have, works. In any case it
hardly makes sense to revere Partch and ignore the music which is
closest to where he was coming from. If we could recreate Oedipus Rex
with not only the words but the music of Sophocles, it would be a
wonderful thing, and no doubt highly enlightening. We can't do that,
but we can listen to the tiny amount of Greek nusic which remains;
speaking for myself, my introduction to this (which fit nicely onto a
single CD, alas) made a bigger impression on me than Partch. Sue me.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >People have tried to reconstruct wholes, but as you say that is
> >speculative. However, you could make the same claim of "dead wrong"
> >about Bach if you want to push the matter far enough.
>
> Huh? We've got the music, and a direct pedagogy going back to
> him, and excellently-preserved samples of the instruments from
> the period.

And we can't seem to agree on how he should be performed or what
tuning should be used.

> >The sad little fragments we have left can be found here:
> >
> >http://www.oeaw.ac.at/kal/agm/index.htm
>
> This was posted here years ago.
>
> >I think it is a safe bet that the actuality of this music was a great
> >deal more than what this shows, but this is already enough to show
> >that dismissive contempt is hardly an apporopriate position to take on
> >it--least of all from microntonalists.
>
> Who dismissed it with contempt?

Martin. However, you seem well able to restrain your enthusiasm.

> Perhaps you, Gene, would like to detail where the meantone analysis
> went wrong. Which numbers have an SD problem?

If we have an SD of 30 cents for "B", then two SDs up compared to two
down is an error margin of 120 cents for the tuning of "B". What in
hell can you conclude from that? The other deviations are smaller, but
a 15 SD standard deviation gives us 2 SD error bars 60 cents wide.

>We have the fragments which have come down to us, and we have the
>theory, with its emphasis on nuances of intonation.

There are volumes of theory in the Western tradition that have no
basis in reality -- endless conjurings by Ptolemy, the 'ideal' of
the just major scale presumably put forth by Zarlino and others,
various serialist machinations and their "set theory" descendants,
Schlesinger's proposed Greek scales, the notion that free-pitched
ensembles are locked in 12-et among present-day microtonalists, the
descriptive-turned-prescriptive theory of the common practice era,
which calls every failure of the ruleset a work of genius. . .

>I think it's preposterous to assume all of that had nothing to do
>with the reality, especially considering that what little we have,
>works.

How hard is it for an arbitrary interpretation of those fragments
to "work"?

>it hardly makes sense to revere Partch and ignore the music which
>is closest to where he was coming from.

He was inspired by his vision of Greek music. But most important
was not the tuning, but the artistic fusion of theater, music,
dance, ritual.

I think that's a cool artistic direction, and I dig microtonal
melodies and extended-JI chromelodeon parts, but none of this is
why I revere Partch.

I revere Partch because he was a great composer. If I knew what
*that* meant, we wouldn't need great composers.

-Carl

>And we can't seem to agree on how he should be performed or what
>tuning should be used.

The variety of performance is part of the art of music, and it
seems likely that the variety of Bach interpretations is not
fundamentally less today than it was in Bach's time, since the
the error rate at which human performers' can mimic sounds at an
instrument is probably a key limiting factor. Keeping in mind
that Bach's keyboard music was mostly pedagogical until long
after his death.

While we can't agree on *the* tuning for *Bach*, the performing
musicians of the world continue apace. I personally think
Kellner makes a strong case, but Werckmeister III is obviously
appropriate. As I posted here once long ago, tunings were not
codified then as today, and even today different tuners have
different quirks, even when setting the same temperament on the
same instrument. While Bach would have tuned his harpsichords
and clavichords, he had to take his organs as they were. That
included everything from 1/4-comma meantone to stuff just shy
of Young. It's clear Bach advocated well temperament. The fact
that he didn't advocate anything more specific should send an
important message to all the armchair 'find the secret Bach
tuning' nuts out there.

>> Who dismissed it with contempt?
>
>Martin.

I didn't see him mention Greek music, just "the West". Maybe I
missed it.

>However, you seem well able to restrain your enthusiasm.

Maybe I haven't heard the right stuff. What was that cd you
mention?

>> Perhaps you, Gene, would like to detail where the meantone
>> analysis went wrong. Which numbers have an SD problem?
>
>If we have an SD of 30 cents for "B", then two SDs up compared to
>two down is an error margin of 120 cents for the tuning of "B".
>What in hell can you conclude from that? The other deviations are
>smaller, but a 15 SD standard deviation gives us 2 SD error bars
>60 cents wide.

That does sound pretty bad.

Also, I tend not to trust any artifacts coming out of China.

-Carl

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> It's not playing fast and loose to see that ancient Greek music must
> have been very impressive.

It IS if you talk in terms of being able to _reconstruct_ a music from what fragments we have. We have tantalizing glimpses, we have indications of the grandeur and pervasive nature of the music. We do not have the whole of it, or even more than small parts of it.

> If you can't, speaking as a musician, hear
> that, clear the wax from your ears and the cobwebs from your brain.

I didn't think I'd ever have to say this to you, because you are a thorough and (I mostly note) careful participant: read what I wrote -

"This objection coming from someone - me - who not only believes that the Greeks had a great thing going, but that it has been lost and only touched on by a few."

I have long admired not only the musical contributions of that society, but the all-embracing nature of the arts within the thread of their lives. My ears are clean, my brain is spic-and-span, and my soul is pure. I've got this nagging rash, however...

> I repeat--contempt for the microtonal past hardly makes sense
> on list list.

Well, I don't know what vintage you're into up north tonight, but I not only don't have comtempt for the past, I revere it. The simple grandeur of what the Greeks gave us (what is left) and what probably we don't know about, would bury most of the microtonal rubbish I've been witness to.

And I proudly put "musician" above "microtonalist" any day of my life; to have the latter without the former would be a rather hollow endeavor.

Cheers,
Jon

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> I didn't see him mention Greek music, just "the West". Maybe I
> missed it.

He's talking of "the West" of 2500 years ago, when Athens was at its
apex.

> >However, you seem well able to restrain your enthusiasm.
>
> Maybe I haven't heard the right stuff. What was that cd you
> mention?

Musique de la Grece Antique, Harmonia Mundi.

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Gene,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > It's not playing fast and loose to see that ancient Greek music
must
> > have been very impressive.
>
> It IS if you talk in terms of being able to _reconstruct_ a music
from what fragments we have. We have tantalizing glimpses, we have
indications of the grandeur and pervasive nature of the music. We do
not have the whole of it, or even more than small parts of it.

What did you think I meant by reconstruct, or why I chose the word?

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Musique de la Grece Antique, Harmonia Mundi.

Oh, man, that is an *incredible* recording!! That opening sound - pardon me for forgetting the Greek word for it (and for not getting up and looking at the liner notes), where they 'clear the air for what is about to come'. Oh, that is a fiendishly intoxicating recording, and has been enjoyed in my house for many a year.

Of course, we have no idea that that is what Greek music sounded like, and I don't imagine that is what it was like. But that would be conjecture on my part.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> What did you think I meant by reconstruct, or why I chose the word?

I figured you meant to "construct again", probably from what remains one would find. In the instance of Greek music, and what fragments there are, I would not trust that such a 'reconstruction' would necessarily have anything but the slightest resemblance to the original.

If someone wants to do what amounts to be a fantasia on Greek musical fragments, that is a different pot of gumbo. In fact, I think that is what the Atrium Musicae disc most resembles.

A fantasia, not gumbo.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Meanwhile, do we have a clue about what these Chinese bells were
> actually used for?

Yes. This is why I published the report. You might know that musical
archeology is not my main job.

The report shows for the first time that this chime ensemble has an
eight-fold DEFGAC scale. The way the bells were hung up, and the way
they are tuned, strongly indicates that they were played in a
orchestral way, very similar to the way in which sarons and bonangs
are played in a Gamelan orchestra.

Apparently the Chinese had not yet found this out themselves,
probably because they were mislead by more or less dark theoretical
fragments from ancient times. Remember, there is more than an ocean
between that what instrument makers and musicians do and that what
writing people write about it.

One day the Chinese will have good replicas of these bells, and you
will then hear them all over the world, in an orchestral sound that
is closer to contemporary Gamelan sound than to that of contemporary
Chinese orchestras.

That's why I did this work.

> That they can produce two different tones show the
> Chinese were up to something interesting, but the tuning evidence
> hardly allows one to conclude the something in question was
meantone.

The report does not deal with the mean-tone issue.

> It certainly does not support some idiotic anti-Greek bias.

The report does not mention anything Greek. It does not suggest that
the Chinese of those days had better music than any other culture. It
simply states that both bell-casting and musical acoustics was on a
level that Europeans only reached 2000 years later. These are the
empirical facts that we have. Had the ancient Greeks had an
integration of thirds and fifths in scale construction, we probably
would have a few ancient Greek words about it. We haven't.

Martin

> tuning system of the 65 Zeng bells from 433 B.C.

I will address a couple thing here.
First I remember when these bells went on tour maybe 20 years ago and i saw them and talked breifly with some of the Chinese officals with the tour, Also scientic american did an article on them. It is my opinion is that they don't know what the tuning was and they are using them for
propaganda puposes to prove, "China had it first".
Jim French has reconstructed quite a few Auloi and periodically plays them over the phone in the subharmonic series that Schlesinger mentions. Doug Leedy has done quite a bit of work reconstructing greek music just based on the text and how Homer was recited. It is interesting that
Ptolemy mentions how "in practice" the tones in one of the tetrachords are played higher in pitch than the lower one if the two where placed side by side.
I believe that Johnny pointed out that Paniaugua on the harmonia mundi album just used Quartones to play this music. I really love this album cause it is great music and very imaginative but it is probably much "cleaner" and much more gregorian sounding than real greek music. Greek is not
western anymore than these bells prove that the chinese invented the major scale (which they claim elsewhere) . the romans had little to do with there theroy whereas the Persians took it up whole heartedly. This is where Europe got Greek theroy, from the east

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> > tuning system of the 65 Zeng bells from 433 B.C.
> First I remember when these bells went on tour maybe 20 years
> ago and i saw them and talked breifly with some of the Chinese
> officals with the tour,

What you saw was a first replication of the ensemble, with a
different tuning and a much poorer sound quality. This is also the
ensemble that you can hear on a CD that is internationally marketed.

In the 1980s, in China, you could also buy a cassette tape with a
test performance of the original bells. I don't know if it is still
on sale today. Possibly the owners of the rights of the replica music
have prevented a further marketing, because the originals outclass
the replicas.

> Also scientic american did an article on them. It is my opinion is
that they don't know what the tuning was and they are using them for
> propaganda puposes to prove, "China had it first".

As yet, Chinese music theory has not been in the condition to prove
much in this respect. The ones who have done most of the job are
Lothar von Falkenhausen and me. And none of the two has been bought
or bribed by anybody in China.

Martin

on 20/6/03 4:04 am, Jon Szanto at JSZANTO@ADNC.COM wrote:

> This objection coming from someone - me - who not only believes that the
> Greeks had a great thing going, but that it has been lost and only touched on
> by a few. And current culture is going away from even those touches...
>
> Cheers,
> Jon
>

I second that.

a.m.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

/tuning/topicId_5844.html#44858

> >> Theory isn't up for consideration here.
> >
> >Yes it is, because it lets us reconstruct ancient Greek music,
>
> Many would argue this is not the case.
>
> I wonder if John Chalmers has anything to say about Greek
> theory vs. practice, and if any original instruments have
> been reverse-engineered?
>
> -Carl

***Boy, I sure don't want to get into this morass... but I will say
that it's frequently claimed that not enough is known of Greek music
from the theory to adequately reconstruct it. At least, that's what
*I've* always heard... dunno.

J. Pehrson

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

/tuning/topicId_5844.html#44860

> >It's not playing fast and loose to see that ancient Greek music
must
> >have been very impressive. If you can't, speaking as a musician,
hear
> >that, clear the wax from your ears and the cobwebs from your brain.
> >I repeat--contempt for the microtonal past hardly makes sense on
list
> >list.
>
> I must have missed the post where Greek music was deprecated. These
> mofos had slamin' theater, philosophy, architecture, etc, etc. Why
> wouldn't they have slamin' music too?
>
> -Carl

***My understanding was that it was *very* significant, only just not
adequately preserved... As I recall, it was a big part of their
poetry and, I believe, theatre...

J. Pehrson

In a message dated 2003:06:19 11:50:15 PM, "Gene Ward Smith"
<gwsmith@svpal.org> writes:

>Yes it is, because it lets us reconstruct ancient Greek music, which
>as I said was damned impressive. What have we got for the allegedly
>meantone Chinese bells?

- also:
> [ . . . ] do we have a clue about what these Chinese bells were
>actually used for? That they can produce two different tones show the
>Chinese were up to something interesting, but the tuning evidence
>hardly allows one to conclude the something in question was meantone.

A "re-creation" based on the idea of a chromatic 12-fixed-tone scale is
_The Imperial Bells of China_ by the Hubei Song and Dance Ensemble [Fortuna
records 17075-2]. These "re-creations" are based on the "educated" guesswork and
fieldwork in Southern China's folk-musics by northern Mainland Chinese
archaeomusicologists and ethnomusicologists. The bells they use are reproductions
(therefore already suspect).
But I like this CD anyway... as (modern Chinese) music.

A contemporary use of the BianZhong bells in a modern composition is Tan
Dun's _Symphony 1997 (Heaven Earth Mankind)_ [Sony]. It seems Tan Dun got to
use the actual bells to celebrate the Re-Unification of Hong Kong with China.
And to my ears, the bells do not seem either fixed-toned or meantone.

Based on listening to & reading about Korean, Japanese, South East Asian,
and Balinese musics (& scales/modes) that have had a strong ancient Chinese
influence/substrate and, have in some cases preserved ancient Chinese ritual
and court music nearly intact (ie. Korean _A-ak_ {Confucian ritual music} &
_T'ang-ak_ {Chinese T'ang & Sung Dynasty pieces} - and Japanese _togaku_ - form of
_gagaku_ based on pieces of Chinese & South Asian Indian origins), my
personal pet theory is that ancient Chinese music was diversely polymicrotonal at
least, and nonJI/nonET polymicrotimbral (xenotonality ;) at most. Or even aspects
of both.

One has to remember that tone-colour is of more importance than even
melody in Chinese music (harmony being more of a "Western" preoccupation).
Each note is a microcosm... every tone has a "living essence" emanating
from the Tao. Additionally, sound and silence, time and space, are also "alive"
and in dynamic ever-changing, timeless flux.

In a message dated 2003:06:19 11:50:15 PM, Carl Lumma writes:

>Also, I tend not to trust any artifacts coming out of China.

It is interesting to note that the Confucianists and Communists (mainly
Northern Mandarin-speakers) propagate the idea of pentatonicism and its
12-tone-fixed-toned extension meanwhile all other regions of China (i.e. Southern,
Western and Tibet, Far North/Manchuria & tribal non-Han Chinese territories) -
at best/at most - tend to preserve and continue the more cosmopolitan musical
diversity that began in the Golden Age of the Silk Road, the T'ang Dynasty.

Also worth noting is that Taoist music - esp'ly on the 7-stringed
fretless long-board zither _ch'in_/_qin_ - is equally pentatonic, heptatonic,
microtonal and, most importantly, timbral (and even dronal).
From ancient times to the present-day, most literature and poems about
this wonderful instrument describe very precise playing methods in terms and
metaphors taken from nature (i.e. wind in pine trees, waterfalling over rocks,
leaves falling into water, ants scurrying to defend the nest, rock slide, bird
taking flight, cat pouncing, etc.), with an implied or indirect emphasis on
tone-colouration and timbre more so than melody.
Similarly, ... the Korean long-board zithers and Japanese koto, biwa,
shamisen and shakuhachi...
... pretty much wherever Taoist-influenced Ch'an/Zen Buddhism went...

---
Hanuman Zhang,
musical mad scientist (no, I don't wanna take over the world, just the sound
spectrum...)

"What strange risk of hearing can bring sound to music - a hearing whose
obligation awakens a sensibility so new that it is forever a unique, new-born,
anti-death surprise, created now and now and now. .. a hearing whose moment
in time is always daybreak." - Lucia Dlugoszewski

"The wonderousness of the human mind is too great to be transferred into
music only by 7 or 12 elements of tone steps in one octave." - shakuhachi master
Masayuki Koga

"There's a rabbinical tradition that the music in heaven will be microtonal"
-annotative interpretation of Schottenstein Tehillim, 92:4, the verse being:
"Upon a ten-stringed * instrument and upon lyre, with singing accompanied by
harp." [* utilizing new tones]

NADA BRAHMA - Sanskrit, "sound [is the] Godhead"

"God utters me like a word containing a partial thought of himself." -Thomas
Merton

LILA - Sanskrit, "divine play/sport/whimsy" - "the universe is what happens
when God wants to play" - "joyous exercise of spontaneity involved in the art
of creation"

...improvisation is about change, about flux rather than stasis. ... you have
to be aware of the fact that improvisation is about a constant change. -
Steve Beresford

improvisation: "a process of liberation, a working around the assumptions
that define our civilization, and the results are open-ended." - John Berndt

--- In tuning@yahoogroups.com, czhang23@a... wrote:

> A contemporary use of the BianZhong bells in a modern
composition is Tan
> Dun's _Symphony 1997 (Heaven Earth Mankind)_ [Sony]. It seems Tan
Dun got to
> use the actual bells to celebrate the Re-Unification of Hong Kong
with China.
> And to my ears, the bells do not seem either fixed-toned or
meantone.

I have that symphony, but I guess the significance of these bells
escaped me. I'll put it on and listen for them.

> One has to remember that tone-colour is of more importance than
even
> melody in Chinese music (harmony being more of a "Western"
preoccupation).

The mere fact that these bells have this remarkable dual function led
me to think that something like this was likely to be true about how
they were used.

>
> Subject: Re: tuning system of the 65 Zeng bells from 433 B.C.
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > Meanwhile, do we have a clue about what these Chinese bells were
> > actually used for?
>
> Yes. This is why I published the report. You might know that musical
> archeology is not my main job.
>
> The report shows for the first time that this chime ensemble has an
> eight-fold DEFGAC scale.

This is not a chinese sounding scale nor is it really a scale nor are there 6 tone scales found anywhere in the region or otherwise. It is safe to say that most of the scales in the region are from the Chinese who were great at mathematics already predicting eclipes at this time. It is known
for one that indonesia got there scales from China. The Chinese also had the Pythagorean chain and as far as we know were equal if not surpassed Greece at this time. I would guess that you have gotten most of the notes but this sequence is just not right. Can you direct me to your data
again, i lost it. I imagine this is less likely, but is it possible a note might be missing.

> The way the bells were hung up, and the way
> they are tuned, strongly indicates that they were played in a
> orchestral way, very similar to the way in which sarons and bonangs
> are played in a Gamelan orchestra.

This would make sense since their influence elsewhere would imply that we would find such instruments at some point at this point of origin

> Apparently the Chinese had not yet found this out themselves,
> probably because they were mislead by more or less dark theoretical
> fragments from ancient times.

I imagine the data and ancient wisdom they have to deal with is overwhelming and possibly takes a great of mind to figure it out.

> Remember, there is more than an ocean
> between that what instrument makers and musicians do and that what
> writing people write about it.

But if these are "Court" instruments which therir longevity alone implies, the best mathematical and musical minds would have been working together. The two fields, as in Greece, were already connected. Tuning in the ancient word was a sacred act conected to mathematics , astronomy and music.
One did not want to makes sounds that where not harmonious in some way with these observations.

>
>
> One day the Chinese will have good replicas of these bells, and you
> will then hear them all over the world, in an orchestral sound that
> is closer to contemporary Gamelan sound than to that of contemporary
> Chinese orchestras.

This makes sense for the reasons i stated above. It is known for instance that the Gagagku in Japan came from China but it is also known that it originally came from a lost civilazation some where in afganistan. It is possibly this wave of imported music that replaced this older music. The
Chinese and Koreans also have Stone plates. Have measurements been taken of these?

>
>
> > That they can produce two different tones show the
> > Chinese were up to something interesting, but the tuning evidence
> > hardly allows one to conclude the something in question was
> meantone.
>
> The report does not deal with the mean-tone issue.

There is nothing in any music with a thousand miles that has ANY relationship to meantone. thirds were not and for the most part still arn't considered consonant tones in this whole broad area

> > It certainly does not support some idiotic anti-Greek bias.
>
> The report does not mention anything Greek. It does not suggest that
> the Chinese of those days had better music than any other culture.

If this music was exported to indonesia at this time and this is what we have the remants of. the chinese would have had comparable music to the greeks. It would not be surprised if it was not vastly surperior. To assume otherwise is nothing but western conceit. Considering what little we
know of greece which is more persian than roman in culture

> It
> simply states that both bell-casting and musical acoustics was on a
> level that Europeans only reached 2000 years later.

and there mathematics were quite a bit ahead. They had already been pouring over Pascal triangle ( MT Meru) for 1600 years by this point.

> These are the
> empirical facts that we have. Had the ancient Greeks had an
> integration of thirds and fifths in scale construction, we probably
> would have a few ancient Greek words about it. We haven't.

The greeks were not concerned with harmony from what we know just like their persian neighbors who they share their culture with. These were all on the Silk Road. the information highway at the time.
As an aside , you find many instruments in Africa that resemble the greek ones. The lyre is one not that far removed from the kora which has always made me believe that a large amount of greek culture was imported from this direction via the nile. Not to mention all the bow instruments
that are based on the harmonics of the string. Harmony in thirds maybe came from africa

>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

Kraig:

> > The report shows for the first time that this chime ensemble has an
> > eight-fold DEFGAC scale.
>
> This is not a chinese sounding scale nor is it really a scale nor are
> there 6 tone scales found anywhere in the region or otherwise.

1) Famous 6-tone scales are the so-called "hexachords" of the European
Middle Ages. Scales like CDEFGA were used from the early 11th century
onwards and were the foundation of our system of music notation.

2) The two-tone bells produce even-numbered tone scales. The basic unit of
the Zeng ensemble are three-bell groups, that is three pairs of tones: DF,
EG, and AC. Of course, when performing, the musicians were free to declare
one tone of the six as "out-of-bounds" and then play 5-tone music. What the
musicians actually did cannot be derived from any contemporary Asian music.
The knowledge to cast the two-tone bells got lost about 200 B.C., and the
bells that were not buried in a forgotten tomb were melted down to cast
military equipment when a less musical ruler or war took over.

3) The data of the Zeng bells unequivocally show the DEFGAC scale:

http://w1.570.telia.com/~u57011259/Bellstab.htm

> > The report does not deal with the mean-tone issue.
>
> There is nothing in any music with a thousand miles that has ANY
> relationship to meantone. thirds were not and for the most part still
> arn't considered consonant tones in this whole broad area

The term "mean-tone" would not be appropriate for the bell ensemble, because
it refers to the size of the interval of the second, which is not at issue
here. But the bell casters had learned that the bells with an intrinsic
interval of a minor third or a major third sounded better than other bells.
This is simply a matter of the vibration physics of the bells. Also the two
tones of a bell can ring simultaneously if struck between the two ordinary
strike points. Thus you can strike 3-tone and 4-tone chords with just two
bells. Also the note-name system of the bells indicates that thirds were
considered as consonant. Again, contemporary Asian concepts are not of much
help when interpreting things. The knowledge to cast the two-tone bells got
lost about 200 B.C.

Martin

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

>The Chinese also had the Pythagorean chain and as far as we know
were equal if not surpassed Greece at this time.

Equal in what, surpassed in what? This kind of claim cannot be
examined because it is so vague. It's highly unlikely the two musics
were much alike, and we don't have a lot of data with which
to make a judgment.

> This makes sense for the reasons i stated above. It is known for
instance that the Gagagku in Japan came from China but it is also
known that it originally came from a lost civilazation some where in
afganistan.

Eh? Citation?

> If this music was exported to indonesia at this time and this is
what we have the remants of. the chinese would have had comparable
music to the greeks. It would not be surprised if it was not vastly
surperior. To assume otherwise is nothing but western conceit.

(1) The Greeks were not making Renaissance-type music, and would not
have sounded "Western" to modern ears.

(2) This is exactly the kind of anti-Greek prejudice I complained of.
I suggest you learn someing about a given topic before spouting off.

Considering what little we
> know of greece which is more persian than roman in culture

We know *a lot* about Greece of 2500 years ago--much more than about
China, because of the unfortunate destruction of written records
there. The Greeks would have gagged at the idea of being
called "Persian", and the Romans were strongly influenced by Greece.

> > It
> > simply states that both bell-casting and musical acoustics was on
a
> > level that Europeans only reached 2000 years later.
>
> and there mathematics were quite a bit ahead. They had already been
pouring over Pascal triangle ( MT Meru) for 1600 years by this point.

Oh, please. Now the Greeks were mathematical duffers as well? They
*invented* the idea of a mathematical proof, which Chinese
mathematicians never did arrive at.

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> The term "mean-tone" would not be appropriate for the bell
ensemble, because
> it refers to the size of the interval of the second, which is not
at issue
> here. But the bell casters had learned that the bells with an
intrinsic
> interval of a minor third or a major third sounded better than
other bells.

Can you actually get a major or minor third out of a single bell, and
if so, with what tuning?

Gene Ward Smith:
> Can you actually get a major or minor third out of a single bell, and
> if so, with what tuning?

Yes. The report says:

"Of the 33 bells in the melody section of the Zeng ensemble, 21 have a
sui-gu interval of a minor third (mean 312.4 Cent, SD 13.8), 10 have one of
a major third (mean 403.1 Cent, SD 18.1), and two have apparently mistuned
ones with 224 and 342 Cent (details below)."

The exact Cent values for the intrinsic intervals of all 33 melody bells can
be derived from the data table Part A, and some of them can directly be read
out from data table Part B (watch out which of these are one-bell and which
are two-bell intervals).

The link to the tables is:
http://w1.570.telia.com/~u57011259/Bellstab.htm

The bell-intrinsic interval could be predicted BEFORE casting, by parameters
which have still not been determined today.

AFTER casting the bells were fine-tuned by taking away bronze material from
the inside of the bell. Both up- and down-tuning was done, by taking away
material at different places. They knew the vibration nodes. Also the bosses
on the bells were made to fully separate the respective partials of the two
tones. This knowledge could be reconstructed in modern experiments.

Martin

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Can you actually get a major or minor third out of a single bell,
> and if so, with what tuning?

Carillon bells are each tuned with a series of vibrational frequencies: the fundamental, an octave above (which is the heard pitch), then a minor third, fifth, and another octave. Bell makers tune up to seven partials above that, and the bottom five (as described above) are produced mostly through the shape of the bell in the casting, and fine tuned by carefully thinning the instide of the bell at selected heighths.

Efforts in the mid-1980's in The Netherlands to replace the minor-third bell with a corresponding major-third were successful in designing a bell (the shape was altered employing a technique for structural optimization using finite element methods).

From "Science of Percussion Instruments", Thomas D. Rossing, World Scientific, 2000 (Chapter 11 - Church Bells and Carillon Bells)

Cheers,
Jon

>
> From: "Martin Braun" <nombraun@telia.com>
> Subject: Re: Re: tuning system of the 65 Zeng bells from 433 B.C.

Hello Martin!
This does clear up some things as it does appear there is some form of 6 tone scale. although the deviation from the letter names we use are arbitrary frame of referance.
You cannot use statistics in this case . if you take all the Pelogs in kunst book you will end up with a similar answer. Also i do not as a rule deal with such data in cents as it "hides" phenomenon and use ONLY Vibrations per second. No one hears in Cents derivation to something where as
vibrations per second although one has the arbitrary "second" the ratios are perceptable. BTW there are scales out of Mt Meru that come closer to this series than this series comes to equal temperment.I need to see the data in VPS to proceed any further and if the data already exist in this form
it would save me a bit of time. please inform as to whether this exist or not.
-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:

> "Of the 33 bells in the melody section of the Zeng ensemble, 21
have a
> sui-gu interval of a minor third (mean 312.4 Cent, SD 13.8), 10
have one of
> a major third (mean 403.1 Cent, SD 18.1), and two have apparently
mistuned
> ones with 224 and 342 Cent (details below)."

Again, these SDs are rather large, and calling the two most anomalous
ones "mistuned" seems like quite a leap. The mere fact that they all
are sounding a third/wide second type of interval is fascinating, and
clearly seems to point to how the bells were used, but the data
hardly supports the idea that this was done with much precision or
that meantone fifths would have helped any.

> The bell-intrinsic interval could be predicted BEFORE casting, by
parameters
> which have still not been determined today.

How do you know this?

Gene Ward Smith:

> .... The mere fact that they all
> are sounding a third/wide second type of interval is fascinating, and
> clearly seems to point to how the bells were used, but the data
> hardly supports the idea that this was done with much precision or
> that meantone fifths would have helped any.

"much precision" is very relative ;-) The data tables, Part B, show that in
the main chord of the ensemble, D-F-A-C, the majority of thirds are "more
precise" than on the contemporary piano.

As in Europe a few centuries ago, "meantone fifths" are an epiphenomenon of
third-oriented tuning. The means of the tones CGDAE suggest that the bell
casters possibly had an equally-tempered normative scale from another
instrument. There were 125 musical instruments in the tomb, including 12
large zithers (se) and two small zithers (qin).

> > The bell-intrinsic interval could be predicted BEFORE casting, by
> parameters which have still not been determined today.
>
> How do you know this?

Thomas Rossing tried to determine the parameters and failed (google). He
concluded that the bell casters might have cast on chance and then melted
down all bells that were unfit. You can judge for yourself what type of
conclusion THIS is. No comment from my side. Just remember that bell casting
is extremely expensive and time consuming. Then, the intrinsic interval is
not determined by floating magic, but by physics, and the bell casters had
several centuries of experience to build on. They also put the tone names on
the bells before casting them (putting them in the molds, that is).

Martin

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:

>
> Thomas Rossing tried to determine the parameters and failed (google). He
> concluded that the bell casters might have cast on chance and then
melted
> down all bells that were unfit. You can judge for yourself what type of
> conclusion THIS is. No comment from my side. Just remember that bell
casting
> is extremely expensive and time consuming.

Trial and error is often the only available technique. (Think about
helicopters which fly wihtout having a solid theory for design. A lot
of guesses and a handfull of test flight accidents go into each
helicopter.)

Casting is cheap, forged and beaten metal is expensive, and in
laborintensive countries time maybe cheap enough to be not relevant.
If you like you can order instruments from Java (by internet even).
Instruments with cast brass are a fraction of the price of instruments
with cast bronze keys which are a tiny fraction of instruments with
forged and beaten keys. There are good recent doctor-theses on gong
smithing, one from Sweden another from Varsanyi Andras in Mu"nchen.

Gabor

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:

> But the bell casters had learned that the bells with an
intrinsic
> interval of a minor third or a major third sounded better than other
bells.
> This is simply a matter of the vibration physics of the bells.

can you elaborate?

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:

> "much precision" is very relative ;-) The data tables, Part B, show
that in
> the main chord of the ensemble, D-F-A-C, the majority of thirds
are "more
> precise" than on the contemporary piano.
>

Martin,

But this is "more precise" relative to 6:5 minor thirds which are not
even remote a target of 12 tone equal temperament. More relevant
would be to compare 5:4 thirds on a harpsichord in meantone, amd I am
certain the harpsichord will be better because of common harmonics to
compare and remove beats. On whole, good piano tunings do a good job
of tuning 12 tone equal temperament while scaling for inharmonicity.
I bet if you could get a group of top piano tuners to agree on a set
of instruments they believe are being tempered well, and then make
allowance for individual inharmonicity, you would find a much lower
SD.

Gabor

Gabor:

> > ..... Just remember that bell casting
> > is extremely expensive and time consuming.
>
> Casting is cheap, forged and beaten metal is expensive, ......
> If you like you can order instruments from Java (by internet even).
> Instruments with cast brass are a fraction of the price of instruments
> with cast bronze keys which are a tiny fraction of instruments with
> forged and beaten keys.

It must be like that. What they cast in Java are the bars of the sarons and
perhaps some other xylophone-like instruments. These bars have very simple
forms and the molds for them are standardized and probably re-usable. This
allows cheap mass production. Perhaps things are partly similar in carillon
production in the Netherlands. But in church bell casting, even today, each
bell is calculated and manufactured individually in a process that takes
several weeks. They do not have re-usable molds. We don't know if the bell
casters in ancient china had re-usable molds. Due to the very complicated
surface structure of their bells, the molds probably had to be broken after
casting or were damaged otherwise.

Martin

Paul:

> > But the bell casters had learned that the bells with an intrinsic
> > interval of a minor third or a major third sounded better than other
> > bells. This is simply a matter of the vibration physics of the bells.
>
> can you elaborate?

Sinyan Shen (ref in article) wrote that the silent, or very weak, partials
of the other, non-struck tone have an influence on the timbre. Thus
harmonical relations between the partials of A-tone and B-tone also make
each tone alone more harmonical.

Martin

Gabor:

> > "much precision" is very relative ;-) The data tables, Part B, show
> > that in the main chord of the ensemble, D-F-A-C, the majority of thirds
> > are "more precise" than on the contemporary piano.

> I bet if you could get a group of top piano tuners to agree on a set
> of instruments they believe are being tempered well, and then make
> allowance for individual inharmonicity, you would find a much lower
> SD.

Quite right. I did not say that the piano is less well tuned. I said that
the thirds on a (properly tuned) piano are less "precise" (further away from
5:4 and 6:5) than in the bells.

Martin

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> Paul:
>
> > > But the bell casters had learned that the bells with an
intrinsic
> > > interval of a minor third or a major third sounded better than
other
> > > bells. This is simply a matter of the vibration physics of the
bells.
> >
> > can you elaborate?
>
> Sinyan Shen (ref in article) wrote that the silent, or very weak,
partials
> of the other, non-struck tone have an influence on the timbre. Thus
> harmonical relations between the partials of A-tone and B-tone also
make
> each tone alone more harmonical.
>
> Martin

if you're speaking of resonance relations between the partials, then
this would make perfect sense, except that you're still evading the
question of what the series of partials actually is for these tones!
the probability that they form an exact harmonic series, or anything
even close to it, is virtually nil.

Paul:

> > Sinyan Shen (ref in article) wrote that the silent, or very weak,
> > partials
> > of the other, non-struck tone have an influence on the timbre. Thus
> > harmonical relations between the partials of A-tone and B-tone also
> > make each tone alone more harmonical.
>
> if you're speaking of resonance relations between the partials, then
> this would make perfect sense, except that you're still evading the
> question of what the series of partials actually is for these tones!

Paul, I am not evading any question. I said that the bells I wrote about had
not been analyzed in this respect. Because there are some other 2-tone bells
in European and American museums, I assume there must be some spectral data
somewhere.

The best person to ask would be Thomas Rossing. The answer would not give
you any certainty on the Zeng bells, but an idea on the general principles
in this type of 2-tone bell.

> the probability that they form an exact harmonic series, or anything
> even close to it, is virtually nil.

No, the probability is actually very high. Without a section of an
approximately harmonic series we could not hear pitch. From the sound sample
in the article you can hear that the bells have a very clear pitch. We also
know the sections of the harmonic series in church bells and in carillons
(see Jon's post from two days ago).

According to Sinyan Shen (ref in article), ancient Chinese two tone bells,
of the type found in Zeng, have an approximation to the following partial
series across the two tones:
- for a minor third bell: 1 : 1.2 : 2.4 : 2.81 : 3
- for a major third bell: 1 : 1.25 : 2.5 : 2.81 : 3

Further, as opposed to church bells and carillons, the lowest partial of
each strike tone corresponds to the pitch that we hear (f0).

Martin

Martin

I asked Daniel Wolf last night and he said that bonang, kenong, saron
and gender could be cut, cast or beaten. Cut iron and brass are
cheapest. Cast brass and bronze are still cheap and not so good as
beaten. Beaten are 4-10x more expensive. The lower gongs can only be
beaten (bronze) or welded (brass and iron), because they have thin
surfaces like membrane-instruments.

In the Budapest metal museum is a display on bell casting. Each size
of bell has its own wooden frame in which a ceramic mold sits. The
mold is made direct from a bell to be copied and is broken off the
bell after the cast. The mold can be scaled up or scaled down by
adding or removing ceramic to make higher or lower bells in same
proportion. All the formulas for doing this scaling are from centuries
of trial and error. All bells are then fine tuned. You can see the
scratching inside the bells, also at trial and error positions. In
Hungary we only tune the F1 but in other countries other Fs are tuned too.

So it is no surprise that there are no molds in chinese bells, the
bells are themselves the molds.

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> Gabor:
>
> > > ..... Just remember that bell casting
> > > is extremely expensive and time consuming.
> >
> > Casting is cheap, forged and beaten metal is expensive, ......
> > If you like you can order instruments from Java (by internet even).
> > Instruments with cast brass are a fraction of the price of instruments
> > with cast bronze keys which are a tiny fraction of instruments with
> > forged and beaten keys.
>
> It must be like that. What they cast in Java are the bars of the
sarons and
> perhaps some other xylophone-like instruments. These bars have very
simple
> forms and the molds for them are standardized and probably
re-usable. This
> allows cheap mass production. Perhaps things are partly similar in
carillon
> production in the Netherlands. But in church bell casting, even
today, each
> bell is calculated and manufactured individually in a process that takes
> several weeks. They do not have re-usable molds. We don't know if
the bell
> casters in ancient china had re-usable molds. Due to the very
complicated
> surface structure of their bells, the molds probably had to be
broken after
> casting or were damaged otherwise.
>
> Martin

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> Paul:

> > the probability that they form an exact harmonic series, or
anything
> > even close to it, is virtually nil.
>
> No, the probability is actually very high. Without a section of an
> approximately harmonic series we could not hear pitch. From the
sound sample
> in the article you can hear that the bells have a very clear pitch.
We also
> know the sections of the harmonic series in church bells and in
carillons
> (see Jon's post from two days ago).

i was pleasantly surprised to see that post.

> According to Sinyan Shen (ref in article), ancient Chinese two tone
bells,
> of the type found in Zeng, have an approximation to the following
partial
> series across the two tones:
> - for a minor third bell: 1 : 1.2 : 2.4 : 2.81 : 3
> - for a major third bell: 1 : 1.25 : 2.5 : 2.81 : 3

could you segregate these by which tone each belongs to?

so which cross-resonant intervals (between the two bell tones) would
one target based on the above series?

> Further, as opposed to church bells and carillons, the lowest
partial of
> each strike tone corresponds to the pitch that we hear (f0).

hmm . . . one tone has a harmonic 3rd partial and the other a
harmonic 2nd partial. yes? then there's that 2.81 . . . where does
that go? and the cross-resonance would have to be a partial shared
between the two -- is that one of the above?

Gabor:

> I asked Daniel Wolf last night and he said that bonang, kenong, saron
> and gender could be cut, cast or beaten.

Thank you for the inquiry. Do they really cast bronze bonangs? If they
do, I bet that they are either extremely expensive or they sound
horrible. Good bonangs are of thin metal sheets.

> So it is no surprise that there are no molds in chinese bells, the
> bells are themselves the molds.

You mean the bells could have been the molds for the molds. This is
possible, if they applied the piece-mold technique. But don't think that
this is easy or cheap. The complete mold then had to consist of (at least) 6
to 10 pieces which had to be fit together and held together with utmost
care. Most of the job is making the clay molds. Here you need several layers
of different clay composit mixtures, long intermediate periods for drying,
and finally very careful burning.

Martin

Paul:

> > We also
> > know the sections of the harmonic series in church bells and in
> > carillons (see Jon's post from two days ago).
>
> i was pleasantly surprised to see that post.

Great!

> > According to Sinyan Shen (ref in article), ancient Chinese two tone
> > bells, of the type found in Zeng, have an approximation to the following
> > partial series across the two tones:
> > - for a minor third bell: 1 : 1.2 : 2.4 : 2.81 : 3
> > - for a major third bell: 1 : 1.25 : 2.5 : 2.81 : 3
>
> could you segregate these by which tone each belongs to?
>
> so which cross-resonant intervals (between the two bell tones) would
> one target based on the above series?

Ok, Paul, perhaps you are right. This is not an easy game. But perhaps you
are better at it than I am.

Sinyan Shen gives more figures in "Chinese Music, Vol 10 (1987), No 1,
10-19". The problem with these figures is that I have no way of knowing what
is empirically derived and what is theoretically derived. You see, his
reports are just not scientific by American or European standards. Too much
information is missing, and too much just sounds good. The general problem
with these bells is that European and American authors make them worse than
they are (with most ridiculous methods) and Chinese authors make them better
than they are.

Sinyan Shen's figures:
- for a minor third bell:
-- partial series across the two tones: 1 : 1.2 : 2.4 : 2.81 : 3
--- A-tone: 1 : 3
--- B-tone: 1.2 : 2.4 : 2.81

- for a major third bell:
-- partial series across the two tones: 1 : 1.25 : 2.5 : 2.81 : 3
--- A-tone: 1 : 3
--- B-tone: 1.25 : 2.5 : 2.81

If these figures are real, that is, empirically derived, they are indeed
interesting. They would reflect the following frequency ratios, within tones
and across the 2 tones:
- for a minor third bell: 6:5, 2:1, 7:6, 15:14, 12:5, 7:3, 5:4, 14:5, 5:2,
and 3:1

- for a major third bell: 5:4, 2:1, 9:8, 15:14, 5:2, 9:4, 6:5, 14:5, 12:5,
and 3:1

I am sure these ratios will tell you more than they tell me. Of course the
more beautiful (that is, the "exact") figure for the minor third bells would
be "2.8" instead of "2.81". Perhaps the author wanted to emphasize the
similarity between the two bell types. But perhaps this "deviation" is small
compared to the deviations between the maths and the real bells. Still,
considering how beautiful these jobs ring, Sinyan Shen may very well be on
the right track.

Martin

Martin wrote...
>> No, the probability is actually very high. Without a section of
>> an approximately harmonic series we could not hear pitch.

Actually, I'm not sure this is true. Check out this site with
me (actually, the like may have come from one of these lists)...

http://www.hibberts.co.uk/index.htm

-Carl

Carl

Cool URL. The wavanal program is fine.

Martin

The cast bronze bonang sound best on the high tones (all of
bonangpanerus) where the forged and beaten pots often go bad. The high
tones need to be thick on top compared to low tones.

Do you know the book by William A. Sethares, "Tuning Timbre Spectrum
Scale"? Cool for bells and gamelans.

Gabor

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Martin wrote...
> >> No, the probability is actually very high. Without a section of
> >> an approximately harmonic series we could not hear pitch.
>
> Actually, I'm not sure this is true. Check out this site with
> me (actually, the like may have come from one of these lists)...
>
> http://www.hibberts.co.uk/index.htm
>
> -Carl

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> Paul:
>
> > > We also
> > > know the sections of the harmonic series in church bells and in
> > > carillons (see Jon's post from two days ago).
> >
> > i was pleasantly surprised to see that post.
>
> Great!

yes, jon has apparently looked up the information for himself, after
disagreeing with me that such a standard set of bell partial tunings
even exists. i'm very heartened at this turn of events, and hope that
jon continues making such positive contributions!

> > > According to Sinyan Shen (ref in article), ancient Chinese two
tone
> > > bells, of the type found in Zeng, have an approximation to the
following
> > > partial series across the two tones:
> > > - for a minor third bell: 1 : 1.2 : 2.4 : 2.81 : 3
> > > - for a major third bell: 1 : 1.25 : 2.5 : 2.81 : 3
> >
> > could you segregate these by which tone each belongs to?
> >
> > so which cross-resonant intervals (between the two bell tones)
would
> > one target based on the above series?
>
> Ok, Paul, perhaps you are right. This is not an easy game. But
perhaps you
> are better at it than I am.

well, if what you were saying has any substantive backing, it should
be quite easy. too bad the information isn't more "scientific", as
you say.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Martin wrote...
> >> No, the probability is actually very high. Without a section of
> >> an approximately harmonic series we could not hear pitch.
>
> Actually, I'm not sure this is true. Check out this site with
> me (actually, the like may have come from one of these lists)...
>
> http://www.hibberts.co.uk/index.htm
>
> -Carl

what here makes you think martin's claim is untrue? i've made this
same claim like a million times on these lists . . . it most
certainly applies to bells, the "hum tone" is at the location of a
missing fundamental beneath a pretty precise harmonic series subset
(formed from many, but not all, of the bell's partials).

Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
> yes, jon has apparently looked up the information for himself,
> after disagreeing with me that such a standard set of bell
> partial tunings even exists.

Hey, bite me. I didn't "look it up for himself", as I've owned that book for a few years and had already read it. I objected to your particular phrasing, and also pointed out that this is something that has been refined and is most prominantly featured in modern-day carillons. Bells did not always display these qualities, and one need only travel and hear for themselves a wide variety of bells and carillons in the cathedrals and churches around the world to realize this.

Frankly, I value, honor, and celebrate the bells that speak each for themselves, and don't exhibit the qualities of clone-like identity that would eventually evolve.

> i'm very heartened at this turn of events, and hope that
> jon continues making such positive contributions!

Jon always tries to make positive contributions, and no event turned. Maybe your perception is undergoing some transmogrification or something...

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Paul,
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> > yes, jon has apparently looked up the information for himself,
> > after disagreeing with me that such a standard set of bell
> > partial tunings even exists.
>
> Hey, bite me.

okay . . .

> I didn't "look it up for himself", as I've owned that book for a
>few years and had already read it. I objected to your particular
>phrasing, and also pointed out that this is something that has been
>refined and is most prominantly featured in modern-day carillons.
>Bells did not always display these qualities,

well, i didn't ever intend to imply otherwise. it seems we had a
simple misunderstanding! so sorry . . .

>Maybe your perception is undergoing some transmogrification >or
something...

maybe. anyway, i like the factual, informative posts and hope they
continue!

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
> well, i didn't ever intend to imply otherwise. it seems we had a
> simple misunderstanding! so sorry . . .

hmmph.

> anyway, i like the factual, informative posts and hope they
> continue!

I'm vacilating about my residency. But if I stick around, I plan on posting "factual, informative" (which are very subjective terms) material, as well as fictional and non-essential items. It seems to me that we all need both kinds of testimony.

Cheers,
Jon

> > Ok, Paul, perhaps you are right. This is not an easy game. But
> > perhaps you are better at it than I am.
>
> well, if what you were saying has any substantive backing, it should
> be quite easy. too bad the information isn't more "scientific", as
> you say.

Paul, if you say that the ratios of Sinyan Shen (repeated below) would be of
a particular interest (provided they are backed up by real spectral data), I
would start a search campaign to see if there are any such data, somewhere
in the world. Small numbers of similar bells might have been analyzed
spectrally in a useful way, somewhere.

If, however, you say that such ratios are what one would expect anyway from
strange, but well-sounding bells, the effort may not be justified.

Martin

------------------------------------
Sinyan Shen's figures:
- for a minor third bell:
-- partial series across the two tones: 1 : 1.2 : 2.4 : 2.81 : 3
--- A-tone: 1 : 3
--- B-tone: 1.2 : 2.4 : 2.81

- for a major third bell:
-- partial series across the two tones: 1 : 1.25 : 2.5 : 2.81 : 3
--- A-tone: 1 : 3
--- B-tone: 1.25 : 2.5 : 2.81

If these figures are real, that is, empirically derived, they are indeed
interesting. They would reflect the following frequency ratios, within tones
and across the 2 tones:
- for a minor third bell: 6:5, 2:1, 7:6, 15:14, 12:5, 7:3, 5:4, 14:5, 5:2,
and 3:1

- for a major third bell: 5:4, 2:1, 9:8, 15:14, 5:2, 9:4, 6:5, 14:5, 12:5,
and 3:1
---------------------------------

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

/tuning/topicId_5844.html#45068

> I'm vacilating about my residency.

***Jon, if your vacillating about your residency, you might as well
at least spell it right... :)

[just joking around...]

JP

>> >> No, the probability is actually very high. Without a section of
>> >> an approximately harmonic series we could not hear pitch.
>>
>> Actually, I'm not sure this is true. Check out this site with
>> me (actually, the like may have come from one of these lists)...
>>
>> http://www.hibberts.co.uk/index.htm
>>
>> -Carl
>
>what here makes you think martin's claim is untrue?

I haven't read it yet, which is why I say, "with me".

It's Martin's 2nd sentence I'm *not sure is true*.

-Carl

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> ***Jon, if your vacillating about your residency, you might as well
> at least spell it right... :)
>
> [just joking around...]

Would you believe: I actually pulled down the Webster's to check on "vacilate", and forgot to put in the second in the word!? Gad how I hate to answer online when I don't have Eudora's spell check to back me up!

Cheers,
Jon

Gabor:
> The cast bronze bonang sound best on the high tones (all of
> bonangpanerus) where the forged and beaten pots often go bad. The high
> tones need to be thick on top compared to low tones.

OK, if they are small and thick, they may not be expensive.

> Do you know the book by William A. Sethares, "Tuning Timbre Spectrum
> Scale"? Cool for bells and gamelans.

Thanks. Yes, I heard about his views concerning Gamelan, which agree with my
experience and results. But the Chinese 2-tone bells play in a slightly
different league. They have a more harmonic spectrum and were made for
harmonic musical scales. What does Sethares say about these bells?

Martin

Paul:

> ....... too bad the information isn't more "scientific", as you say.

I have now found real spectral data. They are empirical and can be
considered as reliable. Thomas Rossing published them in the book that Jon
quoted. They are from a replica bell, where the A-tone is an exact B4 and
the B-tone an exact D5 (re A440), the interval being 299 Cent.

Rossing only published the holographic interferograms of the main 30
vibrational modes (15 for each of the two tones) together with the
frequencies. He neither analyzed nor commented upon the spectrum.

The 30 pictures are also twice on the web (frequencies illegible):

http://www.acoustics.org/press/133rd/2pmu1.html

http://www.russianbells.com/acoustics/rossing.html

I analyzed the frequency data (thanks to Jon for sending them) and compared
them with Sinyan Shen's idealized concept of partial frequencies.

Sinyan Shen's figures:
- for a minor third bell:
-- partial series across the two tones: 1 : 1.2 : 2.4 : 2.81 : 3
--- A-tone: 1 : 3
--- B-tone: 1.2 : 2.4 : 2.81

Measured figures from a modern replica:
- a minor third bell (B4-D5):
-- partial series across the two tones: 1 : 1.19 : 2.83 : 3.02 : 3.11
--- A-tone: 1 : 3.11
--- B-tone: 1.19 : 2.83 : 3.02

So, Shen's ideal figures match the real ones of the replica fairly well, but
they partly appear in different vibration modes. The complete tables with
all 30 frequencies and all possible ratios are at:

http://w1.570.telia.com/~u57011259/PartialsA-tone.htm
http://w1.570.telia.com/~u57011259/PartialsB-tone.htm
http://w1.570.telia.com/~u57011259/PartialsA+B-tone.htm

These tables are interesting, because they show that apparently only the two
fundamentals were fine-tuned after casting. They further show that this
replica has no multiple pitches. There are no sections of an approximately
harmonic partial series that could evoke the perception of an additional
pitch. This is a bell with two fundamentals plus partly harmonic noise.

The results also agrees with what I hear on the CD "Imperial Bells of
China", which is based on such replicas. You can hear that these replicas
can produce good music. But acoustically they differ greatly from the
originals (see below). Many sound samples from the CD are at:

http://entertainment.msn.com/album/Default.aspx?song=1828619&album=223718

http://www.amazon.com/exec/obidos/tg/detail/-/B0000007V1/qid=1057057451/sr=1
-1/ref=sr_1_1/002-6592779-5133619?v=glance&s=music

Replicas of this kind are even on sale (prices stated) on the web:
http://www.maui.net/~lgi/chinesevases/bianzhong.htm

In summary, the modern replicas can have extremely exact fundamentals with
an inharmonic, but non-interfering, spectrum. The originals have less exact
fundamentals, but - presumably - a more harmonic spectrum. For my ears at
least, the originals are more pleasant to listen to and less tiring.

There is a slight chance that I get spectral data from ancient bells in
August. It remains to be seen, how the ratio tables look for them. I'll come
back in that case.

Comments on the spectral results are very welcome, and I wonder how others
hear the difference between the originals and the replicas.

Martin

Dear Martin Braun,

I found your paper on the Zeng Bells absolutely fascinating. Thank you for making it available on the web.

I would like to make a number of comments and suggestions.

I find your use of the term "equally tempered" to describe the fifths between the notes CGDAE to be quite problematic in two ways.
1. Some readers will assume you mean "as in our common 12-note equal temperament".
2. Even if they realise that you only mean "tempered by the same amount", this is not true. You are using pitches averaged over all octaves of all sets, while failing to take into account the fact that the octaves are stretched on average by 13 cents.

The overall mean, and extreme deviations, for octaves (actually playable within one set) are:
1213 -36 +63 cents

These stretched octaves also render invalid your claims about F being a "norm tone" or tuning standard. When you do not assume any intention to tune octaves to a precise 1:2 ratio and compare, between sets, only the same note in the same octave, you find that there is no clear winner for the title of "norm tone". Of those pitches which occur in all three sets, G4 has the lowest variance.

Given the names inscribed on the bells, it seems likely to me that any standard tuning note (norm tone), if it exists, would be one we've translated as C, G, D, or A since these are the names that do not consist of a suffix added to the name of another note.

I also looked for evidence of systematic shifts in frequency between the 3 sets, such as is found in gamelan. There is none.

By the way, you should have translated gong zeng, zhi zeng, shang zeng as Ab, Eb and Bb, not G# D# and A#, so that all the nominal(in chinese) thirds would also be spelled as such in western notation (i.e. as thirds, not diminished fourths).

When we look at the actual CGDAE fifths between the actual (not averaged) notes, and only between pitches in the same set, we find the following.

Deviations from mean
Fifth Min Max Mean Min Max Range
------------------------------------
C:G 674 724 700 -26 24 50 Overall mean and extreme deviations
G:D 682 725 705 -23 21 43 701 -50 to +64
D:A 651 765 704 -53 62 114
A:E 671 743 706 -35 37 72

When we look at the actual fourths we see the following.

Deviations from mean
FourthMin Max Mean Min Max Range
------------------------------------
G:C 478 577 511 -33 66 99 Overall mean and extreme deviations
D:G 491 514 503 -12 11 23 503 -64 to +74
A:D 471 540 505 -34 36 69
E:A 455 533 504 -49 29 78

I find no evidence there that fifths are narrowed, or fourths widened, to favour thirds.

At first I was astounded that, while you are essentially claiming that at least CGDAE are tuned in a meantone temperament, the word "meantone" didn't appear anywhere in your paper. Whether you thought the term was appropriate or not to describe the bell tuning itself, I thought you should at least have compared it with western meantone tunings. I got quite excited at first, thinking, "The Chinese used meantone tuning 2,000 years before the west did". But I now realise this is not a valid conclusion from the data at all, and I now see there is indeed no need to mention meantone temperament.

How one can conclude anything from a nominally 12-note tuning where interval sizes vary +-50 cents, I'm not sure. But if it can be said to approximate any kind of regular tuning, I'd have to say it looks like a incredibly badly tuned 12 note equal division of a stretched octave.

You say "it is obvious that the tuning focus was on pure thirds, not on pure fifths". But I'd say it was treating thirds and fifths approximately as equals. However, given that the bells tend to have an approximate third among their partials, tuning these so that an individual bell sounds harmonious when both of its notes sound simultaneously will force them towards either a 4:5 or 5:6 ratio, and so even if the emphasis for the tuning _between_ bells is entirely on the fourths and fifths, you would end up with a tuning that appeared to favour minor and major thirds as much as fourths and fifths.

Your conclusion of a six note scale is also dubious. Pentatonics have been far more popular historically, the world over, than hexatonics. Given that every bell has two notes, you have to put _something_ in the sixth place, but there is no way to tell whether it was used as an integral member of the scale, or only as an accidental, or to allow the scale to modulate between two pentatonic keys, and if it did, whether those two keys were equally popular.

An alternative theory is that the primary scale was the pentatonic DEGACD or some other mode (rotation) of this such as GACDEG. F may have been as much an accidental as was B. One can argue that F only appeared as often as the other notes because it was a better choice than F# for what to put on the D bells, since it allowed modulation to the GACDFG pentatonic. Or it could be the other way 'round, with GACDFG being primary pentatonic and E being the accidental, as the best choice of what other note to put on the G bell.

In support of GACDFG being the primary pentatonic we have the fact that the sizes of the minor thirds DF and the tones FG have much lower variances than the tones DE and the minor thirds EG. One problem with this argument is that the tone GA, which occurs in both pentatonics, has even greater variance than DE. So both pentatonics seem equally likely to me at this stage.

Notice that the pentatonics can be played with pitch strictly increasing from right to left, whereas the hexatonic would require a counter-intuitive reversal of direction between E and F.

You wrote, "and two [bells] have apparently mistuned [intervals] with 224 and 342 Cent".

Your data table does not show any bell with 224 cents between its two notes, but it does show one with 244 cents (the E6-G6 bell in set I). Perhaps the "224" was a typographical error?

Your data does show a bell with 342 cents between its two notes (the D5-F5 bell in set I) but interestingly, on your data tables page you do not suggest that either of its two notes are mistuned.

With regard to what is mistuned and what isn't. The only place that we agree that something is very wrong is in the low octave of set two, where we find only 14 cents separating Bb from B.

It is not possible to work out from your paper and data tables, which pairs of notes are on a single bell. One can figure out most but not all. Could you please provide this information, or better still, could you please post (or email) the raw data in both Hz and cents (even though they may disagree)? And the 1981 data as well as the 1982? Thanks.

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com/

David Keenan wrote (July 18):

> Dear Martin Braun,
>
> I found your paper on the Zeng Bells absolutely fascinating. Thank you for
> making it available on the web.
>
> I would like to make a number of comments and suggestions.

Dear David,
thank you very much for these detailed and very helpful comments. Replies
follow.

> I find your use of the term "equally tempered" to describe the fifths
> between the notes CGDAE to be quite problematic in two ways.
> 1. Some readers will assume you mean "as in our common 12-note equal
> temperament".

I wrote "these four fifths are equally tempered with a size close to 696
Cent", and "It would be wrong, however, to call the Zeng bells a 12-tone
instrument"

> 2. Even if they realise that you only mean "tempered by the same amount",
> this is not true. You are using pitches averaged over all octaves of all
> sets, while failing to take into account the fact that the octaves are
> stretched on average by 13 cents.

Octave stretching exists only in some cases. It is in no way as consistent
as
in Gamelan tuning. Therefore it seems appropriate to average across octaves.
Further, octave stretching would not affect the size of the fifths in
question.

> The overall mean, and extreme deviations, for octaves (actually playable
> within one set) are:
> 1213 -36 +63 cents
>
> These stretched octaves also render invalid your claims about F being a
> "norm tone" or tuning standard. When you do not assume any intention to
> tune octaves to a precise 1:2 ratio and compare, between sets, only the
> same note in the same octave, you find that there is no clear winner for
> the title of "norm tone". Of those pitches which occur in all three sets,
> G4 has the lowest variance.

Well, I did assume the intention to tune 1:2 octaves, because they had large
zithers, which yield very precise octaves.

> Given the names inscribed on the bells, it seems likely to me that any
> standard tuning note (norm tone), if it exists, would be one we've
> translated as C, G, D, or A since these are the names that do not consist
> of a suffix added to the name of another note.

Other scholars were convinced that C was the main tone of the system,
relying on music theoretical fragments. It is very common, however, that
names and theory differ from practice (just think of the "western" seven
letters for 12 tones). I tried to write down musical practice as visible in
the data.

> I also looked for evidence of systematic shifts in frequency between the 3
> sets, such as is found in gamelan. There is none.

Such a shift is found in some Balinese instruments, but not on Java.

> By the way, you should have translated gong zeng, zhi zeng, shang zeng as
> Ab, Eb and Bb, not G# D# and A#, so that all the nominal(in chinese)
thirds
> would also be spelled as such in western notation (i.e. as thirds, not
> diminished fourths).

"Diminished fourths" only occur in the theory of the so-called "tonal" style
of European music. In contexts of 12-tone descriptions it is now well
established to use only the # for the five "accidentals".

> When we look at the actual CGDAE fifths between the actual (not averaged)
> notes, and only between pitches in the same set, we find the following.
>
> Deviations from mean
> Fifth Min Max Mean Min Max Range
> ------------------------------------
> C:G 674 724 700 -26 24 50 Overall mean and extreme deviations
> G:D 682 725 705 -23 21 43 701 -50 to +64
> D:A 651 765 704 -53 62 114
> A:E 671 743 706 -35 37 72
>
> When we look at the actual fourths we see the following.
>
> Deviations from mean
> FourthMin Max Mean Min Max Range
> ------------------------------------
> G:C 478 577 511 -33 66 99 Overall mean and extreme deviations
> D:G 491 514 503 -12 11 23 503 -64 to +74
> A:D 471 540 505 -34 36 69
> E:A 455 533 504 -49 29 78
>
> I find no evidence there that fifths are narrowed, or fourths widened, to
> favour thirds.

Well, the fourths according to your method are widened. I rejected your
method, however. I knew it from Andr� Lehr in the Netherlands. The bells do
not represent a system that is based on intervals that cross the octave
borders, like our piano. They are for octave confined music, just like the
gamelan instruments, because one player only has one octave in the reach of
his hands. Here, as in Gamelan, we have within-octave intervals and
across-octave chroma consistency. Circles of fifths and fourths, or parts of
it, do not seem appropriate to describe these instruments and their music.

> At first I was astounded that, while you are essentially claiming that at
> least CGDAE are tuned in a meantone temperament,

I never said anything like that. I said the means of these fifths are
equally diminished.

> the word "meantone" didn't
> appear anywhere in your paper. Whether you thought the term was
appropriate
> or not to describe the bell tuning itself, I thought you should at least
> have compared it with western meantone tunings. I got quite excited at
> first, thinking, "The Chinese used meantone tuning 2,000 years before the
> west did". But I now realise this is not a valid conclusion from the data
> at all, and I now see there is indeed no need to mention meantone
temperament.

The term mean-tone tuning only makes sense in a 12-tone instrument. What the
Chinese had 2000 years before the Europeans was a tuning focus on the thirds
at the cost of the fifths. This reflects the same harmony-ranking principles
as in mean-tone tuning, but not mean-tone tuning itself. [It is now known
that these principles seem to have a physiological basis, as well, as shown
on my website.]

> How one can conclude anything from a nominally 12-note tuning where
> interval sizes vary +-50 cents, I'm not sure. But if it can be said to
> approximate any kind of regular tuning, I'd have to say it looks like a
> incredibly badly tuned 12 note equal division of a stretched octave.

They are "incredibly badly tuned", if you apply this standards of
multi-octave string instruments. If you apply the standards of
metallophones, with their non-harmonic - but potentially very interesting -
sound spectra, and the standards of musical practice of Gamelan instruments,
the bells represent sufficiently balanced tuning compromises between scale
precision and pleasant timbres.

> You say "it is obvious that the tuning focus was on pure thirds, not on
> pure fifths". But I'd say it was treating thirds and fifths approximately
> as equals. However, given that the bells tend to have an approximate third
> among their partials, tuning these so that an individual bell sounds
> harmonious when both of its notes sound simultaneously will force them
> towards either a 4:5 or 5:6 ratio, and so even if the emphasis for the
> tuning _between_ bells is entirely on the fourths and fifths, you would
end
> up with a tuning that appeared to favour minor and major thirds as much as
> fourths and fifths.

In octave confined music you simply have more thirds than fourths and
fifths. The data reflect that the bell casters cared more about the thirds
in the octave frame.

> Your conclusion of a six note scale is also dubious. Pentatonics have been
> far more popular historically, the world over, than hexatonics. Given that
> every bell has two notes, you have to put _something_ in the sixth place,
> but there is no way to tell whether it was used as an integral member of
> the scale, or only as an accidental, or to allow the scale to modulate
> between two pentatonic keys, and if it did, whether those two keys were
> equally popular.
>
> An alternative theory is that the primary scale was the pentatonic DEGACD
> or some other mode (rotation) of this such as GACDEG. F may have been as
> much an accidental as was B. One can argue that F only appeared as often
as
> the other notes because it was a better choice than F# for what to put on
> the D bells, since it allowed modulation to the GACDFG pentatonic. Or it
> could be the other way 'round, with GACDFG being primary pentatonic and E
> being the accidental, as the best choice of what other note to put on the
G
> bell.
>
> In support of GACDFG being the primary pentatonic we have the fact that
the
> sizes of the minor thirds DF and the tones FG have much lower variances
> than the tones DE and the minor thirds EG. One problem with this argument
> is that the tone GA, which occurs in both pentatonics, has even greater
> variance than DE. So both pentatonics seem equally likely to me at this
stage.

I think it should be clear from the context of the paper that we are dealing
with a material 6-tone scale, not with a 6-tone scale in musical practice. I
wrote about this at length in a reply to one of Kraig's posts. There is a
possibly corresponding case in Gamelan pelog of Java, where the material
scale always has seven tones in the octave, whereas the three modes that are
used in pelog only select five of them, and different ones depending on
mode.

> Notice that the pentatonics can be played with pitch strictly increasing
> from right to left, whereas the hexatonic would require a
counter-intuitive
> reversal of direction between E and F.

Good point. But for settings with one player per octave (mostly only 3
bells), such a reversal would not have been much of a problem.

> You wrote, "and two [bells] have apparently mistuned [intervals] with 224
> and 342 Cent".
>
> Your data table does not show any bell with 224 cents between its two
> notes, but it does show one with 244 cents (the E6-G6 bell in set I).
> Perhaps the "224" was a typographical error?

Yes indeed. Thanks a lot!!! (apparently I doubled the 2 instead of the 4)

> Your data does show a bell with 342 cents between its two notes (the D5-F5
> bell in set I) but interestingly, on your data tables page you do not
> suggest that either of its two notes are mistuned.

Good point. In the table only assumed mistuning re ensemble is marked, not
bell-internal one. The bell possibly was accepted and not melted down and
re-cast, because it still fitted into the chroma scale of the ensemble, as
shown in data table A.

> With regard to what is mistuned and what isn't. The only place that we
> agree that something is very wrong is in the low octave of set two, where
> we find only 14 cents separating Bb from B.

This supports the view that the six "accidentals" were second-class
passengers in the ensemble.

I hope this clarifies some of the issues. And again, thanks for the thorough
comments.

Martin

>--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
>David Keenan wrote (July 18):
> > 2. Even if they realise that you only mean "tempered by the same
>amount",
> > this is not true. You are using pitches averaged over all octaves of all
> > sets, while failing to take into account the fact that the octaves are
> > stretched on average by 13 cents.
>
>Octave stretching exists only in some cases. It is in no way as consistent
>as
>in Gamelan tuning.

Let's face it, nothing is very consistent in the tuning of these bells,
however you seem quite happy to find significance in mean fifth sizes, why
not mean octave sizes? 23 of the octave intervals are wider than 1200
cents, while 10 are narrower. The mean size is 1213 cents.

> Therefore it seems appropriate to average across
>octaves.
>Further, octave stretching would not affect the size of the fifths in
>question.

Of course it will affect them, and does. You have calculated mean sizes for the fifths in FCGDAE by first reducing all the pitches to the same octave while assuming 1200 cent octaves, then finding the mean pitches, then
finding the fifth sizes between those mean pitches.

I have not made any assumptions at all about the octaves, but have found
the sizes of the actual fifths (not fourths or twelfths) between the actual
pitches (not mean pitches, and only when those pitches are in the same
set), and then I have found the mean size of all the F:C fifths and the
mean size of all the C:G fifths etc. The results are quite different from
yours which I find quite misleading.

F 696 C 700 G 705 D 704 A 706 E

The habit of assuming 1200 cent octave equivalence is a hard one to break,
but we must do so when analysing a tuning from scratch like this.

When I do the same with fourths I get

E 504 A 505 D 503 G 511 C 515 F

> > These stretched octaves also render invalid your claims about F being a
> > "norm tone" or tuning standard. When you do not assume any intention to
> > tune octaves to a precise 1:2 ratio and compare, between sets, only the
> > same note in the same octave, you find that there is no clear winner for
> > the title of "norm tone". Of those pitches which occur in all three sets,
> > G4 has the lowest variance.
>
>Well, I did assume the intention to tune 1:2 octaves, because they had
>large
>zithers, which yield very precise octaves.

I don't see what that has got to do with it. Perhaps they did not _want_
1:2 octaves for the bells. Perhaps they found that the bells sound better
if you tune the octaves a little wider than the octaves obtained using
string harmonics, as is the case with gamelan. Indonesians have stringed
instruments too but choose to widen the octaves for their metallophones.

But as I pointed out, there is no need to assume any particular intended
octave size, just don't octave reduce anything before looking at means and
variances.

> > Given the names inscribed on the bells, it seems likely to me that any
> > standard tuning note (norm tone), if it exists, would be one we've
> > translated as C, G, D, or A since these are the names that do not
>consist
> > of a suffix added to the name of another note.
>
>Other scholars were convinced that C was the main tone of the system,
>relying on music theoretical fragments.

Now that you have sent me the scanned tables showing the Chinese characters
for the notes, it is also reasonably obvious to me that C is the main tone.
i.e. it is the most common tonic (or ending note). This doesn't necessarily
make it the tuning standard. But that would seem most likely, if there
_was_ a tuning standard. But I see no evidence for a tuning standard in the pitch data.

The Chinese pitch names are not as simple as you have indicated in your
article. There are 3 other characters which apparently indicate the
register or octave in terms of the physical size of the bell. Two of them
mean "small" (the TF character) and "smaller than small" (the penguin
skiing character) which seem to be used for progressively higher octaves (but not in the same pitch class), and the other apparently means
"opposite" (the square root of X-bar character) and is less clear. These
are used in conjunction with the single characters for CGDA. They are not
used with F, or any other note name that already has two characters, with
one exception. This is presumably because 3 characters would be
unacceptable. 3 character note names do not occur anywhere in the scanned
tables.

The exception is E. Even though the chinese name for E already has two
characters, meaning "major-third from C", in four cases the octave
modifiers are added to it and the character referring to C is dropped. So
they effectively read "octave above major third" and "two-octvaes above
major third". But an octave above a major third above what? I figure the
"C" can only be omitted because it is the tonic.

The other thing is that the character for C literally translates as
"palace". The palace is the centre of the kingdom, it sets the standards
(makes the laws), all roads lead there.

On that basis, I suspect the primary pentatonic mode was CDEGAC.

I'm unsure about some of the other characters, because the printing or
scanning is unclear. It would be good to have actual photos of the
inscriptions. But I can't find anything among their possible literal
meanings that is even remotely as suggestive of a tonic as is "palace",
except perhaps "to weave or knit" for G, although the zhi character with
that meaning was not the best match. The one with the "fine, delicate"
meaning looks closer.

I have found the following possibilities at
http://www.zhongwen.com/

C gong palace
G zhi to weave or knit, lance+sound, watchtower, fine, delicate
D shang discuss, trade, business, commerce, merchant
A yu feather, wing

> It is very common, however, that
>names and theory differ from practice (just think of the "western" seven
>letters for 12 tones).

I don't understand your point here. Clearly the main tone in western
tunings _is_ one that is named with a single character with no modifiers
(sharp or flat), as the Chinese name for F does not.

> I tried to write down musical practice as
>visible in
>the data.

This is a laudable aim. But I hope you understand now that you have made an
unwarranted and unnecessary assumption and so your calculations are not valid.

> > By the way, you should have translated gong zeng, zhi zeng, shang
>zeng as
> > Ab, Eb and Bb, not G# D# and A#, so that all the nominal(in chinese)
>thirds
> > would also be spelled as such in western notation (i.e. as thirds, not
> > diminished fourths).
>
>"Diminished fourths" only occur in the theory of the so-called "tonal"
>style of European music.

This is not relevant.

> In contexts of 12-tone descriptions it is now well
>established to use only the # for the five "accidentals".

This is only true of 12-tone _equal_tempered_ situations when there is no
particular tonal centre and no consonant intervals being discussed. And
even then it is also quite common to use EbBbFCGDAEBF#C#G# as the default
rather than FCGDAEBF#C#G#D#A#. That is not the case here. Correct spelling
of intervals is important.

For you to use G# D# and A# for what, in the Chinese, are clearly "major
third below" (or "minor sixth above") C G and D, is a travesty. It amounts
to an unwarranted assumption of 12-tone-equal-temperament before you even
start.

> > I find no evidence there that fifths are narrowed, or fourths
>widened, to
> > favour thirds.
>
>Well, the fourths according to your method are widened.

The amount is not significant given the huge variance.

> I rejected your
>method, however. I knew it from André Lehr in the Netherlands. The
>bells do
>not represent a system that is based on intervals that cross the octave
>borders, like our piano. They are for octave confined music, just like the
>gamelan instruments,

What evidence do you have for this? And if it is so, which octaves are we
confined to, G to G, C to C, D to D? And how do you know.

>because one player only has one octave in the reach of his hands.

What does it matter if it is played by one player or three, what has that
got to do with the issue of how to calculate mean interval sizes?

If I am including intervals that cross these imagined octave boundaries,
then so are you.

It seems from the photographs that a single player could easily span any
fifth with two hands. But I do not see this as relevant anyway. Both notes
of a fifth may never be played simultaneously and this would not affect my
point about how to calculate their mean size.

> Here, as in Gamelan, we have within-octave intervals and
>across-octave chroma consistency. Circles of fifths and fourths, or
>parts of
>it, do not seem appropriate to describe these instruments and their music.

How do you know this? It certainly isn't in the data or photographs.

>The term mean-tone tuning only makes sense in a 12-tone instrument.

Perhaps that is so for the literal meaning of "mean tone", but not for the
tempering principle that has come to be known as meantone temperament. This
can be applied to a chain of only four fifths (5 notes) and is simply the
principle of narrowing the fifths from 2:3 to bring the major and minor
thirds closer to 4:5 and 5:6. This is what you are claiming the Zeng bells
are doing for CGDAE.

>What the
>Chinese had 2000 years before the Europeans was a tuning focus on the
>thirds at the cost of the fifths.

I disagree. I don't see any cost to the fifths, if anything the cost falls
on the octaves and fourths. But the tuning errors are so huge it is
ridiculous to draw any such conclusions.

> > How one can conclude anything from a nominally 12-note tuning where
> > interval sizes vary +-50 cents, I'm not sure. But if it can be said to
> > approximate any kind of regular tuning, I'd have to say it looks like a
> > incredibly badly tuned 12 note equal division of a stretched octave.
>
>They are "incredibly badly tuned", if you apply this standards of
>multi-octave string instruments. If you apply the standards of
>metallophones, with their non-harmonic - but potentially very
>interesting -
>sound spectra, and the standards of musical practice of Gamelan
>instruments,
>the bells represent sufficiently balanced tuning compromises between scale
>precision and pleasant timbres.

But aren't you claiming that when struck in the right place there is very
little inharmonicity in the bell tones?

Even if the inharmonicity _is_ responsible, surely you're not seriously
claiming that those +-50 cent errors are _meant_ to be there. I'm afraid
this just doesn't hold water. How do you explain the enormous variations
between what are presumably bell cast from the same mold, in different sets?

I suggest that either their casting was very inaccurate and they had no way
of tuning the bells after casting, or 2,400 years has taken its toll (pun
intended).

Either way, I think the claims you are making cannot be supported by the
data, because of the uncertainty caused by these huge variations.

> > You say "it is obvious that the tuning focus was on pure thirds, not on
> > pure fifths". But I'd say it was treating thirds and fifths
>approximately
> > as equals. However, given that the bells tend to have an approximate
>third
> > among their partials, tuning these so that an individual bell sounds
> > harmonious when both of its notes sound simultaneously will force them
> > towards either a 4:5 or 5:6 ratio, and so even if the emphasis for the
> > tuning _between_ bells is entirely on the fourths and fifths, you would
>end
> > up with a tuning that appeared to favour minor and major thirds as
>much as
> > fourths and fifths.
>
>In octave confined music you simply have more thirds than fourths and
>fifths. The data reflect that the bell casters cared more about the thirds
>in the octave frame.

I'll await evidence of this "octave frame" before I comment on this.

>I think it should be clear from the context of the paper that we are
>dealing
>with a material 6-tone scale, not with a 6-tone scale in musical
>practice.

I'm afraid I did not find that clear. But I'm glad you agree. However there
is still the possibility that the F was not used any more often than say
the B, and just happens to occur in every octave because you have to put
_something_ on the D bell.

>I wrote about this at length in a reply to one of Kraig's posts.

I'm sorry I missed that.

> There is a
>possibly corresponding case in Gamelan pelog of Java, where the material
>scale always has seven tones in the octave, whereas the three modes
>that are
>used in pelog only select five of them, and different ones depending on
>mode.

Yes.

> > Notice that the pentatonics can be played with pitch strictly increasing
> > from right to left, whereas the hexatonic would require a
>counter-intuitive
> > reversal of direction between E and F.
>
>Good point. But for settings with one player per octave (mostly only 3
>bells), such a reversal would not have been much of a problem.

What evidence have you for one player per octave?

> > Your data does show a bell with 342 cents between its two notes (the
>D5-F5
> > bell in set I) but interestingly, on your data tables page you do not
> > suggest that either of its two notes are mistuned.
>
>Good point. In the table only assumed mistuning re ensemble is marked, not
>bell-internal one. The bell possibly was accepted and not melted down and
>re-cast, because it still fitted into the chroma scale of the ensemble, as
>shown in data table A.

Possibly.

> > With regard to what is mistuned and what isn't. The only place that we
> > agree that something is very wrong is in the low octave of set two,
>where
> > we find only 14 cents separating Bb from B.
>
>This supports the view that the six "accidentals" were second-class
>passengers in the ensemble.

It only supports the view that Bb was a second-class passenger, or that
2,400 years underwater and underground is a long time.

Regards,

-- Dave Keenan
Brisbane, Australia
http://dkeenan.com/

> >--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
>
> I rejected your method, however. I knew it from André Lehr in the
> Netherlands.

It seems I am in good company. Dr André Lehr has probably _forgotten_
more about bells than you or I ever knew.

See http://www.eijsbouts.com/history.htm

I'm not sure why we're fooling around trying to figure it out from the
frequencies, which have such enormous variations even in the purported
_unisons_, when it is apparently all explained in writing on the bells
themselves.
See http://www.newyorkqin.org/journal/volume1/volume1no4p2.html
or
http://www.amazon.com/exec/obidos/ASIN/0295979534/ref%3Dnosim/teijn10-20/103-5082020-5230240

And apparently, "The inclusion of five sets of beaters even gives a
fairly strong hint as to how many musicians were required to perform
the bells."
See
http://www.amazon.com/exec/obidos/ASIN/0295979534/ref%3Dnosim/teijn10-20/103-5082020-5230240

Here's an article on the Zeng bells by Andre' Lehr. Unfortunately I
don't read Dutch.
http://www.google.com/search?q=cache:mLxfp9ji0PcJ:www.carillon-museum.nl/dragon.doc+zeng+bells+tuning&hl=en&ie=UTF-8
or as a MsWord document
http://www.carillon-museum.nl/dragon.doc

David C Keenan wrote:

> > I rejected your method, however. I knew it from Andr� Lehr in the
> > Netherlands.

> It seems I am in good company. Dr Andr� Lehr has probably _forgotten_
> more about bells than you or I ever knew.

> See http://www.eijsbouts.com/history.htm

Dear David,

you might like to be more careful about your "good company". Andr�'s most
relevant publication on the Zeng bells is not the one in Dutch that you
cited in your next mail. It is this one:

Lehr, A (1988) The tuning of the bells of Marquis Yi. Acoustica 67, 144-148.

You might like to read this paper and check his figures as careful as you
have checked mine. You'll see that he made his calculations while including
all of the 6 errors in the Shanghai tables, even where they were obvious to
the bare eye. He only used the Cent data and not the Hz data, something a
careful researcher never would have done. One is tempted to assume that he
did it to get closer to his "aims". But this is a small mistake compared to
his other methodological mistakes. The paper is a poor one. It only makes
some "sense", if you consider the fact that the author was the
administrative chief of a carillon factory. The way the paper is written,
one gets the impression he was afraid that cheap copies of the Zeng bells
might threaten his market position.

Martin

David Keenan wrote:

> I'm not sure why we're fooling around trying to figure it out from the
> frequencies, which have such enormous variations even in the purported
> _unisons_, when it is apparently all explained in writing on the bells
> themselves.

As far as I am concerned, I have not been fooling around with anything here.
And nothing of what I reported in the article is "explained" in the
inscriptions of the bells.

> See http://www.newyorkqin.org/journal/volume1/volume1no4p2.html

You are apparently referring to this section of that web page:
"The limestone chimes and bronze bells are the most interesting
musicologically, for, uniquely among rediscovered specimens, they are
extensively inscribed with the names of, and musical instructions for, tones
and scales. These include directions for transposing among the scales of the
principality of Zeng and the relation of these scales to those of the
surrounding state of Chu, and, occasionally, to those of other states, with
all or most of these jurisdictions having independent standards for tuning."

This is poetry. A musicological analysis of this presumed "information" has
not been published, and I doubt that such "information" exists in the first
place. Lothar von Falkenhausen wrote well over 1000 pages (in his Ph.D.
thesis) about the bells and their various contexts. He did not deal with
this presumed "information" on "musical instructions for, tones and scales".

> or
>
http://www.amazon.com/exec/obidos/ASIN/0295979534/ref%3Dnosim/teijn10-20/103
-508\2020-5230240

Here I saw nothing on this issue.

> And apparently, "The inclusion of five sets of beaters even gives a fairly
strong hint as to how many musicians were required to perform
the bells."
See
http://www.amazon.com/exec/obidos/ASIN/0295979534/ref%3Dnosim/teijn10-20/103
-508\2020-5230240

The number of mallets found in the tomb gives no indication as to how many
mallets are needed to play the full ensemble. To conclude otherwise is a
silly error, but it has been repeated again and again in the literature. I
saw film material of a test performance with the original bells. It clearly
showed that one player, with both hands, can best handle three of the melody
bells in the middle tier. To handle the 33 melody bells with just six
T-mallets, as found in the tomb, is definitely not possible.

> Here's an article on the Zeng bells by Andre' Lehr. Unfortunately I
> don't read Dutch.
>
http://www.google.com/search?q=cache:mLxfp9ji0PcJ:www.carillon-museum.nl/dra
gon.\doc+zeng+bells+tuning&hl=en&ie=UTF-8
> or as a MsWord document
> http://www.carillon-museum.nl/dragon.doc

I read Dutch well enough to say this: The article is about historical
aspects of Chinese bells in general and, very roughly, about some aspects of
casting and acoustics. There is not anything specific about the analysis of
the data from the 65 Zeng bells. The drawings in this paper, borrowed from
other authors, are however worth looking at.

Martin

--- In tuning@yahoogroups.com, "Martin Braun" <nombraun@t...> wrote:
> Dear David,
>
> you might like to be more careful about your "good company". André's
most
> relevant publication on the Zeng bells is not the one in Dutch that you
> cited in your next mail. It is this one:
>
> Lehr, A (1988) The tuning of the bells of Marquis Yi. Acoustica 67,
144-148.
>
> You might like to read this paper and check his figures as careful
as you
> have checked mine.

Dear Martin,

I would like to, but I can't justify the time to travel to a library
to copy it. If you want to send me scans of it (preferably no larger
than 2MB total) I will do so.

> You'll see that he made his calculations while including
> all of the 6 errors in the Shanghai tables, even where they were
obvious to
> the bare eye. He only used the Cent data and not the Hz data,
something a
> careful researcher never would have done. One is tempted to assume
that he
> did it to get closer to his "aims". But this is a small mistake
compared to
> his other methodological mistakes. The paper is a poor one. It only
makes
> some "sense", if you consider the fact that the author was the
> administrative chief of a carillon factory. The way the paper is
written,
> one gets the impression he was afraid that cheap copies of the Zeng
bells
> might threaten his market position.

Points taken. I already wondered if he started the successful
computer-assisted effort to design major-third bells after learning of
the Zeng bells.

I also believe you when you say that the inscriptions do not explain
the tuning.

You might still respond to my other post, with arguments based
entirely on your data. And please describe _my_ methodologiocal mistakes.
/tuning/topicId_5844.html#45708

-- Dave Keenan

Dave Keenan wrote (46353):

>--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
>> thanks for pursuing this, dave. it seems both you and martin agree
>> that the tuning reflects an attraction toward the 5-limit, and
>> doesn't simply represent the stereotypically chinese 3-limit or
>> "pythagorean" tuning.

> No Paul, I'm afraid the data doesn't even support _that_ assertion.

> I had not previously tested the fit of a pythagorean tuning (with pure
> octaves) for FCGDAE, against the bell tuning data. Now that I have, I
> can report that the error is 21.9 cents RMS.

This result seemed so improbable to me that I carried out a thorough
statistical analysis. I compared the bell tones with five tuning models.

Results:
1) Phytagorean tuning must definitely be excluded as a model for the bell
casters (p<0.002).
2) 12-tone equal temperament is highly improbable as a model (p<0.05).
3) The best-fitting model is "Equally tempered fifths CGDAE of 696.2 tuned
from D, based on pure minor third D-F".
4) Just intonation and 1/3 comma mean-tone also fit the data, but the
detailed results suggest that they are less probable than the best-fitting
model.

The tested tuning models are here:

http://w1.570.telia.com/~u57011259/tuningmodels.htm

The detailed test results are here:

http://w1.570.telia.com/~u57011259/chinesebellstuningstat.htm

Martin