overtones for brass/woodwinds?

Brass and woodwind instruments have long fascinated me by the manner in
which they use the overtone series to produce their notes. I just
picked up "A Complete Guide to Brass" by Scott Whitener and it goes a
long way in explaining which overtone series the brass instruments use.
But there is still that mystery that Backus talks about in "The
Acoustical Foundations of Music" where he states that "it is not correct
to think that the trumpet, or any other brass instrument automatically
plays in just intonation." (p223).

I believe the reason that the third resonance of "particular trumpet" is
flat 6�; 4th resonance flat 25�; 5th resonance flat 34�; 6th resonance
flat 16� and the 8th resonance flat 54� may be because of the use of
valves require inserting cylindrical section to an otherwise gradual
flaring bore, although he says "actually, there is no reason for
assuming that there is any shape that will put all the modes into exact
harmonic relationship."

Looking at Whitener's book, right at the beginning on page 6 he says
"Because the 7th, 11th, 13th, 14th and 15th overtones of the harmonic
series are not in tune in the equal temperament system in use today,
they are replaced by valve notes."

My question for the list, has anybody calculated where these pitches are
so that they could possibly be used? The same for the woodwinds.

I have a couple of leads. My friend Bruce Brode plays French Horn.
Also an acoustics professor at a music conservatory in Mexico emailed me
on my website. But I was throwing this question out there in case
someone else already knows.

I was kind of surprised when at the Microfest Lou Harrison mentioned
restricting some of his use of brass writing to trombones when I've long
felt that all wind instruments are fair game for microtonal resources.

RT

> I believe the reason that the third resonance of "particular trumpet" is
> flat 6¢; 4th resonance flat 25¢; 5th resonance flat 34¢; 6th resonance
> flat 16¢ and the 8th resonance flat 54¢ may be because of the use of
> valves require inserting cylindrical section to an otherwise gradual
> flaring bore, although he says "actually, there is no reason for
> assuming that there is any shape that will put all the modes into exact
> harmonic relationship."

Be certain that you're making a clear distinction between the partials present in a particular
note on a brass instrument, and the series of pitches that plays when you switch between different
pitches by only adjusting lip tension (I'm trying to avoid the word "harmonic" here, but it's not
easy!). There's no guarantee that the pitches you get from a single valve combination and varying
lip tension will be exactly harmonic, but the partials present in a trumpet tone playing one
nominal pitch are pretty much exactly harmonic.

>
>
> My question for the list, has anybody calculated where these pitches are
> so that they could possibly be used? The same for the woodwinds.

I don't think there's any single formula for calculating the lengths of the tubes added by
depressing a valve. Although I don't know for certain, I would not be at all surprised if each
manufacturer probably has slightly different such lengths.

The toneholes of woodwinds are a largely different problem. It's a very complex topic that I
personally think is only indirectly related to unusual tunings. A good source of information is
Arthur Benade's book. (Ack, the title slips my mind at the moment, and I don't have it here with
me.)

--- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:
> I believe the reason that the third resonance of "particular
trumpet" is
> flat 6¢; 4th resonance flat 25¢; 5th resonance flat 34¢; 6th
resonance
> flat 16¢ and the 8th resonance flat 54¢ may be because of the use of
> valves require inserting cylindrical section to an otherwise gradual
> flaring bore, although he says "actually, there is no reason for
> assuming that there is any shape that will put all the modes into
exact
> harmonic relationship."

I'm wondering whether it isn't the flared bore that makes them
inharmonic. i.e. Different frequencies experience different effective
bore lengths. I find it hard to believe they are that far off just.

> Looking at Whitener's book, right at the beginning on page 6 he says
> "Because the 7th, 11th, 13th, 14th and 15th overtones of the
harmonic
> series are not in tune in the equal temperament system in use today,
> they are replaced by valve notes."
>
> My question for the list, has anybody calculated where these pitches
are
> so that they could possibly be used? The same for the woodwinds.

What do you mean "calculated"? Don't they need instead to be measured?
You've given measurements above. Do you mean you want them converted
to some other form? Which one?

Regards,
-- Dave Keenan

In a message dated 5/20/01 1:06:35 PM, ricktagawa@earthlink.net writes:

<< I believe the reason that the third resonance of "particular trumpet" is

flat 6¢; 4th resonance flat 25¢; 5th resonance flat 34¢; 6th resonance

flat 16¢ and the 8th resonance flat 54¢ >>

That's strange; I was under the impression that a typical trumpet inharmonic
series has increasingly sharp partials. I remember reading research
confirming this several years ago in a relatively recent sourcebook of
acoustical research papers on brass and string instruments, and I don't
recall the name of the book, but I recall that point clearly.
Aaron

In a message dated 5/20/01 3:24:40 PM, MR88CET@TEXAS.NET writes:

<< The toneholes of woodwinds are a largely different problem. It's a very
complex topic that I

personally think is only indirectly related to unusual tunings. A good
source of information is

Arthur Benade's book. >>

I think the book you're citing is HORNS, STRINGS, and HARMONY. Note: most
of the things in this book about harmonics have since been disproven.

Rick, I was searching for similar information several years ago, and I read a
lot of books and articles. The path I ended up taking, which was the most
helpful to me, was to pick up a trumpet and explore the instrument myself.
Then I took a lesson from a pro and asked as many questions as I could.
Otherwise I just used my ears. I learned more about the trumpet from one
lesson and this kind of exploration than I did from all the books.

Aaron

--- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:

/tuning/topicId_23306.html#23306

[Brass microtones]

>
> My question for the list, has anybody calculated where these
pitches are so that they could possibly be used? The same for the
woodwinds.
>

Yes, absolutely. Belgian French hornist Francis Orval made a chart
of virtually ALL the microtonal pitches of the instrument.

I used them in a couple of pieces in the mid-80's, one of which was
just "linked" by Dan Stearns a few messages back.

The chart that Orval made was republished by Johnny Reinhard in his
edition of PITCH, Vol. 1 #4.

In addition, Johnny has MANY fingering charts in that issue that are
PRACTICAL (whoops should be on other site :) ) illustrations of the
majority of microtonal pitches that can be produced with conventional
instruments.

I would contact Johnny about information like this, since he is a
wealth of it....

________ _______ ______ _____
Joseph Pehrson

--- In tuning@y..., Gary Morrison <MR88CET@T...> wrote:

/tuning/topicId_23306.html#23342

It's a very complex topic that I
> personally think is only indirectly related to unusual tunings. A
good source of information is
> Arthur Benade's book. (Ack, the title slips my mind at the moment,
and I don't have it here with
> me.)

It's _Fundamentals of Musical Acoustics_ published by Dover... but
don't forget Bruno Bartolozzi's VERY influential, but now out of
print _New Sounds for Woodwinds_. Oxford University Press...

_______ _______ ______
Joseph Pehrson

--- In tuning@y..., Pitchcolor@a... wrote:
>
> In a message dated 5/20/01 1:06:35 PM, ricktagawa@e... writes:
>
> << I believe the reason that the third resonance of "particular trumpet" =
is
>
> flat 6¢; 4th resonance flat 25¢; 5th resonance flat 34¢; 6th resonance
>
> flat 16¢ and the 8th resonance flat 54¢ >>
>
> That's strange; I was under the impression that a typical trumpet inharmo=
nic
> series has increasingly sharp partials.

It really depends on the instrument how inharmonic the _resonances_ are. Bu=
t on a brass
instrument, blown steadily, the timbre has exactly harmonic _partials_. The=
se are two different
things, as Gary Morrison emphasized (today I think?)

Dave Keenan wrote:

>
> What do you mean "calculated"? Don't they need instead to be measured?
> You've given measurements above. Do you mean you want them converted
> to some other form? Which one?

You're right, I meant measured. Backus gives measurents of resonances 3, 4, 5, 6, and 8 from one
particular trumpet. It would be helpful to know where the 7th and 11th are.

It's amazing to look at all of these overtones series available to trumpets, french horns,
trombones and tubas and lament at all the unused notes. It's really kind of funny, considering
it's been like this since freshman Orchestration 1.

I've been thinking that since the overtone series forms the method for obtaining notes on
aerophones, perhaps one strategy might be to think of the overtones as being in tune and let the
instrumentalist correct for the idiocyncracies of his or her instrument.

Yours,
Rick

--- In tuning@y..., Rick Tagawa <ricktagawa@e...> wrote:

/tuning/topicId_23306.html#23426

> It's amazing to look at all of these overtones series available to
trumpets, french horns, trombones and tubas and lament at all the
unused notes. It's really kind of funny, considering it's been like
this since freshman Orchestration 1.

Hi Rick!

This was absolutely MY thinking upon seeing Francis Orval's chart of
the overtone series for French Horn.

Of course, all the horn players learn NOT to play any of the other
xenharmonic pitches, so there is a certain resistance in that
department.

Also in critics. John Rockwell blasted Orval's performance in Merkin
saying the microtonal pieces were not played as strongly as his
Hindemith... some comparison...

________ ______ ______
Joseph Pehrson