Harmonics of a trumpet

[Abstract Dissonance]

Can anyone explain to me how I can get non-overtone notes off a trumpet
without using valves?

I just starting trying to learn the trumpet a few days ago and I have taken
my tuner(a peterson strobe) and played around with buzzing.

The trumpet is a Bb and these are the tones I can get(w.r.t Bb)

G2, G#2, A2(but drops in volume by about 1/2)

A3(but very "wobbly"), A#3, B3, C4


I don't understand how these notes are possible as I thought basicaly when
you blow in the trumpet you excite the overtones... which is a fixed series.
The fundamental depends on the length of the tubing and the valves just
change the fundamental so you can get different notes(but since I am not
using the valves above this doesn't matter).

if I look at the overtones for C I have

C C G C E G Bb C D E F# G A Bb B C ...

so I can see where the A3 A#3/Bb3 B3 C4 are... its th last 4 notes above...

this would imply that the fundamental of the Bb trumpet is C0?

If what I just said above then where is the G2 G#2 A2 coming from? I read
somewhere about pedal tones, are these it? I can't seem to get anything
below G2 and when I try to go above A2 it doesn't work either(using the same
"embroshure"... well, when I buzz a certain way it will usually jump down
from G3 or so to A2 but I can't go up from A2 to G3 or so).


Thanks

[David Webber]

Post by Abstract Dissonance
I don't understand how these notes are possible as I thought basicaly when
you blow in the trumpet you excite the overtones...

You can create vibration of any frequency. But only some of them will
cause a resonance in the instrument.

Dave

[Dan McGarvey]

Post by Abstract Dissonance
Can anyone explain to me how I can get non-overtone notes off a trumpet
without using valves?

Crooks.

[Dr Matt]

Post by Dan McGarvey

Post by Abstract Dissonance
Can anyone explain to me how I can get non-overtone notes off a trumpet
without using valves?

Crooks.

Any resistance added to the end of the tube will slow the speed of sound
waves exiting the tube, distorting the resonant modes. Players are
used to forcing their instrument to keep in tune while they add things
like wahwah cups, but the instrument will accommodate a glissando during
the effect. Hornists sometimes cultivate this effect. There's some
discussion about what happens when you suddenly jam an obstruction--say
a hand--into the bell of a horn, i.e. whether it drops or rises in
pitch. Essentially, the resonances shift lower in pitch, and the lower
the resonance, the further proportionally it moves (thus the thing
rapidly diverges from its near-harmonic set of partials, making added
challenges for the player). But with the same lip impetus without
transition time, the tube may start resonating at the next higher
partial. Even long before valves were added to horns, hornists
cultivated the art of tuning their lips and their instrument's resonance
together in order to play in tune with the musical context.

[Jerry S.]

Let's see if I understand this right. Your Bb trumpet played "open" is
producing several notes in the 2nd or 3rd octave of a piano. I
routinely play a few of these notes as warm up tones and I think I have
some fairly simple explanations for why they work at all.

First of all, trumpet fingering charts show middle C (C4) as the lowest
open note and G (G4) as next available open note, but remember that a
Bb trumpet is a transposing instrument, so that our low C is really Bb4
(or A#4) and the G is really an F4. But from the physics perspective,
these are the 1st and 2nd overtones-- the "fundamental" of the Bb
instrument based on it's physical length is REALLY an octave below
Bb4-- so that the actual pitch of the fundamental is a Bb3 and the
overtone series goes Bb3, Bb4, F4, Bb5, D5, F5 etc... You almost CAN'T
force the trumpet to play that Bb3, but somehow Bb2 pops out quite
easily if you use a LOT of upper lip in the mouthpiece. It's very
unmusical but it resonates like a moose and with practice you can
easily "lip it" up or down between Bb2 and F2. I think the technical
term for these notes is "sub-harmonics" but a jazz trumpet player I
knew called them "pedal tones" (although music theory has a different
definition for pedal tone).

The valves help a little to clean up the tone, but they don't force the
horn to hit the pitches. The fact that the notes are wobbly or much
softer merely demonstrates why trumpet players never depend on these
notes for conventional music. I once wrote them into a composition for
brass quintet but I was very disappointed with the results.

I'm completely unable to produce a C4 without valves (open). Because
of the transposition, that would be a trumpet's D and is normally
played with valves 1+3.

As for why it's easy to get the octave BELOW the fundamental, I'll
venture an uneducated but experienced guess: it could be that emphasis
on just the upper lip is producing a very modified version of the
action 'good' trumpet players produce using both upper and lower lips.
Just maybe we are producing only half of the "sine wave" so the
frequency comes out an octave below the instruments fundamental. OK- I
know the lips never buzz an actual sine wave. But then I'm not a
physicist either. (I think it's a saw-tooth wave?)

In the long run, and I'm not a trumpet teacher although I did take a
lot of lessons, I think you SHOULD practice long tones daily with your
tuning meter. Spend most of your practice time in the normal range of
the trumpet, and the basic design of the instrument helps to keep the
pitches in tune.
- Jerry

Post by Abstract Dissonance
Can anyone explain to me how I can get non-overtone notes off a trumpet
without using valves?
I just starting trying to learn the trumpet a few days ago and I have taken
my tuner(a peterson strobe) and played around with buzzing.
The trumpet is a Bb and these are the tones I can get(w.r.t Bb)
G2, G#2, A2(but drops in volume by about 1/2)
A3(but very "wobbly"), A#3, B3, C4
I don't understand how these notes are possible as I thought basicaly when
you blow in the trumpet you excite the overtones... which is a fixed series.
The fundamental depends on the length of the tubing and the valves just
change the fundamental so you can get different notes(but since I am not
using the valves above this doesn't matter).
if I look at the overtones for C I have
C C G C E G Bb C D E F# G A Bb B C ...
so I can see where the A3 A#3/Bb3 B3 C4 are... its th last 4 notes above...
this would imply that the fundamental of the Bb trumpet is C0?
If what I just said above then where is the G2 G#2 A2 coming from? I read
somewhere about pedal tones, are these it? I can't seem to get anything
below G2 and when I try to go above A2 it doesn't work either(using the same
"embroshure"... well, when I buzz a certain way it will usually jump down
from G3 or so to A2 but I can't go up from A2 to G3 or so).
Thanks

[Jerry S.]

This is a simpler explanation than my other response!

You are only confused by the transpostion of a Bb instrument.
Historical convention for brass instruments is to write the fundamental
pitch as C regardless of what it really is. When a Bb instrument reads
and plays a C major scale, the notes come out as a "concert" Bb scale.
Therefore, the overtone series for a Bb trumpet with no valves
depressed is:

Bb3(extremely soft) Bb4 F4 Bb5 D5 F5 Ab6(out of tune) Bb6 C6
D6 E(out of tune) etc.

- Jerry

Post by Abstract Dissonance
Can anyone explain to me how I can get non-overtone notes off a trumpet
without using valves?
I just starting trying to learn the trumpet a few days ago and I have taken
my tuner(a peterson strobe) and played around with buzzing.
The trumpet is a Bb and these are the tones I can get(w.r.t Bb)
G2, G#2, A2(but drops in volume by about 1/2)
A3(but very "wobbly"), A#3, B3, C4
I don't understand how these notes are possible as I thought basicaly when
you blow in the trumpet you excite the overtones... which is a fixed series.
The fundamental depends on the length of the tubing and the valves just
change the fundamental so you can get different notes(but since I am not
using the valves above this doesn't matter).
if I look at the overtones for C I have
C C G C E G Bb C D E F# G A Bb B C ...
so I can see where the A3 A#3/Bb3 B3 C4 are... its th last 4 notes above...
this would imply that the fundamental of the Bb trumpet is C0?
If what I just said above then where is the G2 G#2 A2 coming from? I read
somewhere about pedal tones, are these it? I can't seem to get anything
below G2 and when I try to go above A2 it doesn't work either(using the same
"embroshure"... well, when I buzz a certain way it will usually jump down
from G3 or so to A2 but I can't go up from A2 to G3 or so).
Thanks

[Margo Schulter]

Post by Jerry S.
This is a simpler explanation than my other response!
You are only confused by the transpostion of a Bb instrument.
Historical convention for brass instruments is to write the fundamental
pitch as C regardless of what it really is. When a Bb instrument reads
and plays a C major scale, the notes come out as a "concert" Bb scale.
Therefore, the overtone series for a Bb trumpet with no valves
Bb3(extremely soft) Bb4 F4 Bb5 D5 F5 Ab6(out of tune) Bb6 C6
D6 E(out of tune) etc.
- Jerry

Hello, there, and I might add one fine semantic point: describing the
7th harmonic (Bb3-Ab6) and 11th harmonic (Bb3-E6 as written here) as
"out of tune" might best be read simply to say that these tunings differ
from those of intervals in a conventional European system (medieval to
Romantic), not that they are unharmonious or unuseful.

In other words, "Consider them a valuable resource, but exercise some
caution where a clash with other performers might occur."

In fact, the 7th harmonic is the smoothest tuning for a minor seventh
(e.g. Bb5-Ab6 to put the interval within a single octave), and is much
favored in some late 20th-21st century musics. However, a player should
indeed be aware that this is a much narrower seventh at around 969 cents
than in 12-note equal temperament (1000 cents -- 100 cents being equal
to a semitone in this temperament, or 1/12 octave), or even on a string
instrument, for example, tuned in pure 3:2 fifths or 4:3 fourths, where
a minor seventh would be 16:9 or about 996 cents. In other words, 7:4
is to many listeners a pleasant and harmonious interval which differs
from some other tunings of a minor seventh.

Similarly, the small tritone or diminished fifth formed by the 8th
and 11th harmonics (e.g. Bb6-E6 as written here) is a standard interval
in Zalzal's scale, very important in medieval Arabic theory; it has an
intriguing quality, different from a usual European tritone and sometimes
notably "smooth." Again, since some modern tuning systems specifically
seek out 11:8 or close tempered equivalents, I would prefer to call it,
not "out of tune," but "distinct from historical European tunings."

If a trumpeter were playing solo, or with singers or instruments which
can also produce or approximate the 7th and 11th harmonics, I would
consider these valuable musical resources.

Please let me emphasize that I'm trying to strike a balance, taking each
interval size as "in tune" when used in proper context. Thus I would say
neither than a temperament like 12-tone equal is "out of tune" because
some of the intervals notably differ from the simplest harmonic ratios,
nor that the harmonic series is "out of tune" because it likewise differs
from such a conventional temperament.

Most appreciatively,

Margo Schulter
***@calweb.com

[J. B. Wood]

Post by Margo Schulter
Please let me emphasize that I'm trying to strike a balance, taking each
interval size as "in tune" when used in proper context. Thus I would say
neither than a temperament like 12-tone equal is "out of tune" because
some of the intervals notably differ from the simplest harmonic ratios,
nor that the harmonic series is "out of tune" because it likewise differs
from such a conventional temperament.

Well put, Margo. Sincerely,

John Wood (Code 5550) e-mail: ***@itd.nrl.navy.mil
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337

[Jerry S.]

Hi Margo,

Very nicely explained! Let me now pose a similar but slightly
different question regarding trumpet tunings:

Why are trumpets usually in pitched in Bb instead of C? I know that
historically they have be built in many keys, but Bb is by far the most
common-- and of course that forces us to deal with transposed music
notation. But why Bb?

- Jerry

Post by Margo Schulter

Post by Jerry S.
This is a simpler explanation than my other response!
You are only confused by the transpostion of a Bb instrument.
Historical convention for brass instruments is to write the fundamental
pitch as C regardless of what it really is. When a Bb instrument reads
and plays a C major scale, the notes come out as a "concert" Bb scale.
Therefore, the overtone series for a Bb trumpet with no valves
Bb3(extremely soft) Bb4 F4 Bb5 D5 F5 Ab6(out of tune) Bb6 C6
D6 E(out of tune) etc.
- Jerry

Hello, there, and I might add one fine semantic point: describing the
7th harmonic (Bb3-Ab6) and 11th harmonic (Bb3-E6 as written here) as
"out of tune" might best be read simply to say that these tunings differ
from those of intervals in a conventional European system (medieval to
Romantic), not that they are unharmonious or unuseful.
In other words, "Consider them a valuable resource, but exercise some
caution where a clash with other performers might occur."
In fact, the 7th harmonic is the smoothest tuning for a minor seventh
(e.g. Bb5-Ab6 to put the interval within a single octave), and is much
favored in some late 20th-21st century musics. However, a player should
indeed be aware that this is a much narrower seventh at around 969 cents
than in 12-note equal temperament (1000 cents -- 100 cents being equal
to a semitone in this temperament, or 1/12 octave), or even on a string
instrument, for example, tuned in pure 3:2 fifths or 4:3 fourths, where
a minor seventh would be 16:9 or about 996 cents. In other words, 7:4
is to many listeners a pleasant and harmonious interval which differs
from some other tunings of a minor seventh.
Similarly, the small tritone or diminished fifth formed by the 8th
and 11th harmonics (e.g. Bb6-E6 as written here) is a standard interval
in Zalzal's scale, very important in medieval Arabic theory; it has an
intriguing quality, different from a usual European tritone and sometimes
notably "smooth." Again, since some modern tuning systems specifically
seek out 11:8 or close tempered equivalents, I would prefer to call it,
not "out of tune," but "distinct from historical European tunings."
If a trumpeter were playing solo, or with singers or instruments which
can also produce or approximate the 7th and 11th harmonics, I would
consider these valuable musical resources.
Please let me emphasize that I'm trying to strike a balance, taking each
interval size as "in tune" when used in proper context. Thus I would say
neither than a temperament like 12-tone equal is "out of tune" because
some of the intervals notably differ from the simplest harmonic ratios,
nor that the harmonic series is "out of tune" because it likewise differs
from such a conventional temperament.
Most appreciatively,
Margo Schulter

[David Webber]

Post by Jerry S.
Why are trumpets usually in pitched in Bb instead of C? I know that
historically they have be built in many keys, but Bb is by far the most
common-- and of course that forces us to deal with transposed music
notation. But why Bb?

I suspect the Bb instrument had a nice tone. Saxophones existed
(according to legend) in families of F/C as well as Eb/Bb but the former
died out. Again I suspect it was the same reason. The clarinet survived
in Bb and A because the same mouthpiece and reed can be used on both, and
between them they cover all keys with reasonably convenient fingerings.

Don't worry about "being forced to deal with transposed music notation".
It really isn't a problem. You don't think "that is a C" when you read a
C - you translate it directly into a fingering and an embouchure, so
transpositions don't matter. If you habitually write for Bb and Eb
instruments, then the ones at concert pitch start to feel more awkward -
there is really nothing special about them.

And violins, violas, and cellos all using different clefs makes writing for
them just as awkward as if they were transposing instruments. It would
make a lot more sense if they all had music on treble clef with strings
tuned to written G D A E like the violin. The viola and cello would then be
alto violin in F, trasposing a 5th down, and baritone violin in F
transposing a 12th down. :-) If they were invented today, I'm sure that
would be the convention. But they evolved differently - before this more
rational system was thought of. (The result is that a lot more people can
play all of soprano, alto, and baritone sax, than can play violin, viola,
and cello.)

Dave

[Steve Latham]

Post by Jerry S.
Hi Margo,
Very nicely explained! Let me now pose a similar but slightly
Why are trumpets usually in pitched in Bb instead of C? I know that
historically they have be built in many keys, but Bb is by far the most
common-- and of course that forces us to deal with transposed music
notation. But why Bb?

One of my colleagues has a quote from Benge to a student of his saying that
he should stick with the Cornet and that the Trumpet was only used for Jaz
[sic] music. Interesting historical irony, don't you think!

Anyway, I'm with David - probably easier to play repertoire, maybe played in
tune better for the various keys (was a "middle ground"), could be better
tuning to length ratio, and produced more favorable tone as David suggests,
and could just simply be more practical - hey, I can bring three trumpets to
the gig with me, and I can play two of the works on my C, and two of them on
my A, but all three of them on my Bb, or something like that.

Steve

[Margo Schulter]

Post by Jerry S.
Why are trumpets usually in pitched in Bb instead of C? I know that
historically they have be built in many keys, but Bb is by far the most
common-- and of course that forces us to deal with transposed music
notation. But why Bb?
- Jerry

Hi, Jerry, and your question gives me an opportunity humbly to
acknowledge that I'm glad that David and Steve had some ideas to
contribute in an area where I'm uninformed.

It is an interesting question, and maybe the known history might be
interesting to trace.

Most appreciatively,

Margo