Theories about tuba pedal notes

[imperialbari]

We have discussed pedal notes some years ago, where I by pedal notes mean the notes that we usually would call the first partial of a tuba with its various fingering combinations. Not false notes, not second partials with a whole lot of valves pressed.

My terminology isn’t strong enough to make a good archive search on this topic.

I am mostly interested in getting a memory from the old discussion confirmed, or if wrongly remembered having it rejected.

As I remember old discussions, research had it that at least some tubas didn’t really sound proper pedal notes with any significant strength. What we hear as an often strong pedal note then really is an accumulation of the difference notes between adjacent partials. Because the difference note between adjacent partials always is the first partial. But as these difference notes are imaginary insofar that they only exist in the human perception of musical sounds, then they cannot be measured electronically.

Is this memory reasonably correct?

Can somebody please provide links or references to available, preferably online, research reports?

Klaus

[swillafew]

I can keep a better grip by using the terms "overtones" and "harmonic series". I believe overtone is interchangeable with "partial" but sometimes I have my doubts when others use them.

I am always more confused after reading others' posts here.

[Donn]

I think the most recent and extensive discussion here is this one: Pedal Tones (Physics Perspective)???. I'm not sure I can easily make out what came of it, but you may be able to follow it better.

On the specific question of whether pedal tones are real at all and therefore measurable, or purely figments of our imagination - I fired up my cellular phone and tried the tuner applications, and I couldn't make it recognize a tuba pedal -- but could make it recognize a bass trombone pedal. Down to F; Eb was too sloppy. That happened to be the pedal note I was trying for on (Eb) tuba, so I reckon it could very well be me that can't ring the bell on the tuba, not an inherent property of the instrument so much. This may not prove anything - the pitch recognition could very well depend partly on other partials, couldn't it? and thus discover a pitch with no 1st partial present.

My recollection of the conventional wisdom, in any case, is that the pedal 1st partial is present but weak.

[imperialbari]

I can keep a better grip by using the terms "overtones" and "harmonic series". I believe overtone is interchangeable with "partial" but sometimes I have my doubts when others use them.

Overtones are derivates of the fundamental.

Partials include the fundamental, which makes more sense, as fundamental and overtones are thereby connected in the same simple Pythagorean matematical rows, where

F, 2F, 3F, 4F, 5F, ------, nF describes the relationship between frequencies of the partials

and

L/1, L/2, L/3, L/4, L/5, --------, L/n describes the relationship between the lengths of oscillation of the partials.

You may set up mathematical rows for overtones also, but they would be less simple, because your formula would have to compensate for the natural starting point having been removed from the row.

Klaus

[imperialbari]

I think the most recent and extensive discussion here is this one: Pedal Tones (Physics Perspective)???. I'm not sure I can easily make out what came of it, but you may be able to follow it better.

On the specific question of whether pedal tones are real at all and therefore measurable, or purely figments of our imagination - I fired up my cellular phone and tried the tuner applications, and I couldn't make it recognize a tuba pedal -- but could make it recognize a bass trombone pedal. Down to F; Eb was too sloppy. That happened to be the pedal note I was trying for on (Eb) tuba, so I reckon it could very well be me that can't ring the bell on the tuba, not an inherent property of the instrument so much. This may not prove anything - the pitch recognition could very well depend partly on other partials, couldn't it? and thus discover a pitch with no 1st partial present.

My recollection of the conventional wisdom, in any case, is that the pedal 1st partial is present but weak.

Thanks for the link, which I will look at, when I am a bit more awake later in the day.

Your memory of the pedal note’s measurable strength is that it is weak. Mine is that it is without significant strength. I would say that our memories are pretty much in agreement on this matter.

I use a strobotuner app on phone and on iPad. The weak link is about the microphones. While much better than phone microphones of traditional phones of my youth and of most of my adult life, they still are small. And their main purpose still is to catch the human speaking voice, which does not operate in the frequency ranges of the pedals of low brass instruments.

Klaus

[Donn]

This page - Brass Instrument Acoustics at Georgia State University Physics & Astronomy, is mentioned late in the above discussion. Its propositions are

• brass instruments are closed pipes
• for musical purposes the full harmonic series of an open pipe is more convenient
• therefore the bell causes those odd closed pipe harmonics to be compressed to form a full harmonic series
• except for the first, which doesn't work out and becomes an "unused lower resonance" below the artificial series, and the pedal octave is purely the combination of upper partials.

I'm no physicist, but ... I don't find that very convincing at all. In the reeds, it's clear that despite the physical similarity at the top of the clarinet and saxophone, one is "closed" and the other is "open" for acoustical purposes. Or if you like, the saxophone is a "cone" as portrayed at the GSU site, with the same full series properties as an open pipe. They don't need to invent a story about how the saxophone got its full series by artful transformation of the odd series, and of course they have a rather clear and evident first partial there, as that's the main woodwind register. Brass instruments are for sure less solid in the first partial, but it's a matter of a design that revolves around the upper partials - and subject to some variation, taking the bass trombone as an example.

[imperialbari]

No, a compressed odd series that ends up very close to the full Pythagorean series doesn't sound likely.

Klaus

[tuben]

This page - Brass Instrument Acoustics at Georgia State University Physics & Astronomy, is mentioned late in the above discussion. Its propositions are
[list][*]brass instruments are closed pipes

Is this correct?
Open pipes propagate harmonics based on a CC fundamental note:
c0, g0, c1, e1, g1, Bbb1, c2, d2, e2, etc..... If you 'overblow' an open organ pipe, this is the pattern of notes you get.

Stopped pipes propagate:
go, e1, BBb1, etc.... If you 'overblow' an stopped organ pipe, this is the pattern of notes you get.

[Donn]

Stopped pipes propagate:
go, e1, BBb1, etc.... If you 'overblow' an stopped organ pipe, this is the pattern of notes you get.

I see you start at the 2nd or 3rd partial - no fundamental here?

My uneducated hunch is that "closed pipe" is not correct - that they've put together this elaborate story about how the closed pipe is made to sound just like it's an open pipe, but a simpler explanation is that it is acoustically an open pipe. Maybe the cylindrical tube without a bell does come out closer to a closed pipe - just as in the case of the reeds, with the clarinet vs. saxophone.

The effective difference between the two theories is, what happens with that pedal octave. In their odd-partials transformation scheme, it isn't there at all, while in my simple minded version it should be there acoustically speaking (though not necessarily useful.) [And I wouldn't have that "unused resonance" derived from the odd series fundamental.]

[tuben]

Stopped pipes propagate:
go, e1, BBb1, etc.... If you 'overblow' an stopped organ pipe, this is the pattern of notes you get.

I see you start at the 2nd or 3rd partial - no fundamental here?

No, assumes the same fundamental of CC as in the open pipe example.

[bloke]

Just as few tangential layman's observations...
It seems to be the rare tuba which offers easy to play fundamental pitches which are not considerably sharper than 1/2 of the number of hz. of the pitch one octave higher...
... and – hmm - The fundamental pitch seems to want to do anything other than resonate on a typical trumpet, yet a trumpet mouthpiece is an infinitely more easy thing on which to play tunes (with no trumpet attached) than is a tuba mouthpiece (with no tuba attached)...
... most likely, none of this is related at all…

[Donn]

... most likely, none of this is related at all…

Well, at the risk of applying logic in the absence of thorough understanding - if the GSU account of the pedal, as a fictitious pitch formed only by resonance of its harmonics, is correct, it would be interesting to hear them explain why it would have a different intonation tendency than the pitches formed directly by those harmonics.

[sloan]

Short answer: the "harmonic series" that makes so much musical sense is not at all a natural effect in brass instruments. Instead, it is a highly engineered artificial effect. The mouthpiece, the bell, and the taper combine to produce a close approximation to the simple "harmonic series". As with most artificial, engineered solutions, it is possible to move the errors around, increasing the accuracy where it is needed and pushing the gross imperfections somewhere where they don't interfere with normal operations. So it is with the "false tones".
They exist in the THEORY we use to make sense of the "harmonic series", but they don't really exist in reality.

Long answer: see the original thread(s) for citations. Alas, my brass theory library fell victim to my recent downsizing. Perhaps Rick Denney can re-post the references.

Bottom line: brass instruments are engineered to provide a reasonable approximation to PART OF the "harmonic series". You are on reasonably safe grounds in applying simplified musical theory to MOST OF the range. But, there is no "fundamental" (except in your head).

[bloke]

I tend to suspect that the "perfect" harmonic series (numbers/products that are all simple error-free multiplication problems) only exists on paper, and that no conical nor cylindrical tube (regardless of the method of setting a vibration in motion) can be found nor designed which offers pitches which line up perfectly with calculated numbers. (I'm not certain that Dr. Sloan agrees completely with this, but maybe he agrees with some of it...??)

It is interesting, though, how changing a conical taper to move fill-in-the-blank overtone in fill-in-the-blank direction will nearly always result in also moving other fill-in-the-blank overtone(s) in fill-in-the-blank direction.

the human factor interfering... trial-and-error = compromise // sales hype: 'Finally, an instrument that truly plays in tune!' = often, some of the instruments which offer their players some of the most difficult intonation // the more that is known for certain, seemingly, the less predictable are the results...etc...

To fully demonstrate everything that I know about the physical science of acoustics, I'm wondering (based on body type alone) what percentage of macaques actually can play (sans tuba) a tuba's "fundamental", and whether they can do it without a teacher...??
http://i.imgur.com/SE9fTAh.jpg

[pjv]

What, so whatcha all sayin' is that bass trombonists spend 1/3 of their careers playing notes that aren't even there and THEY GET PAID FOR IT?!

[tuben]

Bottom line: brass instruments are engineered to provide a reasonable approximation to PART OF the "harmonic series". You are on reasonably safe grounds in applying simplified musical theory to MOST OF the range. But, there is no "fundamental" (except in your head).

Maybe this is an issue of semantics, but there is a 'fundamental' pitch to any length pipe. Open, closed, tapered, resonator, doesn't matter, there is a pitch that corresponds with the natural length of the pipe that is the 'fundamental'.

Now, in brass instruments like organ reed pipes, the horn or resonator doesn't generate the sound but it does heavily influence its color and timbre. Pitches above the fundamental sound rounder and more dense as the pitch is being reinforced via the resonator numerous times. Pitches below the fundamental (double-pedals in the brass world, 1/2 length resonators in the organ world), still sound as the tone is generated mechanically but are less dense and almost 'hollow' sounding because the resonator is not reinforcing the tone as it does with proper or over length.

[sloan]

Yes, but...the fundamental of a tuba is not part of the harmonic series the player has in mind.

[timothy42b]

I tend to suspect that the "perfect" harmonic series (numbers/products that are all simple error-free multiplication problems) only exists on paper, and that no conical nor cylindrical tube (regardless of the method of setting a vibration in motion) can be found nor designed which offers pitches which line up perfectly with calculated numbers.

I bolded a piece of your post because that's the part I would disagree with.

I agree you can't design anything that will have a simple integer multiple harmonic series. Per our last discussion, if the slot is wide enough you can still play it in tune. But if you start at the bottom of the harmonic series and play up the series, one note at a time, they're all going to vary a bit from that simple relationship.

But I think this is not true if you're playing the fundamental. Then I think that all the overtones that sound above it WILL BE simple integer ratios. Even though these are not quite where the horn would resonate if you were playing one of those overtone notes directly.

[Donn]

Good to see someone trying to untangle the semantic confusion between partials/overtones/harmonics, vs. the pitches that we may play that correspond to a natural (idealized?) partial series for the horn. (Argh, not much untangling happened in that sentence. Oh, well.)

Could you elaborate on why you expect the pitches following that natural series wouldn't quite match the integer-ratios of the corresponding harmonics? If I got that right.

[timothy42b]

Could you elaborate on why you expect the pitches following that natural series wouldn't quite match the integer-ratios of the corresponding harmonics? If I got that right.

When you pluck a violin string, it vibrates at its natural frequencies. If you bow it, the timbre is totally different, because when you are driving a system with an input, as opposed to exciting it and letting it respond, the driven system responds to the input frequencies.

When you drive a wind instrument with a lip buzz, it is my belief that it is forced to respond with overtones that are simple integer ratios.

However it is very clear that the natural series of the horn is different. The different pitches available for a given fingering differ from integer ratios, and in fact differ from horn to horn. A horn is not a cylinder nor a cone, but a complex combination of various size tubing, valves, bends, restrictions, etc. (To the sound wave, a bend represents a wide spot in a tube: the sharper the bend, the wider the diameter if it were straight)