Brass: lips, bells, and a garden hose

Unit 02 · 31 October 2026 · Acoustics

A trumpet has no reed — so what is buzzing, and why do some valve combinations come out sharp?

By Jeremy Pickett

Abstract

A brass player's lips work as a pressure-controlled valve feeding the bore. Acousticians call them a "lip reed", a functional term. Which way the lips swing (outward or upward) is still disputed, and the answer seems to depend on register and measurement method. A bare cylindrical tube closed at the lips supports only odd harmonics. The bell and mouthpiece pull those resonances close to a harmonic series a player can use. Valved brass has intonation trouble built in: valve loops add up in length, but pitch counts ratios, so 1-2-3 comes out about 53.6 cents sharp and needs slide compensation or alternate fingerings. The pedal note is played on both cylindrical and conical bores, while the "ghost note" has been documented on predominantly expanding bass bores (tubas, euphoniums, saxhorns). A garden hose, a mouthpiece and a funnel make a passive home test of the resonance story, no impedance rig needed.

Why you should care

• Teacher: Knowing the "lip reed" is a functional term changes how you cue students to open their embouchure for high notes versus low notes.
• Student: The 1-2-3 fingering is inherently sharp because of valve arithmetic, not "bad tone." Knowing that relieves the frustration and points your attention at the slides.
• Builder: The bell raises lower resonances by shortening effective acoustic length (early reflection), not just by amplifying. That informs flare profile design for better tuning.
• "Well actually" Reviewer: You can't simply say "lips act like a clarinet reed": a clarinet reed is inward-striking, while measurements show brass lips with a strong outward-striking resonance, and Yoshikawa's register-dependent outward/upward classification is his own and labeled speculative. Models also show a trombone or tuba pedal note can be sustained with only the first impedance peak.

1. The Valve That Isn't a Reed

Every brass note starts as a buzz. The question under this whole essay is how that buzz, pushed through a coil of tubing, turns into the particular notes you can play, and why a few of them come out of tune.

Start at the lips. Acousticians call them a "lip reed", which is a functional term, not a physical object. A physical reed is a thin strip of cane, metal, or synthetic material attached to the instrument that vibrates against a mouthpiece or through an opening. A trumpet has nothing like that. The lips themselves form the valve: they open and close periodically, releasing puffs of air into the bore in step with the mouthpiece pressure, and those puffs drive the standing waves in the tube. [1][2]

So two systems are coupled, a mechanical one (the lips) and an acoustical one (the air column). The air column strongly favors certain notes, its resonances. A good player can still bend a pitch off them, steering with blowing pressure, lip tension, the amount of tissue vibrating, and embouchure shape. [1]

Which way do the lips actually swing? Nobody has settled it. Yoshikawa (1995) interpreted the trumpet's lowest playing mode as outward-striking, blown open by mouth pressure, with higher modes shifting toward what he called upward-striking. He labeled that speculative himself. [3] Thirteen years later, Newton, Campbell & Gilbert (2008) measured four semiprofessional trombonists on three notes, plus artificial lips, and found a strong outward-striking resonance alongside weaker inward-striking ones. [4] Those are trombone measurements, and carrying them over to the trumpet is an assumption. Outward versus upward remains debated, depending on the register and the model used. [3][4]

A clarinet reed works the other way: blowing pressure pushes it closed (inward-striking). Same job, door hinged the other way.

Two more findings fill in the lips' side. Boutin, Smith & Wolfe (2020) describe a sweeping flow from the moving lips, and found that trombonists normally play slightly above a bore resonance, with the lipping range roughly symmetric about the peak. [5] And the throat behind the lips? Chen, Smith & Wolfe (2012) found no systematic vocal-tract resonance tuning in seven trumpeters, though their apparatus kept players from reaching their highest notes. [6]

The lips supply the buzz. What the tube does with it is stranger than it looks.

2. The Tube That Isn't a Pipe

On paper, a trumpet should behave like a clarinet. Most of its length is cylindrical tubing closed at the player's end, and an ideal cylinder closed at one end has resonances only at odd multiples of its fundamental (1, 3, 5…). Real tubing only approximates the ideal, and a trumpet is only mostly cylindrical. [7] How mostly depends on where you say the leadpipe taper ends and the bell flare begins. Moore describes most of the roughly 1.4 m of a modern trumpet as cylindrical; other accountings divide it differently. [7]

So why doesn't it play like a clarinet? John Backus went and measured. He took input impedance curves for four setups: plain tubing, tubing plus bell, tubing plus mouthpiece, and tubing with both. He presented them at the April 1975 ASA meeting and published them in JASA in 1976. With the bell and mouthpiece in place, the peaks from the second one up sit close to 2, 3, 4, 5… of a fundamental the bore has no resonance for. The floors are numbered from a lobby that isn't there. The 1976 abstract credits the bell and mouthpiece with putting the resonances in their musically necessary places. [8]

Close to a harmonic series, mind you, not exactly on it. How each part moves the resonances is the subject of the bell and mouthpiece posts and of the next two sections. The upshot, with valves open: the step between the two lowest regular notes, written C4 to G4, is a fifth. Not a clarinet's twelfth, and not the octave you'll often read about. [8]

3. The Bell That Isn't a Megaphone

Point a trumpet at the back row and the bell looks like a megaphone. Loudness is one of its jobs. The quieter job is tuning.

Each frequency turns back at its own point inside the flare. Low frequencies turn back early, so they see a shorter tube and rise in pitch. Higher frequencies travel deeper before reflecting, so they shift less. That drags the low resonances up toward a harmonic series, away from the odd-only pattern of an idealized tube closed at the lips. [9]

Two pieces of fine print. "Shift less" is relative: the flare raises the lower resonances proportionally more than the higher ones. And the odd-only pattern is exact only for an idealized pipe; real cylinders deviate from it because of end effects and wall losses. Higher frequencies are also radiated from the bell more efficiently instead of being reflected, and that shapes the tone. [9]

And the snarl when a section really leans on it? Much of that comes from a different mechanism: nonlinear steepening of the wave along long cylindrical sections, which can form shock waves. The effect is strongest in trumpets and trombones (Hirschberg, Gilbert, Msallam & Wijnands, 'Shock waves in trombones', JASA 99(3), 1754–1758, 1996).

Then there's the question nobody can leave alone: does the metal matter? Whether a horn is yellow brass, gold brass, or sterling silver, and whether it is lacquered, silver-plated, or raw, the wall material and finish have a tiny effect on the radiated sound, and a large, measurable effect on how makers, players, techs, and audiences build, play, hear, value, and look after the instrument. (Where the material is the vibrating part, as with a reed, a string or a drumhead, it matters acoustically too. A brass body isn't that case: the vibrating part is the player's lips, which don't come with the instrument.) [10]

Even the bell can't fully rescue the bottom. On trumpets and trombones, the lowest resonance gets the biggest proportional push of all and still comes up short, falling well below the harmonic series implied by the higher resonances. So it sits out of line and isn't normally played. On tubas the story differs, as Section 5 explains. (The pedal note is a related but separate story.) [11]

The bell takes care of the low end. Something else has to pull the high end down.

4. The Mouthpiece That Isn't Just a Seat

What does the mouthpiece do besides give your lips somewhere to sit? Acoustically, it's a tiny bottle, the shape acousticians call a Helmholtz resonator: the cup is the cavity, and the throat plus backbore form the neck. That little bottle has a resonance of its own. It pulls the horn's high resonances down, most strongly as they approach its own resonance from below, as if the tube grew longer for the high notes. [8]

So the work splits in two. The bell raises the low resonances, the mouthpiece (with the leadpipe) lowers the high ones, and between them you get a nearly harmonic series you can play. It also adds one new resonance in each gap between the original ones, and the peaks are cut off above the mouthpiece resonance. [8]

The split isn't perfectly tidy. The bell radiates high frequencies into the room, so fewer of them reflect back to sustain standing waves, and the tapered leadpipe works with the mouthpiece on the upper resonances. Pop a mouthpiece on its own and you hear a pitch; that 'popping' pitch changes once it's installed in the horn. [8]

Could you just play the odd-only series and skip all this? You could. A plain cylinder played like a didjeridu shows that an odd-only series is playable. (Traditional didjeridus are slightly flared and irregular, so their resonances aren't in harmonic ratios, and players stay almost entirely on the lowest one.) What an odd-only series lacks is the even members that conventional brass playing relies on. The one big exception to "nearly harmonic" is the pedal note, which Section 5 takes up. [11][12]

5. The Pedal Note and the Ghost Note

"The pedal note is just the fundamental." It's a tidy answer, and it blurs two things that need to be kept apart: the lowest passive resonance and the pedal's playing frequency. Their relationship differs among instruments. The lowest resonance can be well below the pedal frequency on a trombone, whereas the first acoustic mode can support the pedal in a tuba model. [11][12]

Whatever it rests on, the pedal note is playable. In a 2022 paper mainly about ghost notes, Mattéoli and colleagues used bifurcation analysis on a B-flat contrabass tuba. They found that the first acoustic mode supports the pedal, and that linear stability analysis alone can't reproduce it. [11] They also cite time-domain simulations in which a trombone or tuba pedal persists with only the first impedance peak. [12]

The ghost note is something else: a regime between the pedal (the first regime) and the second. Mattéoli et al. describe it on the bass brass they studied, tubas, euphoniums and saxhorns, all with predominantly expanding bores. Pedal notes, by contrast, are played on both mainly cylindrical and mainly conical instruments. Whether ghost notes can be produced on other brass is not settled by that study. [11]

How the pedal works is debated and differs by instrument family. [11] (My read: much of that argument is a quillet over naming and labeling, not over what the horn does. It's marked Disputed (minor) below.)

6. The Valve Math That Doesn't Add Up

The bottom of the horn is a debate. The middle is plain arithmetic. Why do some valve combinations play sharp? Because in the simplest design each valve loop is cut for the open horn, and pitch doesn't count inches; it counts ratios. Each interval needs the tube to grow by a fixed fraction of its current length. With valve 1 down, valve 3's loop, sized for the shorter tube, is now too small a fraction to finish the job. Tune each valve to an exact equal-tempered interval and 1-2-3 lands about 54 cents sharp, a little over a quarter-tone. Three right answers, one wrong sum. [14]

"About 54 cents" is an idealized equal-tempered calculation, not a measurement. Here's the arithmetic. In the ideal model, a valve that lowers the pitch n semitones adds 2^(n/12) − 1 of the tube's length: about 0.0595 for valve 2, 0.1225 for valve 1, and 0.1892 for valve 3. Together that's a factor of 1.37113, which lowers the pitch 1200 × log₂(1.37113) ≈ 546.4 cents instead of 600. That's 53.6 cents sharp. Because the error is a ratio, the same model gives the same answer for trumpet or tuba. With just-intonation valve lengths (Monk, in Baines), Monzo gets 1-2-3 at about 572 cents, roughly 28 cents sharp, but only by leaving valves 1, 2 and 3 about 4, 12 and 16 cents flat on their own. [14]

Makers strike the same kind of compromise by building the slides a bit long, leaving each valve alone slightly flat. Players cover the rest with lip, alternate fingerings, and the trumpet's first- and third-valve slides, worked by the left thumb and ring finger.[17] Some horns add a compensating fourth valve, whose tubing is routed back through the other three valves to add small correcting loops.[16] What the fourth valve does depends on the instrument. On tubas, euphoniums and piccolo trumpets it usually lowers the pitch a perfect fourth,[16][17][18] so 2+4 stands in for 1-2-3 (both add six semitones). Uncompensated, the same idealized arithmetic (this essay's own) puts 2+4 at about 575.5 cents below open, roughly 24.5 cents sharp.

The double French horn plays by different rules. On an F/B-flat double, the thumb valve switches between the F and B-flat tubing instead of lowering the pitch, so the 2+4 substitution doesn't apply; players avoid the worst long combinations by choosing the side that tunes better for each note. On some instruments the fourth valve is pitched differently, and there the 2+4 substitution doesn't apply either. None of this is new. Blaikley's British patent 4618, applied for on November 14, 1878, covered only three-valve compensating pistons, with the third valve as master and five passages in each of the first two. It followed Gautrot's earlier four-valve système équitonique, with six passages, and Boosey's four-valve instrument of 1874. [15]

7. The Garden Hose Experiment

Can a garden hose play a bugle call? Mostly, yes. Put a cup mouthpiece in one end and a funnel on the other, and the hose gives you a ladder of natural notes, rougher and less evenly tuned than a bugle's. A traditional signal bugle has no valves, so its calls use that ladder alone, mostly harmonics 2 through 6; Taps (G-C-E-G on a C bugle) uses only 3 through 6. [13] The bottom rung sits out, as it does on trumpets and trombones, where the lowest resonance falls too far below the series to use. [11]

The funnel plays the part of the bell. A brass bell raises the low resonances and the mouthpiece lowers the high ones. [9][8] Our educated guess, not yet measured, is that a kitchen funnel only partly does the bell's job, so the hose's resonances stay off the ideal ratios and the low notes are the hardest to play in tune. The passive test below would settle it. (Every harmonic series is unevenly spaced in pitch; the hose's problem would be mistuning, not spacing.) Hose length changes the pitch.

Even the ideal ladder wobbles: the 7th harmonic sits at about 968.8 cents, roughly 31 cents flat of an equal-tempered minor seventh. [13] Calls still work, largely because your lips bend the pitch, which puts us right back where we started. On a hose, the rungs are more what you'd call guidelines.

Try it yourself, and what Jeremy could measure

Try it yourself (Passive)

• Rig: Palm-slap impulse or small loudspeaker frequency sweep, reference microphone, FFT app.
• Test: Excite the hose without playing (palm-slap over the mouthpiece rim, or a small speaker sweep at the mouthpiece) and record the resonant peaks. Add funnel, record again.
• Confirm: Funnel raises the lowest resonant frequency compared to hose alone.
• Refute: Funnel has no measurable effect on low resonances.
• Note: Played-resonance survey confounded by lip-bending range.

Jeremy could measure (Shop)

• Rig: Reference microphone, tuning software (e.g., Spectrum Analyzer), calipers/cord.
• Test: Measure pitch of open written C4 and 1-2-3 (written F-sharp 3) on a student trumpet. Measure physical tubing lengths of valve loops.
• Confirm: measured loop lengths, combined by the ratio model, predict the 1-2-3 sharpness to within a few cents of a drone-referenced, slides-in reading; expect less than the idealized 53.6 cents if the loops are built long.
• Refute: the measured 1-2-3 offset disagrees with the offset predicted from the measured loop lengths by more than the measurement uncertainty.
• Note: Lab rig (impedance head) required for input impedance curves (Z_in).

Well, actually

• Claim: "Lips act like a clarinet reed."
• Check: Clarinet is inward-striking (pushed closed by pressure); brass lips open (outward/upward). Check Yoshikawa (1995) phase data.
• Claim: "The pedal note is just the fundamental resonance."
• Check: In simulations (Velut et al. 2014, as cited by Mattéoli et al. 2022), a pedal note persists with only the first impedance peak; in the tuba Mattéoli et al. studied, bifurcation analysis ties the pedal to the first acoustic mode. Ghost notes differ by bore expansion (Mattéoli 2022).
• Claim: "Valves are designed perfectly."
• Check: The ideal additive-length model gives 1-2-3 approximately 53.6 cents sharp when each valve alone supplies its exact 12-TET interval; this is not a measured prediction for every trumpet. Compensating systems (Blaikley 1878) exist to mitigate this.

Limits of this research

• What we couldn't find out or measure:
• Calibrated passive input-impedance curves (Z_in) for plain tube vs. full horn (requires wave-separation or capillary impedance rig).
• Phase difference between lip opening area and mouthpiece acoustic pressure across registers (requires transparent mouthpiece + high-speed camera + pressure transducer).
• Who could settle it: UNSW Music Acoustics (Sydney), the BIAS group at the University of Music and Performing Arts Vienna, Edinburgh, or Le Mans (LAUM) for impedance; specialized lab for lip motion.

References

[1] Moore, T. R. (2016). 'The acoustics of brass musical instruments'. Acoustics Today, 12(4), 30–37.

[2] Campbell, M., & Greated, C. (2001). The Musician's Guide to Acoustics. Oxford University Press.

[3] Yoshikawa, S. (1995). 'Acoustical behavior of brass player's lips'. Journal of the Acoustical Society of America, 97(3), 1929-1939.

[4] Newton, M. J., Campbell, M., & Gilbert, J. (2008). 'Mechanical response measurements of real and artificial brass players lips'. Journal of the Acoustical Society of America, 123(1), EL14–EL20.

[5] Boutin, H., Smith, J., & Wolfe, J. (2020). 'Trombone lip mechanics with inertive and compliant loads'. Journal of the Acoustical Society of America, 147, 4133-4144.

[6] Chen, J.-M., Smith, J., & Wolfe, J. (2012). 'Do trumpet players tune resonances of the vocal tract?'. Journal of the Acoustical Society of America, 131(1), 722–727.

[7] Moore, T. R. (2016). 'The acoustics of brass musical instruments'. Acoustics Today, 12(4), 30–37; Wolfe, J. 'Brass instrument (lip reed) acoustics: an introduction', UNSW Music Acoustics.

[8] Backus, J. (1976). 'Input impedance curves for the brass instruments'. Journal of the Acoustical Society of America, 60, 470–480.

[9] Benade, A. H. (1990). Fundamentals of Musical Acoustics. Dover Publications.

[10] PNW Music Series Rule (Jeremy, 2026-10-29).

[11] Mattéoli, R., Gilbert, J., Terrien, S., Dalmont, J.-P., Vergez, C., Maugeais, S., & Brasseur, E. (2022). 'Diversity of ghost notes in tubas, euphoniums and saxhorns'. Acta Acustica, 6, 32.

[12] Velut, L., Vergez, C., Gilbert, J., & Silva, F. (2014). 'Numerical simulation of the production of pedal notes in brass instruments'. Proceedings of the International Symposium on Musical Acoustics (ISMA 2014), Le Mans, France, 295–299.

[13] 'Bugle'. Encyclopædia Britannica, 11th edition (1911), vol. 4.

[14] Monzo, J. (2003). 'Trumpet Intonation'. Tonalsoft.

[15] Myers, A. (2002). 'Brasswind Innovation and Output of Boosey & Co. in the Blaikley Era'. Historic Brass Society Journal, 14, 391–423.

[16] "Tuba". Wikipedia, revision 1382430455 (2026-10-28), sections "Fourth, fifth, and sixth valves" and "Compensating valves". https://en.wikipedia.org/w/index.php?oldid=1382430455 (Tertiary; encyclopedia.)

[17] "Trumpet". Wikipedia, revision 1382388981. https://en.wikipedia.org/w/index.php?oldid=1382388981 (Tertiary; encyclopedia.)

[18] "Brass instrument valve". Wikipedia, revision 1370157540 (2026-08-19). https://en.wikipedia.org/w/index.php?oldid=1370157540 (Tertiary; encyclopedia.)

Dragons ledger

Post	Asterisk	Paid off in	State
1	"Lip reed" is the acousticians' functional term	Section 1	Resolved
1	Which way the lips swing	Section 1	Disputed
2	Ideal cylindrical pipe (odd harmonics)	Section 2	Resolved
2	Backus 1976 curves	Section 2	Resolved
3	Reflection frequency dependence	Section 3	Resolved
3	Lowest resonance out of line	Section 3	Resolved
4	Mouthpiece as Helmholtz	Section 4	Resolved
4	Pedal note mechanism	Section 5	Disputed (minor)
5	1-2-3 sharp ~54 cents	Section 6	Resolved
5	Compensating system	Section 6	Resolved
6	Bugle harmonics 2-6	Section 7	Resolved
6	Funnel is a weak bell	Section 7	Educated guess

Disputed (minor): a live disagreement that is mostly about naming and labeling (Jeremy's read); it doesn't change what a player does. Educated guess: our expectation, untested; the passive test in "Try it yourself" would settle it.

Claim register

Claim (short)	Footnote(s)	Source type	Status
Lips act as pressure-controlled valve	[1]	Primary	Established
Lip swing direction is speculative	[3]	Primary	Speculative
Lips can show outward and inward resonances	[4]	Primary	Disputed
Ideal cylinder has odd harmonics only	[7]	Secondary	Established
Bell and mouthpiece reshape resonances	[8]	Primary	Established
Bell raises low resonances	[9]	Secondary	Established
Material/finish has tiny acoustic, large social effect	[10]	Rule	Established
Mouthpiece lowers high resonances	[8]	Secondary	Established
Pedal note exists on first peak (model)	[12]	Primary	Disputed (minor)
Ghost notes on expanding bores	[11]	Primary	Established
1-2-3 is 53.6 cents sharp (ET)	[14]	Calculation	Established
Fourth valve lowers a perfect fourth (tuba, euphonium, piccolo trumpet)	[16], [17], [18]	Tertiary	Established
Blaikley 4618 is 3-valve only	[15]	Primary	Established
Funnel partially raises low resonances	none	Educated guess	Untested

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Text and original figures: Jeremy Pickett, CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/). Third-party material keeps its own license, credited where it appears.