Three Pipes: what actually makes a woodwind sound like itself

Unit 01 · 31 October 2026 · Acoustics

Same note, three instruments — and a listener behind a curtain can still tell them apart.

By Jeremy Pickett

Abstract

Woodwind register behavior and spectral shape are determined primarily by bore geometry and boundary conditions. Material choice has negligible direct acoustic impact but significant measurable effects on construction, maintenance, valuation, and player perception. The air column inside the instrument is the primary resonator. It selects which frequencies get amplified, depending on whether the tube is cylindrical or conical and whether it is open or closed at the ends. A clarinet overblows at the twelfth because its bore is a closed cylinder, which favors odd harmonics in its impedance spectrum. A saxophone overblows at the octave because its bore is a cone, which supports the full harmonic series despite being closed at the reed. Measured data indicates that wall vibration in standard instruments is typically 37 dB to 48 dB below the radiated sound, making it acoustically negligible for timbre definition. Material choices significantly influence price, durability, and maintenance requirements, but double-blind listening tests have generally failed to identify materials by sound alone when geometry is controlled. Tone holes function as a filter lattice rather than simple length shorteners, establishing a cutoff frequency that determines the passband of the instrument. This essay lays out the physical mechanisms, looks hard at some common teaching simplifications, and proposes experiments whose uncertainty and practicality are still to be worked out.

Why you should care

• Music Teacher: Explains why the register key exists without teaching the "no even harmonics" myth, so overblowing and intonation can be taught accurately.
• Student: Separates "material tone" marketing from playability and durability realities, so money doesn't go to acoustic upgrades that are only perceived.
• Builder: Puts bore profile and tone-hole lattice ahead of exotic wood selection for acoustic stability, and puts resources into geometry and machining tolerances.
• Industry Insider / Reviewer: Provides the specific mechanisms (thermal loss, surface roughness, end correction) where material does interact with acoustics, plus the math for verification.

1. Introduction: The Same Note, Different Voice

Put a flute, a clarinet, and a saxophone behind a curtain and have them play the exact same note. A listener can still tell them apart. That's the fundamental puzzle of woodwind acoustics, and it's the one question this whole essay is chasing. Same pitch means the same fundamental frequency, so the difference has to live in the relative strength of the overtones: the spectral envelope, or timbre.[1] The argument here is that the air column inside the instrument determines that spectral envelope, and the material of the tube walls doesn't.[2]

Each instrument is an oscillator coupled to a resonator. The oscillator is the reed (single or double) or, on the flute, the air jet; the resonator is the air column in the bore.[3] The reed works as a pressure-controlled valve. Feedback from the bore's impedance peaks locks it into a periodic oscillation, and the harmonics of that oscillation are shaped by the coupled reed-bore system.[10]

Post 1 Dragon: Material Matters.

The social post said "material matters far less than you'd think." Here's the longer version. Where a claim is about body material, finish, plating, lacquer, or aging, the material and the finish have a tiny effect on the sound, and a large, measurable effect on how makers, players, techs, and audiences build, play, hear, value, and look after the instrument.[5] Where the material is the vibrating part (a reed, a string, a drumhead, a membrane), it matters acoustically, and the small-body-material-effect generalization doesn't apply. The series rule keeps its emphasis on the human consequences.[1]

How small is the effect on the sound? Measurements of wall vibration in standard commercial woodwinds put the sound radiated directly by the vibrating walls at least 37 dB below the normal radiated sound across all instruments checked, with specific measurements at 48 dB below the normal radiated sound in artificial-blowing conditions.[2] That indicates wall vibration doesn't contribute significantly to the steady-state timbre the audience hears.

How large is the effect on everything else? Start with price. The seven flutes in Widholm's 2001 study, otherwise identical, ran from US $1,000 to $70,000. That's a 2001 figure, not a current market range.[7] Then the upkeep. One maker's care manual warns that a wooden (grenadilla) clarinet body can crack with sudden changes of temperature or humidity, while its ABS-resin models are weather resistant but can deform near heat.[16]

All three make sound the same way: a pressure source drives an air column. What differs is the shape of that column. A clarinet has a cylindrical bore and a saxophone a conical one; a flute's bore is cylindrical too, but it acts acoustically as a pipe open at both ends. Those geometric differences decide which frequencies are supported. "Supported," though, turns out to be a slipperier word than it looks.

2. Resonance vs. Radiation

Does a clarinet produce even harmonics? It sounds like a yes-or-no question. The impedance curve seems to say no, a microphone says yes, and both are reporting something real. The trick is to keep two things apart: the instrument's input impedance peaks (passive resonances) and the sound wave radiated into the room (active radiation). Do that, and the common myth about clarinet harmonics falls over on its own.

2.1 Passive Resonances (Impedance)

Play a low note on a clarinet and the reed opens and closes periodically while the air column reacts to that pressure. The impedance spectrum shows, as peaks, where the column resonates easily. For a cylindrical pipe closed at one end (the reed) and open at the other (the bell), those passive resonances fall at odd multiples of the fundamental frequency: 1f, 3f, 5f, 7f.[8]

The pattern cuts both ways. In a closed cylinder, the impedance maxima (peaks) sit at the odd harmonics, and the impedance minima (anti-resonances) sit at the even ones.[9] That's what people mean when they say the clarinet "favors" odd resonances. Its second resonance is the third harmonic, an octave plus a fifth above the fundamental, and that geometry explains the jump of a twelfth when you overblow.

2.2 Radiated Sound (Harmonics)

So far, so tidy. The trouble is that the sound in the room isn't a copy of the passive impedance spectrum. The reed's motion is nonlinear, so even though the resonances sit at odd frequencies, the reed's nonlinear oscillation generates even harmonics in the radiated sound.[10]

Post 5 Dragon: Clarinet Evens.

The claim that a clarinet has "only odd harmonics" is incorrect. The evens are weak, not missing. In low clarinet notes they're often weaker than their odd neighbors, that contrast fades in the higher registers, and any one harmonic's level still depends on the note and how it's played.[8] In the low register, the even-numbered harmonics are weak, which gives the clarinet its dark, hollow color. The saxophone's cone supports the full series, so more overtones crowd in, and it sounds thick.[11]

"Only odd harmonics" is a sturdy little mumpsimus that outlives its corrections, and it still doesn't hold.[8]

The deeper point: a radiated harmonic level can't be read straight off the input-impedance curve. On low-register (chalumeau) clarinet notes, the second harmonic is present thanks to nonlinear reed clipping, though markedly weaker than the fundamental and third harmonic. Weak, that is, rather than completely absent, as a naive reading of the passive impedance anti-resonance would suggest.[8]

2.3 Nonlinear Generation

If the bore doesn't favor the evens, where do they come from? The reed, acting as a nonlinear valve. That nonlinearity ensures the radiated sound contains a full harmonic series, although the even harmonics are attenuated by the bore's impedance minima.[10] For anyone doing spectral analysis, the distinction matters. The claim that the clarinet lacks even harmonics confuses impedance peaks with radiated partials. It keeps using that word, "harmonics," and the word does not mean what it thinks it means.

Post 5 Dragon: Flute Purity.

The claim that the flute sounds "purer" because it has fewer strong upper overtones needs a qualifier. The flute spectrum depends heavily on dynamics and on the player, and 'timbre' is also attack and transients, not just steady-state overtones.[8]

3. Geometry: Cylinders, Cones, and Boundary Conditions

A clarinetist overblows and lands a twelfth up. A saxophonist makes the same move and lands an octave up. Same move, different result, and the reed isn't the reason. The shape of the tube decides which harmonic series the oscillator gets to work with: three main woodwind types, three sets of boundary conditions.

3.1 The Clarinet: Closed Cylinder

A clarinet bore is effectively closed at the reed end. In the ideal closed–open cylinder, the closed end is a pressure antinode and a node of acoustic volume velocity. Real instruments are messier. A real reed only approximately closes the end, and where the effective open end sits depends on the fingering, with tone holes, bell and radiation all playing a part.[1] In the ideal closed cylinder, the fundamental wavelength is four times the length of the tube (λ = 4L), and the next available resonance is at three times the frequency (3f), a twelfth up.[9]

Post 3 Dragon: Clarinet Closed End.

The claim that the "clarinet cylinder closed at reed favors odd resonances" is accurate for the passive impedance. The reed end is a pressure antinode, not a literal wall. The first step up is the third harmonic, an octave and a fifth.[8]

Post 3 Dragon: Register Key Compromise.

The clarinet does have a register key instead of an octave key, but the mechanism is a compromise: the register vent doubles as the throat B-flat key. On common soprano clarinets, the vent assists second-register playing and also serves as a tone hole for throat B-flat. Debut and colleagues explicitly exclude the B-flat function from their register-hole optimization.[12] The paper gets to leave B-flat out. The clarinet doesn't.

3.2 The Saxophone: Conical Bore

A saxophone has a reed and a closed end, just like a clarinet. So why does it overblow at the octave? Because its bore is a cone, not a cylinder. A cone closed at its narrow end has resonances that line up with the full harmonic series, the same pattern as an open pipe.[9] Oboes and bassoons are conical too, and they overblow the octave as well. The bore shape, not the reed, sets the overblowing interval.[11]

Post 4 Dragon: Truncated Cone.

A real sax is a truncated cone. The mouthpiece volume stands in for the missing tip, and it only works over part of the range; the same goes for oboe and bassoon reeds and staples.[9] A complete theoretical cone would have its vertex at the reed. In practice, the mouthpiece volume adds acoustic length that compensates for the truncation.

3.3 The Flute: Open Cylinder Approximation

The flute is the odd one out. There's no reed at all, and it acts like a pipe open at both ends, so its resonances follow the full harmonic series: 1, 2, 3, 4… The first step up is the octave.[8]

Post 3 Dragon: Flute Embouchure.

The flute's 'open' end is an embouchure hole plus a cork cavity, tuned on purpose. The modern Boehm flute is cylindrical with a tapered head, and the embouchure hole acts as an open end plus an upstream cavity.[13] Where the headjoint cork sits and how the embouchure hole is cut are critical for tuning the effective length.[1]

3.4 End Correction

Measure a tube with a tape and you get its physical length. The air doesn't go by the tape. The air just past the open end joins in the vibration, so the acoustic length runs a little longer than the tube, and the adjustment for that is the end correction.

Post 6 Dragon: Octave Drop.

In the PVC experiment, stopping one end drops the pitch by about an octave, because a closed pipe's fundamental wavelength is twice as long as an open pipe's of the same length.[14] End corrections keep the ratio from landing on exactly 2.0. For a 1 m unflanged cylindrical pipe of 2.00-inch (0.0508 m) internal diameter, Levine and Schwinger's (1948) low-frequency end correction (0.6133a per open end) yields an idealized open-to-stopped fundamental frequency ratio of R = 2(1 + 0.6133×0.0254)/(1 + 1.2266×0.0254) ≈ 1.970, not 1.9 or 2.0.[14]

4. The Cutoff Frequency: The Tone Hole Lattice

So what is actually vibrating inside a woodwind? The air, not the wood. The length of the air column sets the pitch, and every tone hole you open shortens it.[8] That's the standard version, and it's an approximation. In practice, tone holes act as a filter (cutoff frequency), not just length shorteners.[11]

4.1 Tone Hole Lattice

A row of tone holes forms a "lattice," and the lattice behaves differently depending on frequency. Below a certain frequency (the cutoff frequency), the holes act as leaks that shorten the effective length of the tube. Above the lattice's first cutoff, waves can propagate along the open-hole section instead of decaying evanescently. Radiation and losses generally weaken its resonances, but reflection still occurs. Passband, here, means propagation through the lattice.[15]

Post 2 Dragon: Tone Hole Shortening.

The claim that "every tone hole you open shortens it" is the standard approximation. Open tone holes don't cleanly cut the tube; the fuller story runs through the tone-hole lattice, cross-fingerings, and the cutoff frequency (Benade).[11] Cross-fingerings alter the downstream acoustic load and shift resonances by frequency-dependent amounts. Their effects can't be reduced to shortening the tube, or to one universal change in cutoff.[11]

Post 2 Dragon: End Correction.

The claim that "the length of the air column sets the pitch" leaves out the end correction. The air column is acoustically longer than the tube, so the end correction has to be added to the physical length to calculate frequency.[14]

4.2 Local vs. Global Cutoff

Suppose the tone holes don't make a geometrically tidy row. Does the lattice idea survive that? Local cutoff estimates describe single cells of the tone-hole lattice; the measured global cutoff describes the instrument as a whole. Moers and Kergomard show that a geometrically irregular clarinet lattice can still be close to acoustically regular.[15] The drawing can be messy and the acoustics still close to tidy.

5. The Material Question: Wall, Surface, and Human Consequences

If the air column and the tone holes do this much of the work, what's left for the wood? Does a wooden body make a darker sound? Is a gold flute warmer than a silver one? The effect of body material on sound is the most contentious claim in woodwind acoustics, so it gets its own section. The dragon in this one is the belief that material determines tone.

5.1 Wall Vibration and Radiation

How do you measure what the walls alone contribute? Backus's answer in 1964 was to blow a clarinet artificially and absorb the normal radiation from the open holes and bell, leaving the walls to speak for themselves. He reported that the sound radiated by the walls measured about 48 dB below the normal radiated sound at the same location, and that wall radiation was at least 37 dB below normal sound in the instruments he tested.[2]

Claim: Wall vibration negligible (Backus 1964).

Status: Established (for steady-state radiated sound).

Caveat: Backus's numerical findings concern setup-specific radiated sound, not a universal mechanical-vibration or audibility threshold.

5.2 Surface Dissipation

That doesn't make wood acoustically inert. The inside surface does something measurable: surface finish and porosity do affect acoustic attenuation. Boutin et al. (2017) measured acoustic dissipation in wooden pipes and ranked it, from largest attenuation factor to smallest, as maple, boxwood, pear wood, and African Blackwood, both before and after internal bore polishing.[6]

Claim: Surface finish/porosity affects dissipation (Boutin 2017).

Status: Established (for attenuation factors).

Caveat: Boutin measures dissipation without demonstrating the asserted playability consequences. The link to "audible playability" remains a proposal requiring controlled perceptual testing.

5.3 Blind Tests and Perception

Then there's the test everyone actually wants: can people hear it? Coltman (1971) had flutes made of silver, copper and wood, in different wall thicknesses, and found no evidence that experienced listeners or trained players could tell them apart.[4] Thirty years later Widholm and colleagues tried again, with seven otherwise identical Muramatsu flutes that differed only in wall material, from silver-plated to platinum. They ran double-blind tests with 15 experienced professional flutists, and no flute was identified correctly. The best score was 22%, for the 24-karat gold flute. The material made differences that were "just measurable but not perceivable" (under 0.5 dB in sound color), while the differences between players were large.[7] The flutes differed less than the flutists did.

Claim: Widholm and colleagues did not establish reliable identification of flute material in their reported tests.

Status: Supported for the tested instruments and protocol; not a universal impossibility result.

Caveat: The commercial instruments were not strictly geometry-matched, so the study does not isolate material alone.

Caveat: Confounds material with manufacturing variance; hard to isolate in blind tests.

5.4 Human Consequences

None of that makes material unimportant. For ordinary woodwind bodies, material and finish generally have small direct acoustic effects, while their practical and human consequences can be large. Matching the bore geometry doesn't by itself establish matching acoustic losses, or that listeners can't tell them apart.[5]

• Price: In the 2001 study the seven flutes ran from US $1,000 to $70,000, and listeners could not reliably tell them apart. The mean dynamic range differed by 1.5 dB between the flutes with the smallest and largest range, a gap the authors say could vanish with more players.[7]
• Maintenance: Wooden clarinet bodies require precautions against abrupt temperature and humidity changes that can cause cracking or joint problems. Yamaha describes its ABS-resin models as weather resistant, not immune to damage. Source: Yamaha Clarinet Owner's Manual; manufacturer with a commercial interest.
• Repair: Repairability depends on the material, construction, and specific damage. This essay has not established a general metal-versus-wood repairability ranking.

Post 1 Dragon: Material and Finish.

Where a claim is about body material, finish, plating, lacquer, or aging, the essay says that the material and the finish have a tiny effect on the sound, and a large, measurable effect on how makers, players, techs, and audiences build, play, hear, value, and look after the instrument.[5]

6. The Bench Experiment: PVC and the Missing Octave

Want to check the end correction yourself? You need a meter of PVC pipe, a tuner, and a hand to stop one end. Here is a reproducible bench experiment for it.

Post 6 Dragon: Pitch Drop.

The claim that "the pitch drops by about an octave" is true, but the ratio is ~1.97x due to unequal end corrections (Levine & Schwinger).[14]

6.1 Method

1. Rig: 1m PVC pipe (verify internal diameter), digital tuner (phone app), mic for spectrum.
2. Measurement: Measure frequency of open-open tube (f_open). Measure frequency of open-closed tube (f_closed) by stopping one end with a palm or cap.
3. Calculation: Calculate Ratio R = f_open / f_closed.
4. Verification: Compare R with the prediction from the measured length L and radius a = D/2, where D is the measured internal diameter.

6.2 Theoretical Baseline

For a 1 m unflanged cylindrical pipe of 2.00-inch (0.0508 m) internal diameter, the internal radius a = 0.0254 m.

Levine and Schwinger (1948) end correction is 0.6133a.

Open-Open Effective Length L_{eff, open} = L + 2(0.6133a).

Open-Closed Effective Length L_{eff, closed} = L + 0.6133a.

Frequency is inversely proportional to length (f ∝ 1/L).

Ratio R = 2L_{eff, closed} / L_{eff, open}.

An open-open pipe has fundamental wavelength λ_open = 2 L_eff,open with two open-end corrections (L_eff,open = L + 2 × 0.6133a). A pipe stopped at one end has λ_closed = 4 L_eff,closed with only one open-end correction (L_eff,closed = L + 0.6133a). Their fundamental frequencies are therefore f_open = c / (2 L_eff,open) and f_closed = c / (4 L_eff,closed), and the open-to-stopped frequency ratio is:

Substituting L = 1 m and a = 0.0254 m gives:

6.3 Uncertainty

The model predicts a ratio of 1.970, which is 1200 log₂(1.970/2) ≈ −26 cents from an octave. (A tuner that only reads to the nearest note can't tell the difference.) So before reading anything into agreement or disagreement, report the uncertainty in the frequency estimates, the spread across repeated trials, the dimensional tolerances and the boundary conditions. None of those numbers exist yet.

7. Conclusion: The Instrument as a System

Back to the curtain: same note, three instruments, and a listener who can tell them apart. What was the listener hearing? No single factor explains everything, but the hierarchy is clear. Geometry matters most, then the reed and the player, then the material.

• Geometry: Determines resonance series (cylinder/closed=12th, cone/closed=octave).
• Player: Nonlinear excitation generates harmonics (evens and odds).
• Material: Affects durability, price, and minor dissipation factors, but not the primary timbre.

Every dragon in the social posts has a full story, and each of those stories is grounded in acoustic physics. The air column is the instrument. The material is the casing. It can be a lovely casing; it just isn't the one doing the singing.

Try it yourself

1. PVC End Correction Verification

• What: Measure frequency of open-open tube, then stop one end. Calculate ratio.
• Rig: 1m PVC pipe (verify internal diameter), digital tuner (phone app), mic for spectrum.
• Confirm: Ratio ~1.97 (within uncertainty of boundary conditions).
• Test of the model: A reproducible ratio inconsistent with the prediction, after accounting for measurement uncertainty, challenges the model's applicability to this setup. Investigate the boundary assumptions and measurement method rather than declaring the result erroneous in advance.
• Jeremy: Measure internal diameter with calipers; report uncertainty.

2. Spectrum Analysis (Clarinet vs. Sax)

• What: Record clarinet and sax at the same sounding pitch, stating each instrument's written note and fingering; repeat at several pitches and dynamics. FFT plot.
• Rig: Portable recorder, reference mic, spectrum software.
• Confirm: On a low-register clarinet note (e.g., written E3), the 2nd harmonic is well below the 3rd; on a clarion note (e.g., written G5) the 2nd harmonic is relatively stronger; the sax shows a strong 2nd harmonic throughout.
• Jeremy: Document mouthpiece/reed, room, gain settings.

3. Material Comparison (Blind)

• What: Record identical notes from two instruments (same make/model, different material if available).
• Rig: Repeated, randomized recordings, saying exactly who is blind to which instrument is which. Measure geometry, setup and each instrument's own variability; use several instruments per material before claiming anything about the material.
• Analysis: Fix the spectral measures and the statistics in advance, from pilot repeatability data. Test audibility separately, with listeners. No 1 dB or 3 dB threshold is established here.
• Jeremy: Label this "Proposed" unless instrument access is verified.

Well, actually

• Myth: "Clarinets have no even harmonics."
• Check: Real clarinet spectra commonly contain even harmonics. The approximately odd-multiple resonance pattern is a useful low-frequency model, not an exact description of every resonance or played note.
• Myth: "Material determines tone."
• Check: Backus (1964) shows wall radiation is too weak to be the source of timbre differences.
• Myth: "Stopping one end of a pipe drops it exactly an octave."
• Check: End corrections make the open/stopped ratio ~1.97 for an idealized 1 m, 2-inch pipe; overblown-register intervals on real instruments are a separate question (e.g., slightly wide low twelfths on clarinet, Debut et al.).

Limits of this research

• Vocal Tract: In normal playing, amateurs and experts alike keep their vocal-tract resonances moderate and don't tune them to the note. Expert saxophonists playing altissimo tune a strong tract resonance to the note they want, and clarinettists bending pitch in the clarion register steer it with a tract resonance as strong as the bore's own.[3]
• Artificial Blowing: An artificial mouth improves repeatability for the conditions it's set to, but its settings and limits have to be documented. Questions about playing and perception still need human players and listeners.
• Human Consequences: While dissipation is measurable (Boutin), the link to "audible playability" remains a proposal requiring controlled perceptual testing.
• Material Access: Matched geometry instruments (different materials) are rare; commercial comparisons often conflate material with build quality.
• Scope: The proposed experiment's feasibility, equipment availability, cost, and uncertainty remain undocumented. A specified protocol, verified inventory or access arrangements, and a budget would settle these practical questions.
• Rights: The precise rights status of each proposed illustration remains asset-specific. Inspect the original figure, any exception to Euphonics's default license, the proposed redraw, and the intended use before declaring it cleared.

References

[1] Fletcher, N. H., & Rossing, T. D. (1998). "The Physics of Musical Instruments". Springer. (Secondary; Standard Text).

[2] Backus, J. (1964). "Effect of Wall Material on the Steady-State Tone Quality of Woodwind Instruments." J. Acoust. Soc. Am., 36(10), 1881–1887. DOI: 10.1121/1.1919286. (Primary; Acoustic Measurement).

[3] Chen, J.-M., Smith, J., & Wolfe, J. (2010). "How players use their vocal tracts in advanced clarinet and saxophone performance." Proc. International Symposium on Music Acoustics (ISMA 2010), Sydney. (Primary; Human Interaction).

[4] Coltman, J. W. (1971). "Effect of Material on Flute Tone Quality." J. Acoust. Soc. Am., 49(2B), 520–523. DOI: 10.1121/1.1912381. (Primary; Excitation).

[5] Pickett, J. (2026-10-29). "Material and Finish Series Rule." pnwmusic.com (Internal). (Primary; Series Rule).

[6] Boutin, L., et al. (2017). "Acoustic dissipation in wooden pipes." J. Acoust. Soc. Am., 141, 2840. (Primary; Material Dissipation).

[7] Widholm, G., Linortner, R., Kausel, W., & Bertsch, M. (2001). "Silver, gold, platinum – and the sound of the flute." Proc. ISMA 2001, Perugia. Author's copy: https://www.widholm.at/wp-content/uploads/2021/01/2001_Silver__gold__platinum___and_the_sound_of_the_flute.pdf. (Primary; Blind Test).

[8] UNSW (Phys Acoustics Group). "Clarinet Acoustics." phys.unsw.edu.au/jw/clarinetacoustics.html. (Secondary; Educational Summary).

[9] Woodhouse, J. "Euphonics." euphonics.org. (CC BY-NC-SA 4.0; Redraw from equations only).

[10] Woodhouse, J. "11.3 Reed instruments." Euphonics. (Secondary; Internal pressure spectra and radiated harmonics).

[11] Benade, A. H. (1990). "Fundamentals of Musical Acoustics". Dover. (Secondary; Standard Text).

[12] Debut, V., Kergomard, J., & Laloë, F. (2005). "Analysis and optimisation of the tuning of the twelfths for a clarinet resonator." Applied Acoustics, 66(4), 365–409 (arXiv:physics/0309051, 2003). (Primary; Register Key Design).

[13] Benade, A. H., & French, J. W. (1965). "Analysis of the Flute Head Joint." J. Acoust. Soc. Am., 37(4), 679–691. DOI: 10.1121/1.1909393. (Primary; Flute Headjoint Acoustics).

[14] Levine, H., & Schwinger, J. (1948). "On the Radiation of Sound from an Unflanged Circular Pipe." Phys. Rev., 73, 383. (Primary; End Correction).

[15] Moers, E., & Kergomard, J. (2011). "On the cutoff frequency of clarinet-like instruments. Geometrical versus acoustical regularity." arXiv:1101.4742 (Primary; Tone Hole Lattice).

[16] Yamaha Corporation. Clarinet Owner's Manual, "Precautions" and care sections. Manufacturer's care manual (commercial source). https://usa.yamaha.com/files/download/other_assets/0/335910/clarinet_en_om_b0.pdf

Dragons ledger

Post	Simplified Phrase	Full Story (Tagged)	Section	State
1	"Material matters far less than you'd think"	Wall vibration negligible (Backus 1964); surface finish affects dissipation (Boutin 2017); human consequences large (price/maintenance).	Section 5	Resolved (Nuanced)
2	"The length of the air column sets the pitch"	Physical length + end correction sets effective length (Levine & Schwinger); tone-hole lattice creates cutoff (Benade).	Section 4	Resolved
2	"Every tone hole you open shortens it"	Shortening is approximation; opening changes impedance curve and leakage (Moers & Kergomard 2011).	Section 4	Resolved
3	"Flute acts like a pipe open at both ends"	Modern Boehm flute is cylindrical with tapered head; embouchure hole acts as open end + upstream cavity.	Section 3	Resolved
3	"Clarinet cylinder closed at reed favors odd resonances"	Resonances favor odd multiples in low register; radiated sound contains evens (nonlinear reed).	Section 2	Resolved
4	"Cone closed at narrow end lines up with full harmonic series"	True for complete cones; real instruments are truncated (mouthpiece compensates) at low frequency.	Section 3	Resolved
5	"Clarinet evens are weak, sax sounds thick"	Clarinet even harmonics weak below cutoff, strong above; flute spectrum dynamic dependent.	Section 2	Resolved
6	"Pitch drops by about an octave"	Drop is ~1.97x ratio due to unequal end corrections (Levine & Schwinger).	Section 6	Resolved

Claim register

Claim (Short)	Footnote(s)	Source Type	Status
Air is primary resonator	[3]	Primary	Established
Wall vibration negligible	[2]	Primary	Established
Clarinet overblows 12th	[8]	Secondary	Established
Sax overblows octave	[9], [11]	Secondary	Established
Wall radiation 37-48 dB below	[2]	Primary	Established
Radiated sound contains even harmonics	[10], [8], [10]	Primary/Secondary	Established
Tone holes act as filter lattice	[15], [11]	Primary/Secondary	Established
End correction ratio ~1.970	[14]	Primary	Established
Material identity in blind tests	[7]	Primary	Established
Material affects price/maintenance	[7], [16]	Primary/Secondary	Established
Flute embouchure + cork cavity	[13], [1]	Primary/Secondary	Established
Clarinet register key / B-flat	[12]	Primary	Established
PVC ratio 1.970 calculation	[14]	Primary	Established
Widholm et al. (2001) report 15 listening-test participants, 111 opinion-survey respondents, with an abstract discrepancy noting 110 testpersons	[7]	Primary	Established
Nonlinear reed motion	[10]	Primary	Established
Truncated cone compensation	[9]	Secondary	Established
Dissipation factors by wood type	[6]	Primary	Established
Human consequences of material	[5]	Editorial policy (PNW Music has an interest in this framing)	Each consequence needs its own source
Limits: Vocal tract involvement	[3]	Primary	Established
Limits: Material access/variability	none (editorial)	Unknown	Open
Limits: Rights status of figures	none (editorial)	Unknown	Open

---

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.