Bore width of wind instruments

[Enthalpy]

Hello, dear music lovers!

I often read that a broader bore gives wind instruments a mellower sound. This comparison holds for the bugle and tuba versus trumpet and trombone, but I claim it should not be extended to woodwinds, especially not to double reed instruments.

Make your opinion with two bassoons, both playing very well Saint-Saëns' sonata
French system

Heckel system

More artists have played the sonata, and in every case the Heckel bassoon is prompt to become tinny.

The instruments diverged in the 19th century. The French bassoon continued to evolve, but less so than the Heckel system, which was a more radical development from the older instruments. The Heckel system has a broader bore, and its tone holes get wider at the low notes, but it has kept the very long tone holes. The hole system, keyworks and fingerings differ enough to demand re-learning the instrument.

The big drawback of the French bassoon: it isn't loud enough! Insufficient in an orchestra. Julien Hardy luckily played with a civilized pianist. And for a solo over a symphonic orchestra: no chance. So it has but disappeared.

[Enthalpy]

An other bassoonist playing the same sonata on a Heckel system instrument:
https://www.youtube.com/watch?v=joKtwJL1Xq8
He has a softer sound (and plays damn well too). The difference with the narrower French bassoon remains.

[Enthalpy]

The first record of the sonata on a Heckel system bassoon (by Sophie Dartigalongue) was removed from Youtube, but here's one piece of it:

 

[Enthalpy]

A direct comparison of the French (narrower) bassoon and the Heckel system (wider bore):
https://www.youtube.com/watch?v=IIKc_1iCxMQ
this time by the same musician. Very few people play both systems, as both are complicated and they differ enough to fool one.

The video doesn't tell if the musician uses the same reed on both instruments - I suppose he does. Though, the narrower French system would take a smaller reed, which makes the sound softer. Anyway, the conclusion stands.

[Enthalpy]

The full conference about French vs Heckel system bassoons, with exciting commentaries:
f6DgNBHPw9o music begins at 52:10
I'm pretty sure the musician uses for both the same reed, which is too big for the narrower bore of the French system, so the comparison is a bit biassed.

Edited March 9, 2019 by Enthalpy

[Enthalpy]

It's not a bassoon, but an ancestor: the rackett or cervelas had a double reed on a conical bore, and the long bass tube was folded many times to fit in a single compact cylinder.
Rackett
The original instruments belong in museums. Those played today are  often very approximate copies whose users had no professor and usually spent little time learning the instrument, just to play a few notes of ancient music re-enactment. Though, this record has a decent sound, proving that the instrument isn't to blame:
JIy86HTy9oc
The musician hopes to improve the sound after practising.

Edited March 15, 2019 by Enthalpy

[Enthalpy]

I had believed Dr Zubke used some Buffet-Crampon for his comparison with the Heckel system
f6DgNBHPw9o
but it's an Atelier Ducasse bassoon, with significant changes
ateliersducasse.fr

• The bore is narrow, as traditionally on French bassoons.
• The boot got a wide smooth turn. I thought this was standard on recent French bassoons.
• Ducasse proposes the French system or the Heckel on their instruments. Zubke plays the Heckel system on both, no miracle.
• Ducasse uses heavy stiff wood combined with a plastic lining. German systems use maple with lining.

The piece starting at 52:03 climbs to E in treble clef, Zubke too comments at 52:50 that high notes are much easier in the French bassoon due to the narrower bore, and gives examples to 54:06.

I keep open the possible further cause that stiffer wood too helps the high notes, just like grenadilla eases the piccolo's high notes against metal.

A smaller reed made exclusively for the narrower bore would ease the high notes further.

[Enthalpy]

In the first message, the link to (previously Dartigalongue) Sophie Dervaux playing Saint-Saëns' sonata is broken, but here's an other record:
i0M1AIDLX8Y at 39:50
the very caring pianist let the bassoon play at a reasonable volume hence with a softer sound. The difference with the narrower French bassoon played by Julien Hardy remains.

[Enthalpy]

The contraforte has a wider bore than the contrabassoon, wider tone holes, and somewhat different fingerings. Compare on the same piece by the same professional musician, there:
voices.washingtonpost.com

The baritone oboe has a rather narrow bore
jwu8WS5MAvA&t=325
the lupophone too but has wide tone holes
-6gVdShhltg
while the heckelphone has a wider bore
Gxj0OLftfFk&t=30 - Gxj0OLftfFk&t=149 - Gxj0OLftfFk&t=274 - Gxj0OLftfFk&t=324
I wish to hear Katrin Stühle on a baritone oboe.

I disagree that a wider bore gives a mellower sound. The sound is just - wider.

[Enthalpy]

More records of French (narrower) versus German (wider) bassons

French system
Wnz1t7rYKhk (Buffet-Crampon), Marie Boichard (wow, wish more!)
qWA_VZ0q-ug and more (Buffet-Crampon), Jean-Michel Alhaits

German system
Ziry7HpmbXw - ezV5uf_X3gI (luthier unknown), Bálint Mohai
kbDcFWTPfjk - HOkOYSekLBE - OJtZ0aF71N8 (Moosman), KyuSun Pyo
xhh5d1l-wYs - cH0dWWIyK1k at 0:18 - h4uB0Q3Z7lw (Heckel 1937), Judith LeClair
WVQk5qDeEFM - XRXys1vQzvI at 0:38 (Püchner), Sophie Dervaux and Fábio Cury

[Enthalpy]

On 6/12/2020 at 12:17 AM, Enthalpy said:

Marie Boichard (wow, wish more!)

She did it! 😀 Here are more records of French (narrower) bassoons:
MXHwvFqc3Tc (Buffet-Crampon), Marie Boichard
j3DtZkUToxY (Yannick Ducasse), Louise Lapierre
20th century is too recent for some listeners, but the second movement of Jolivet's concert is easier, jump here:
j3DtZkUToxY at 07:22

[Enthalpy]

A wide bore eases low notes, a narrow one high notes. That's quickly checked by sounding a few tubes like a Pan flute. The tenor, bass and contrabass trombones confirm it. Theobald Boehm chose early, as a compromise on the flute's 3 octaves range, the 19mm bore that persists today. Can physics explain this?

The radiation resistance of a small source increases like F², the reactance X of a tube of constant length like F, and the friction and heat loss resistance of the air against the walls like sqrt(F). The Q-factor X/R drops at high and at low frequencies, but do figures match?

R fits P=RI² with I in m³/s rms. I adapted known formulas to a cylinder, not a cone, where I varies as a sine of the position. A woodwind's holes are lossy too, but simplicity lets me neglect them, big error source.

For the flute's lowest C=262Hz, the lambda/2=2L air column is ideally 0.67m long and D=19mm wide. Friction and heat dissipate R=13kohm while a single end radiates negligible 0.4kohm. X=0.12Mohm per lambda/4 provide Q=18 only.

For the flute's high C=2093Hz, the first big open hole is a C at 0.33m or 8 lambda/4 from the ideal blowhole position. The air column does vibrate down to the open G#, F and further, but how strongly? I neglect that, big error source too. A single end would radiate 49kohm, I take 98kohm for both because 2*lambda separation lets them interact little. Friction and heat dissipate 18kohm.

Over the 8 lambda/4, X=9.4Mohm provide decent Q=81, but an other limit appears. If the end of a 100 waves long air column provided no reflection, Q would still be excellent, but the oscillation would be impossible. So I compare with the D=19mm column's 1.5Mohm wave impedance. 49kohm radiation reflect only 0.94* the wave pressure at each end, or 0.88* on a round trip. At G=3136Hz a fifth higher, where emission becomes badly difficult, 108kohm radiation let *0.75 the wave pressure on a round trip, hindering oscillation.

This effect, well studied at brass flares, differs from Q. I define E=Z_c/R where R cumulates the radiative losses, here R~98kohm, then E=15 for the high C on a flute. I would not compare with Q=18 to predict some optimum bore width.

More limits exist: competition with lower resonance modes, and friction losses at the tone holes, which aren't much shorter than lambda/2pi. The adequation of the air column with the blow hole must matter even more at flutes.

==========

The bore D would scale like sqrt(lambda) for instrument family to keep the lowest note's Q.

The alto flute would scale to 22mm, but it's rather 24mm, even 26mm at Boehm's trials. Favouring the alto's role, the low notes, is a good reason. Trying to compensate its inadequate blow hole wouldn't. The piccolo would scale to 12.7mm, but its low notes are sacrificed.

According to sqrt(lambda), the Boehm bass clarinet to written low C scales to 23.2mm, rather 24mm on existing instruments. The contralto scales to 28.4mm and the contrabass to 32.8mm, but both existing instruments have 30mm.

==========

Low instruments have a broader range, as an observation. My explanation is that, once the bore scales like sqrt(lambda) for Q at the low notes, the highest note scales its lambda like the bore to keep E. A tone added to the low range loses only a semitone of the upper range.

So a piccolo flute scaled to 11.3mm bore to play decently down to F# rather than C, a frequency 2.83* higher than the soprano flute, would reach decently up to A rather than C at same difficulty as the soprano flute, and hardly extend beyond C. This resembles the observation.

A Boehm bass clarinet with written low C scaled to 24mm bore would reach notes written 3 semitones higher than the soprano at identical difficulty.

Marc Schaefer, aka Enthalpy

[sethoflagos]

23 hours ago, Enthalpy said:

A wide bore eases low notes, a narrow one high notes. That's quickly checked by sounding a few tubes like a Pan flute. The tenor, bass and contrabass trombones confirm it. Theobald Boehm chose early, as a compromise on the flute's 3 octaves range, the 19mm bore that persists today. Can physics explain this?

To vibrate a reed (or lip) we need to create a periodic displacement - (generally) to permit the flow of air through it.

From Hooke's Law, we know that displacement = force x length / (elasticity x x-section)

Only somewhat loosely, we can equate force / x-section to characterise the gauge pressure required to open the air pathway into the instrument.

Also, we note that force/displacement is the 'stiffness' term in the analysis of simple harmonic motion, which yields the result that natural undamped frequency is proportional to the square root of the stiffness. 

Therefore by adjusting the stiffness of our reeds (or lips), we increase both the pressure required to maintain vibration and the natural frequency of that vibration.

In short, there is a strong correlation between the pressure amplitude and frequency of the air column. And with a higher pressure amplitude the required x-section area is reduced in proportion to achieve any given acoustic intensity.

Hence high-pitched wind instruments tend to feature narrower bores than their lower-pitched relatives.

I've skated over (ignored) a huge amount of fine detail here, but the above line of reasoning summarises the underlying physics as I understand it. Hope this helps. 

 

[Enthalpy]

One can build instruments for the same pitch with varied bore width. Essentially, the range  is smaller when the bore width is inadequate.

The tubax is one example. One of them goes as low as the Eb contrabass saxophone but is a wide as a tenor or baritone.

The mouthpiece and reed must match the instrument. This is commonly done at woodwinds with reeds more or less big and stiff, with mouthpieces more or less open. The instrument's height wouldn't impose the bore through the reed and mouthpiece's dimensions.

[exchemist]

There is an informative, though very long, article here about the physics of organ pipes that may be relevant: https://www.academia.edu/24411933/The_Physics_of_Organ_Pipes

Buried in this is a bit about the effect of width of the pipe. It seems that a wide pipe is effective at resonating for the lower harmonics only, while a narrower one allows higher harmonics to resonate more and thus sounds brighter.

So yes, a softer or mellower tone will be produced by a wider bore, but it may sound rather dull.   

 

[sethoflagos]

As you can probably guess from my avatar (from a 50 year-old newspaper article) my musical activities were (until quite recently) mainly high brass. 

I've a number of Bb trumpets ranging in nominal bore from an 11mm small bore German rotary to a 12.2 mm wide bore Wild Thing; an 11.9mm wide bore C trumpet, and a 12.5mm bass trumpet.

The lowest available musical note available in each of them, for any performer, is set absolutely by the 2nd harmonic of the tubing length. 

The highest pitch available comfortably attainable by any reasonable player is set by the maximum stiffness of their lip. For me, pretty well throughout my playing career, this was a concert high D. This was the case for every instrument I've played over 50+ years (a lot!). Better players than me could usually get a bit higher, some considerably more so. But most serious professionals I've discussed this with (again, a lot) report the same personal experience: they top out at the same pitch on any trumpet irrespective of bore size.

So much for personal testimony.

Technical literature on the influence of bore size on pitch is hard to locate. If there were such then one would expect papers such as ...

An Exploration of Extreme High Notes in Brass Playing (Proceedings of the International Symposium on Music Acoustics (Associated Meeting of the International Congress on Acoustics) 25-31 August 2010, Sydney and Katoomba, Australia (2010) (J. Chick, S. Logie, J. Kemp, M. Campbell, R. Smith)} & Its all in the bore! (Journal of the International Trumpet Guild (USA), 42-45 (May 1988) (R. Smith))

... both available at https://smithwatkins.com/library/technical-papers.html to at least refer to the phenomenon. 

Bore size certainly changes the balance between oral cavity pressure and air volumetric flow for a given pitch and intensity - wide bore instruments trade a higher flowrate for a lower pressure compared to smaller bore instruments. This lower pressure amplitude directly results in lower characteristically 'brassy' distortion in passages that are high and/or loud. Hence they sound relatively 'mellower' which was the thrust of your OP. On that point at least we are agreed.

 

[exchemist]

1 hour ago, sethoflagos said:

As you can probably guess from my avatar (from a 50 year-old newspaper article) my musical activities were (until quite recently) mainly high brass. 

I've a number of Bb trumpets ranging in nominal bore from an 11mm small bore German rotary to a 12.2 mm wide bore Wild Thing; an 11.9mm wide bore C trumpet, and a 12.5mm bass trumpet.

The lowest available musical note available in each of them, for any performer, is set absolutely by the 2nd harmonic of the tubing length. 

The highest pitch available comfortably attainable by any reasonable player is set by the maximum stiffness of their lip. For me, pretty well throughout my playing career, this was a concert high D. This was the case for every instrument I've played over 50+ years (a lot!). Better players than me could usually get a bit higher, some considerably more so. But most serious professionals I've discussed this with (again, a lot) report the same personal experience: they top out at the same pitch on any trumpet irrespective of bore size.

So much for personal testimony.

Technical literature on the influence of bore size on pitch is hard to locate. If there were such then one would expect papers such as ...

An Exploration of Extreme High Notes in Brass Playing (Proceedings of the International Symposium on Music Acoustics (Associated Meeting of the International Congress on Acoustics) 25-31 August 2010, Sydney and Katoomba, Australia (2010) (J. Chick, S. Logie, J. Kemp, M. Campbell, R. Smith)} & Its all in the bore! (Journal of the International Trumpet Guild (USA), 42-45 (May 1988) (R. Smith))

... both available at https://smithwatkins.com/library/technical-papers.html to at least refer to the phenomenon. 

Bore size certainly changes the balance between oral cavity pressure and air volumetric flow for a given pitch and intensity - wide bore instruments trade a higher flowrate for a lower pressure compared to smaller bore instruments. This lower pressure amplitude directly results in lower characteristically 'brassy' distortion in passages that are high and/or loud. Hence they sound relatively 'mellower' which was the thrust of your OP. On that point at least we are agreed.

 

Yes, I agree, I don't think I would expect bore width to affect pitch. As I understand it, that will be a function of tube length, as you say. What the article I linked seems to say is that width affects  the degree to which various harmonics are excited, which alters the character of the tone rather than its pitch. 

[sethoflagos]

1 hour ago, exchemist said:

Yes, I agree, I don't think I would expect bore width to affect pitch. As I understand it, that will be a function of tube length, as you say. What the article I linked seems to say is that width affects  the degree to which various harmonics are excited, which alters the character of the tone rather than its pitch. 

Your point was well taken and agreed with.

Your 'harmonic excitation' = My 'brassy distortion'. 

Different words, same tune.

[sethoflagos]

On 7/18/2017 at 4:29 PM, Enthalpy said:

The big drawback of the French bassoon: it isn't loud enough! Insufficient in an orchestra. Julien Hardy luckily played with a civilized pianist. And for a solo over a symphonic orchestra: no chance. So it has but disappeared.

In the league table of contributory factors leading to the relative 'mellowness' of French bassoons, I'd put this observation high on the leaderboard. Lower acoustic volume gives lower distortion. 

I say 'league table' since the tone quality of a musical instrument is invariably the sum overall effect of many design decisions taken in combination. Because of the complexity of multiple interactions between these factors, and the impossibility of adjusting a single parameter without impacting many others, it is entirely possible, for design differences taken in isolation, to produce apparently counterintuitive results,

Top of the league table, I'd like to suggest playing style. Traditionally French stylistic tastes are quite distinct from traditionally German styles :- a 1930's Besson Brevete trumpet is consequently quite a different beast to a 1920's Heckel (yes, related to the bassoon Heckels!). The Besson was both designed and played to optimise the appeal to French stylistic tastes, and imho, the playing style is the greater influence.

On 3/16/2019 at 2:59 AM, Enthalpy said:

 

• The boot got a wide smooth turn. I thought this was standard on recent French bassoons.

  Bend design is definitely in there. They can act as low-pass filters - but there are exceptions.

On 3/16/2019 at 2:59 AM, Enthalpy said:

 

• Ducasse uses heavy stiff wood combined with a plastic lining. German systems use maple with lining.

Another very good point. Not all the energy of the acoustic wave is inside the air column. A proportion of it is carried in the shell of the instrument causing complex coupling interactions, and this can have a dramatic effect on tone (particularly for the performer!) 

Edited April 9, 2021 by sethoflagos