How closely do main slide positions (room temperatures) line up with predictions (based on physics calculations)?

[bloke]

I'm noticing (although I'm a flawed human, and human observations OFTEN are FAR from totally accurate) that - with my very large bore 6/4 BB-flat tuba - the "A=440" position for my main slide (68° F. ROOM TEMPERATURE tuba/air column - ie. "cold" - "at first playing") is about 1/8th-inch out, compared to ( 76° F. ROOM TEMPERATURE, but the tuba is WELL WARMED UP...ie...WELL INTO a practice session) is about 1-and-1/8" out...so at least an inch (TWO inches of actual LENGTH - being a slide) of difference in "pull".

(When I first owned this tuba, I actually had to SHORTEN the instrument to get the main slide WITHIN this range, for my personal use and "the way that I blow")...

...so I've given TWO double-factor extremes:

(taking away the above "wordiness" for - hopefully - more clarity)

1/ tuba and it's air column are COLD, and the room is only heated to 68° F.
2/ tuba and it's air column are PLAYER WARMED UP, and the room is cooled down to 76° F.

...How closely does that (2 inches of difference in length) line up with any physical (ie. physics) predictions...and are there TOO MANY factors here to predict?

[gocsick]

I don't have an answer, but at a conference I asked a colleague who specializes in non-linear acoustics a similar question. The answer was "dunno, conical instruments are hard" and pointed me to this book

Campbell, M., Gilbert, J. and Myers, A., 2021. The science of brass instruments (Vol. 436). Switzerland: Springer.



My question was about how is it possible for me and my son to need to move slides to both play in tune on the same horn/mouthpiece combination.

[peterbas]

.

[bloke]

I knew there had to be more factors than just two or three.
Thnx

[arpthark]

I don't have an answer, but at a conference I asked a colleague who specializes in non-linear acoustics a similar question. The answer was "dunno, conical instruments are hard" and pointed me to this book

Campbell, M., Gilbert, J. and Myers, A., 2021. The science of brass instruments (Vol. 436). Switzerland: Springer.



My question was about how is it possible for me and my son to need to move slides to both play in tune on the same horn/mouthpiece combination.

I work for a library and just noticed this is available to us as an e-book. I can't post due to copyright laws, but it is interesting with quite a bit of data. Here are some chapter headings:

Part I The Musician’s Experience and the Scientific Perspective
1 The Musician’s Experience of Brass Instruments........................ 3
1.1 Creating Music from Lip Vibration: Labrosones Through the Ages . 3
1.1.1 Labrosones from Found Objects.............................. 4
1.1.2 Early Metal Labrosones....................................... 6
1.1.3 Labrosones in Renaissance and Baroque Music ............. 9
1.1.4 The Nineteenth-Century Labrosone Revolution ............. 12
1.2 The Musician’s Interpretation of the Brass Playing Experience ...... 13
1.2.1 Musical Pitch Notation ........................................ 13
1.2.2 Natural Notes and Harmonics: The Musician’s View ....... 14
1.2.3 Nominal Pitches of Brass Instruments ....................... 15
1.2.4 Compass ....................................................... 16
1.2.5 Intonation Control ............................................. 17
1.2.6 Dynamic Range................................................ 20
1.2.7 Timbre ......................................................... 20
1.2.8 Blowing Pressure and Air Flow .............................. 21
1.2.9 Resistance and Playing Effort ................................ 22
1.2.10 Responsiveness and Rapid Articulation ...................... 23
1.2.11 Wrap, Directivity and Ergonomics ........................... 24
1.3 Subjective and Objective Evaluation of Brass Instrument Quality ... 25
1.3.1 Sound Quality and Playability ................................ 26
1.3.2 Descriptive Terms Used by Musicians to Describe
Brass Instrument Behaviour .................................. 27
1.3.3 Biases in Quality Evaluation of Musical Instruments ....... 28

2 The Scientist’s Perspective on Brass Instrument Behaviour ............ 31
2.1 Scientific Measurements of Brass Instrument Behaviour ............. 31
2.1.1 Sound Radiated from a Brass Instrument .................... 33
2.1.2 Sound Measured Inside a Trombone Mouthpiece ........... 36
2.1.3 Pressure Measured Inside a Brass Player’s Mouth........... 38
2.1.4 Lip Vibration and Air Flow: The Valve Effect Sound Source 41
2.1.5 Is Air Flow Through the Instrument Tube Important?....... 43
2.1.6 Is Sound Radiation from the Vibrating Bell Important? ..... 44
2.1.7 Warming Up a Brass Instrument.............................. 46
2.2 An Approach to Modelling Brass Instruments ........................ 47
2.2.1 The Scientific Case for Simplified Models................... 48
2.2.2 Coupled Systems and Feedback Loops....................... 50
2.2.3 Natural Notes and Harmonics: The Scientific View ......... 52
2.2.4 Self-Sustained Oscillations ................................... 57
2.2.5 The Wind Instrument Paradox ................................ 58

Part II Acoustical Modelling of Brasswinds
3 Buzzing Lips: Sound Generation in Brass Instruments ................. 63
3.1 The Nature of Lip Vibration ............................................ 63
3.1.1 The Brass Player’s Embouchure .............................. 63
3.1.2 Experimental Studies of Vibrating Lips ...................... 65
3.1.3 Time Dependence of the Lip Opening Area ................. 66
3.1.4 The Lip Opening Area-Height Function ..................... 70
3.1.5 Two-Dimensional Motion of the Brass Player’s Lips........ 72
3.1.6 Experiments with Artificial Lips.............................. 76
3.2 An Equation of Motion for the Lips.................................... 79
3.2.1 A One-Mass Model of the Lips............................... 79
3.2.2 The Sliding Door Lip Model.................................. 81
3.2.3 The Swinging Door Lip Model ............................... 83
3.2.4 Inward-Striking and Outward-Striking Reeds ............... 85
3.3 The Mechanical Response of the Vibrating Lips ...................... 89
3.3.1 Resonances of Artificial Lips ................................. 89
3.3.2 Resonances of Human Lips ................................... 91
3.4 Why Do the Lips Buzz? ................................................ 93
3.5 Volume Flow in Buzzing Lips.......................................... 96
3.5.1 Acoustic Volume Flow Through the Lip Aperture........... 96
3.5.2 Acoustic Volume Flow Equation ............................. 98

4 After the Lips: Acoustic Resonances and Radiation ..................... 101
4.1 Internal Sounds in Brass Instruments .................................. 101
4.1.1 Lumped and Distributed Resonators ......................... 102
4.1.2 Travelling Waves .............................................. 104
4.1.3 Standing Waves................................................ 109
4.1.4 Frequency Domain and Time Domain ....................... 112
4.1.5 Impulse Response and Reflection Function .................. 114
4.1.6 Input Impedance ............................................... 116
4.2 Measuring Input Impedance ............................................ 120
4.2.1 Capillary-Based Methods ..................................... 120
4.2.2 Complementary Cavity Methods ............................. 123
4.2.3 Wave Separation Methods .................................... 123
4.2.4 Acoustic Pulse Reflectometry................................. 125
Contents xiii
4.3 Bore Profiles of Brass Instruments ..................................... 126
4.3.1 Different Parts of the Bore .................................... 126
4.3.2 Cylindrical Tubes.............................................. 128
4.3.3 Conical Tubes ................................................. 132
4.3.4 Equivalent Fundamental Pitch and Equivalent Cone Length 136
4.3.5 The Mouthpiece as a Helmholtz Resonator .................. 138
4.3.6 Mouthpiece Effects on Intonation and Timbre ............... 142
4.3.7 Sound Waves in Flaring Bells................................. 147
4.3.8 A Theoretical Example: The Bessel Horn.................... 150
4.3.9 A Practical Example: The Complete Trombone ............. 155
4.3.10 Instruments with Predominantly Expanding Bore Profiles.. 157
4.4 Toneholes................................................................ 159
4.5 Mutes .................................................................... 164
4.5.1 Straight Mutes ................................................. 165
4.5.2 Effects of Internal Resonances in the Straight Mute ......... 167
4.5.3 Harmon Mute .................................................. 170
4.5.4 Plunger and Cup Mutes ....................................... 172
4.5.5 Transposing Mutes ............................................ 174
4.5.6 Hand Technique on the Horn ................................. 178
4.6 Radiation of Sound from Brass Instruments........................... 179
4.6.1 Near Field and Far Field ...................................... 180
4.6.2 Monopole Radiation........................................... 181
4.6.3 Transition from Internal to External Sound Fields........... 183
4.6.4 Mapping the Radiation Fields of Brass Instruments......... 185
4.6.5 Visualising Wavefronts with Schlieren Optics ............... 187
4.6.6 Far Field Directivity in Brass Instruments ................... 191
4.7 Going Further: Calculating Input Impedance .......................... 197
4.7.1 Analytical Calculations ....................................... 197
4.7.2 Lossless Plane Wave TMM Calculations..................... 200
4.7.3 Including Losses in TMM Calculations ...................... 203
4.7.4 TMM with Non-Cylindrical Elements ....................... 205
4.7.5 Radiation Impedance .......................................... 207
4.7.6 Multimodal Calculations...................................... 209
4.7.7 Bends in Brass Instruments ................................... 212
4.8 Going Further: The Wogram Sum Function ........................... 214

5 Blow That Horn: An Elementary Model of Brass Playing ............. 217
5.1 The Three Equations of the Brass Instrument Model ................. 218
5.1.1 The First Constituent Equation: Lip Dynamics .............. 220
5.1.2 The Second Constituent Equation: Flow Conditions ........ 221
5.1.3 The Third Constituent Equation: Instrument Acoustics ..... 222
5.2 Crossing the Threshold: Small Amplitude Oscillating Solutions..... 222
5.2.1 Phase Relationships in the Lip Valve ......................... 223
5.2.2 Silence or Sound? Stability Analysis of Brass Instruments . 228
5.3 Beyond Pianissimo: Modelling Realistic Playing Amplitudes........ 232
5.3.1 Analysis of Brass Performance Using Simulations.......... 233
5.3.2 Bifurcation Diagrams ......................................... 237
5.4 Going Further: From Linear Stability Analysis to Oscillation
Regimes ................................................................. 240
5.4.1 Introduction: A Van der Pol Self-Sustained Oscillator ...... 241
5.4.2 State-Space Representations of the Elementary Brass
Playing Model ................................................. 246
5.4.3 Linear Stability Analysis Applied to Brass Instruments..... 251
5.4.4 The Trombone Pedal Note Regime ........................... 255
5.4.5 Bifurcation Diagrams of Reed and Brass Instruments....... 257
5.4.6 Multiphonics................................................... 264

6 Shocks and Surprises: Refining the Elementary Model ................. 271
6.1 Why Brass Instruments Sound Brassy ................................. 271
6.1.1 Brassy Sounds in Music....................................... 272
6.1.2 Experimental Evidence for Shock Waves in Brass
Instruments .................................................... 274
6.1.3 To Infinity and Beyond: Nonlinear Propagation in Tubes ... 276
6.1.4 The Brassiness Potential Parameter .......................... 280
6.1.5 Elephants, Exhausts and Angels: Some Surprising
Sources of Brassy Sounds..................................... 285
6.2 Going Further: Nonlinear Propagation ................................. 287
6.2.1 From the Fundamental Fluid Dynamic Equations to
the Nonlinear Wave Propagation Equation................... 288
6.2.2 The Burgers Equations ........................................ 291
6.2.3 Brassiness of Flaring Bells.................................... 294
6.3 The Player’s Windway .................................................. 296
6.3.1 Coupling of Upstream and Downstream Resonances ....... 296
6.3.2 Tuning of Windway Impedance Peaks ....................... 298
6.3.3 Other Effects of the Player’s Windway....................... 299
6.3.4 Respiratory Control ........................................... 301
6.4 Improving the Lip Model ............................................... 302
6.4.1 Evidence from Mechanical Response Measurements ....... 302
6.4.2 Evidence from Measurements of Threshold Playing
Parameters ..................................................... 303
6.4.3 Models with More Than One Degree of Freedom ........... 308
6.5 Playing Frequencies of Brass Instruments ............................. 308
6.6 The Influence of Wall Material on Brass Instrument Performance ... 311
6.6.1 Factors Affecting the Choice of Wall Material............... 312
6.6.2 Experimental Studies of Brass Instrument Wall Vibrations . 312
6.6.3 Pathological Wall Vibration Effects in Wind Instruments... 316
6.6.4 Frequency-Localised and Broadband Effects of
Structural Resonances in Brass Instruments ................. 317
6.6.5 Mechanical Vibration at the Lip-Mouthpiece Interface ..... 325
6.7 Going Further: Analytical Modelling of Vibroacoustic
Coupling in Ducts....................................................... 326
6.7.1 Basic Vibroacoustic Theory................................... 327
6.7.2 Effect of Vibroacoustic Coupling on Input Impedance ...... 329
6.7.3 Some Experimental Tests of Vibroacoustic Modelling ...... 332

Part III Historical Evolution and Taxonomy of Brass Instruments
7 The Amazing Diversity of Brass Instruments............................. 337
7.1 What Are Important Features of Brass Instruments? .................. 337
7.1.1 Taxonomic Labels Based on Tube Length ................... 338
7.1.2 Bore Profile and Brassiness ................................... 339
7.2 The Different Kinds of Brass Instrument .............................. 340
7.2.1 Instruments with the Shortest Tube Lengths ................. 342
7.2.2 Instruments with Very Short Tube Lengths in C and B ..... 343
7.2.3 Instruments with Short Tube Lengths in G, F, E and D .... 345
7.2.4 Instruments with Short Tube Lengths in C and B ........... 349
7.2.5 Instruments with Medium Tube Lengths in G, F, E and D . 351
7.2.6 Instruments with Long Tube Lengths in C and B ........... 355
7.2.7 Instruments with Long Tube Lengths in G, F, E and D..... 359
7.2.8 Instruments with Very Long Tube Lengths in C and B ..... 364
7.2.9 Instruments with Very Long Tube Lengths in G, F, E
and D........................................................... 365
7.3 Families.................................................................. 366
7.4 Mouthpieces............................................................. 369
7.5 Going Further: Trumpets and Cornets—Are They Different? ........ 371
7.6 Going Further: Alternative Taxonomies ............................... 374
7.7 Going Further: Mouthpiece Parameters................................ 375
7.8 Going Further: The Bass Brass Instruments of Berlioz ............... 378
7.8.1 The Trombone ................................................. 380
7.8.2 The Serpent .................................................... 382
7.8.3 The Ophicleide ................................................ 385
7.8.4 The Bass Tuba ................................................. 386
7.8.5 Berlioz and Pedal Notes....................................... 388

8 How Brass Instruments Are Made ......................................... 391
8.1 Materials................................................................. 391
8.2 Design ................................................................... 392
8.3 Metal Forming .......................................................... 393
8.4 Valves.................................................................... 396
8.5 Assembly ................................................................ 398

9 Looking Back and Looking Forward ...................................... 401
9.1 Brass Instruments in the Ancient World ............................... 402
9.1.1 Etruscan Cornu and Lituus.................................... 402
9.1.2 The Celtic Carnyx ............................................. 405
9.2 Brass Instruments in the Digital World ................................ 408
9.2.1 Optimisation in Instrument Design ........................... 409
9.2.2 Modification of Instruments Using Active Control .......... 411
9.2.3 Live Electronics and Augmented Instruments ............... 413

[peterbas]

.

[bloke]

In the past, trial and error worked for some makers, luck worked for others, and - lately, it seems - the combination of those - along with some acoustical technology (LOL and complete copying) - has worked out.

Those who aren't as particular buy the models which aren't particularly good...and everyone's happy.

yeah...different topic, but so what?


me...??
I'm experimenting (trial and error plus gained knowledge from past trial-and-error) to see if I might be able to come up with a "helleberg" style mouthpiece that I myself might use on certain types/models of instruments. Some others (and I'm really grateful) are willing to follow me down the path.
I'm hoping (with the next version) I might arrive there.
Others (I'm hoping, as they purchased them) are hopefully happy with previous versions.

[peterbas]

.

[bloke]

We tend to be rather arrogant too our ancestors at the knowledge level or lack thereof.
But a lot of acoustics laws where discovered in the 1600 and 1700 with Galileo, Newton...

I wouldn't argue with that...but I'm comparing my 5450 (which I sold, but was a fine playable-in-tune instrument to its predecessor, the 2155 (rotary), which was wretched, and my jumbo Miraphone model 98 (which can be played easily in tune - and spot-on in tune with some #1 slide manipulation - and all with "beginner book" charts' valve combinations) to previous models of kaiser tubas which (as with the 2155R) ofter(ed) wretched intonation. I have no understanding of formulas (quite obviously, recently developed) which offer "least bad/best of the worst" - etc. - intonation characteristics of expanding tubes, but I'm damned thankful for them. Maybe (??) Gebr. Alex., Cerveny, et al should have met up with Galileo, Newton, et al, way before they apparently did.

Looking at it from a different perspective, take a look at my F tuba ("mash buttons and blow", no slide-pulling, barn-door-wide "slots"...built in a dirt-floor building in Communist East Germany)...They didn't have any tricky formulas, and none of their other models played anywhere close to as in-tune (and no F tuba made today plays any better in tune)...thus me clinging to offering a tremendous amount of credit to "trial-and-error" (English term meaning, "I wonder what would happen if we - specifically - changed this aspect?"...though I suspect you're familiar, as your English is so excellent.)

me...??
I'm so dumb, that (today, when practicing on the model 98) I started noticing that tuning "just wasn't working out" (sharp/sharper/sharpest) UNTIL I realized actually HOW far I had to move my main slide OUT to compensate for "well into spring" temperatures with me (the cheapskate) NOT turning on the air-conditioning.

[Mary Ann]

"My question was about how is it possible for me and my son to need to move slides to both play in tune on the same horn/mouthpiece combination."

Since no one addressed this -- On my (French) horn, pre-and post-dystonia embouchure / air: post-, the slide is all the way in almost all the time, and I have some trouble at times getting up to pitch. Pre-, the slide was always out somewhat, and I never struggled to get up to pitch. It is a difference in my use of air -- before, I was "more chops and less air," and after, I am "more air and less chops." My tone was never bad, but "after," it is (heh heh) "world class tone," for the range that I have, which is not a pro range.

So -- you and your son have different ratios of chops to air, plus different oral cavities, tooth structure, etc etc etc but this one thing I know personally will affect pitch, and therefore slide position.

[peterbas]

.

[matt g]

The most amateur band horn players I come across seem to have a problem with tuning (441/442) too high.
Their tuning slide is pulled to the point of falling out.
Any idea if this is a common problem?

Is this an airflow problem or a hand position problem? Horn technique gets tricky that way. Shoving a hand in the bell too far and possibly moving the reflection point inward could explain them playing too sharp.

[bloke]

The most amateur band horn players I come across seem to have a problem with tuning (441/442) too high.
Their tuning slide is pulled to the point of falling out.
Any idea if this is a common problem?

remarkably common.
I always expect community bands to play sharp.

...the following...please don't interpret as "talking down" or "we professionals" crap... me?? I play tuba "pretty good" and suck at tons of stuff...
oh yeah: and I catch myself playing OUT OF TUNE.
--------------------------------------------------------------------------------------------------------
NOT playing sharp is remarkably challenging as so MANY things (when playing winds) seem to cause it...
- playing really loud
- playing really soft
- playing "tight" (closed down throat/lips/whatever...ie. pinching ONE or MORE parts of the human body)
- playing certain naturally sharp (compared to equal temperament tuning) pitches
- and more...

playing flat...It's just not as common (either the B-grade or A-grade players)
So many sopranos/tenors (operatic/church soloists/etc.) tend to SING above pitch...as well as soprano instrumentalists (as it's easier to HEAR, and producing above-proper-frequency pitches is easier than "projecting").

common (joke) expression in the USA (amongst both amateurs and professionals, but more head amongst professionals)
"Better sharp than out-of-tune."

[jtm]

Looking at it from a different perspective, take a look at my F tuba ("mash buttons and blow", no slide-pulling, barn-door-wide "slots"...built in a dirt-floor building in Communist East Germany)...They didn't have any tricky formulas, and none of their other models played anywhere close to as in-tune (and no F tuba made today plays any better in tune).

Are the slots wide because that tuba is so very conical?

Whatever the reason, a really great feature is that the higher partials, with much more focused slots, are also in tune!

[bloke]

If yours is similar to mine, and a whole lot of other F tubas, eighth partial D and C-sharp tend flat. Those can be pushed in tune, but I automatically play those with 4 and 2-4. They are no less secure than the standard fingerings, and are actually far more secure - as they are in tune. In the past, I used to think I needed third valve for the lower D's and some sort of substitute for D-flat, but I eventually determined that I was wrong and poor playing habits were simply causing me to blow sharp... believe it was a bit like those people who claim that C below the staff is a problem pitch, because they're trying to play it like an open C on a tuba built in C, whereby the way to approach that pitch is much more like playing a sixth position F on a trombone - perhaps even a somewhat small trombone. "Playing by feel" is not a particularly good idea, and my view, and I really strive to play by sound. That C might not "feel" good - if played properly, but it will sound great.

feel-schmeal