Why Do Brass Instruments Sound Like That?

One of the many nerdy obsessions that I have with music is to not only understand how instruments sound but also why they sound the way they do. I'm fascinated by the reasons why certain instruments are constructed or shaped the way they are and what that has to do with their sound.

The interesting fact is that acoustic instruments are so complex in their work principle with an insane amount of variables that take an influence that it is mostly impossible to simulate its construction in a computer but manufacturers mainly base their construction on continuous trial and error.

It should also be noted that even the standard instruments are still evolving in their playing technique and construction. So some shortcomings that you might read in older orchestration literature are not relevant  anymore on modern instruments.

One question that I kept asking myself is how brass instruments sound so different. I understood that the different tone generation on woodwinds was probably responsible for the different colours of the instruments but with brass, I always felt that they are all basically the same. Buzzing lips create a tone that is amplified through the tubing of the instrument which can be lengthened through valves or slides, making the chromatic scale available by moving through the harmonic scale by changing lip tension. So why do horns sound so different than for instance trumpets? I knew already that all these bent tubings couldn't have that much influence on the sound as I heard Aida trumpets which didn't sound radically different from regular trumpets:

https://www.youtube.com/watch?v=bp7-m2ahxGA

So what was it that actually shaped the different timbres?

There are effectively two construction features that fundamentally define the sound of a brass instrument. Bore and Mouthpiece.

Bore:

There are effectively two different bores for brass instruments. Either cylindrical or conical.

Instruments with a cylindrical bore maintain the same diameter of the tubing for a quite long distance of its entire length while conical bores keep gradually growing in diameter over their length.

Typical cylindrical instruments are trumpets and trombones (which wouldn't even work with their slide if the bore wasn't cylindrical). 

Conical bores like with the Tuba do favor the fundamental frequency of the harmonic scale more, generally sounding more substantial and boomy while with cylindrical bores it is trickier to make the actual fundamental speak and even if it speaks, it doesn't have as much substance. In a way does the cylindrical bore even out the volume between the lower and higher frequencies of the harmonic spectrum while the conical bore is more weighed towards the lower frequencies.

Just imagine a Trombone and a Tuba playing the same low note. The Tuba note will be considerably more carrying and round while the trombone will be more edgy (of course also depending on dynamics).

Mouthpiece:

The even stronger influence on the sound has the mouthpiece.

Many of their construction features are relevant for the players and theirplaying comfort in certain registers. E.g. a flatter cup makes playing higher notes easier and a deeper cup makes it easier to play lower notes for them. However, the physically relevant part for the actual sound characteristics of the instrument is the edge that leads from the cup to the throat. The sharper this edge is, the more compression will happen and the more harmonics will be created.

Here's a comparison between different mouthpieces (not super accurate (e.g. the graphic above represents a trumpet mouthpiece shape much better than below) but you get the idea).

For every instrument there exist a wide array of different mouthpieces from different manufacturers, which all however do not change the fundamental properties of the mouthpiece. For instance the horn uses a wedge shaped mouthpiece. Here's a chart by a manufacturer that shows the difference in their mouthpiece for more high and more low horn players:

You see that the differences are really super small and far from changing the overall construction. But you can see that there is hardly any edge between the "cup" and throat, which explains the generally more round sound of the horns compared to trumpets/trombones. 

Interestingly, if you play a brass instrument with a mouthpiece from a different brass instrument, the sound quality will shift quite considerably to the sound of the instrument that the mouthpiece is from.

Unfortunately I could only find this super old video in bad quality from a guy who plays a trumpet with a horn mouthpiece:

https://youtu.be/Zwq_2Oschss?t=152

It really sounds like a weird mixture of the two instruments with a quite strong french horn "vibe". If he would cover the bell with his hand (to simulate the horns playing with their hand in the bell) he would get even closer to that horn sound.

Of course, this is more of a fun experiment than an actually valuable new instrumental colour as all the parts of the individual instruments are optimized to work best in their "natural" configuration so just creating a Frankenstein instrument by combining different parts with each other will not necessarily create a well to handle or nice sounding new instrument.

Still, I find it incredibly fascinating to understand and learn such things as they really give a deeper understanding of instruments, and also satisfy that nerd in me.