There are tons of theories, many substantiated on how a trumpet works. This can be in terms of intonation, color of sound, density of sound, projection and impedance (resistance). It is commonly known that each individual player is different AND the expectations as to what should come out of the horn are equally different.
I am interested in getting "to the meat" as in my following example. I welcome any info that could increase our understanding!

Please understand that the math behind much of this stuff is very complicated and my explanations are kept very general so that most players can benefit to a certain extent! I make no claims to absolute accuracy but can back up the comments with existing published research.

1) Tone Color is basic frequency response. A darker sound has less high harmonics, a brighter sound more. We can influence the frequency response with the mouthpiece (a deeper cup filters out higher frequencies), bell shape (a faster flare amplifies the high frequencies more) and with the bell material, temper and thickness (a bell that inhibits radiation of sound from the outside of the bell will sound more "brilliant", denser materials like red brass and copper CAN also sound "brighter" than conventional brass if the temper is the same). We can combine these factors to produce a wide range of basic hardware colors.

2) Efficiency is the proportion of energy in to energy out. In horn design, we get improved efficiency when increasing the resistance at the throat (the mouthpiece in our case) compared to the mouth (the bell). The problem that we have as trumpet players, is that we need to breathe to stay alive and play. That means that we need a certain amount of "inefficiency" to use our air up in the time that our body requires fresh air. A too free blowing horn on the other hand sacrifices efficiency and limits our ability to phrase because our air is gone too quickly.

3) Intonation is the correspondence of the pitch that our ear wants to the natural partials designed into the horn. We can affect the intonation of the partial series with mouthpiece throat and backbore, leadpipe design and the size of the bell. Trumpet designers have to juggle many factors to get an instrument to perform reasonably with a wide variety of mouthpieces. The reason that the pro classical world did not go rampant with the poor intonation of many older C trumpets, is that the players had large, inefficient mouthpieces that gave a lot of leeway to bending notes in tune. Lead trumpet players with smaller, more efficient mouthpieces would not have been able to use these instruments.

4) Slotting is a term for an instruments ability to lock into a tone. The physics term for this phenomenon is Q - the ability of a resonant system to tune to a particular note. More efficient systems slot better, this can be a blessing or curse depending on the basic INTONATION of the instrument.

5) Projection is the ability of a horn to make itself heard at a distance. It is a combination of tone color and efficiency as well as the bells capability to keep the sound from spreading after leaving the bell.

That should be enough to get us started! More details on request.

Thank you,Robin.

Originally Posted by rowuk

3) Intonation is the correspondence of the pitch that our ear wants to the natural partials designed into the horn.

Great post, Robin! Intonation is, for me, the biggest issue in trumpet design, and it is a strange and complicated issue as well, because what the ear wants is often contrary to the natural partials designed into the horn. A "perfect" natural trumpet, pitched in c will have e's exactly 14 cents too flat and g's exactly 2 cents sharp, because of the natural overtones. If we play a c loudly enough, all the natural tones will be present as overtones. If we somehow design a horn to play those e's in tune, they won't be able to "come to life" very well as overtones, and the sound quality will be changed.

My (totaly subjective) experience has been that the best sounding trumpets (more so with pistons than rotaries) have been the least "in tune" (according to equal-tempered tuning devices). In part, I think it is the result of these trumpets being friendly to their natural partials.

We are, I believe at a crossroads, in which not missing notes is of paramount importance, which requires trumpets that slot like crazy. With such trumpets, pitches are almost impossible to "lip" into tune, so we require an equal-tempered trumpet, that in turn sounds different, and to these tired old ears, not as fine and noble and beautiful as in "the good old days."

Nothing new, this mini-rant, for back in the day the players of natural instruments complained about the sound of the new fangled valved instruments. Our collective ears (players and public alike) adjusted over time as tastes changed, and will continue to adjust, but dang, those old "out of tune" instruments sure sounded great!

Originally Posted by Vulgano Brother

My (totaly subjective) experience has been that the best sounding trumpets (more so with pistons than rotaries) have been the least "in tune" (according to equal-tempered tuning devices). In part, I think it is the result of these trumpets being friendly to their natural partials.

The issue of tempering is a complicated one, but the essence is that our western scales are a compromise our ears have learned to accept. Octaves and 5ths are favored and other intervals suffer and are degraded. Pythagoras figured out a perfectly intervalled scale, but it did not sound right, especially when playiing chords, and ever since we have been tinkering to get something that does. Another complication to add to the mix! Perfect intonation is a myth.

BTW, Nick Drozdoff has written a wonderful piece on the physics of the trumpet: Essays on Trumpet/Brass Physics

[QUOTE=veery715;317739]

Originally Posted by Vulgano Brother

....... Perfect intonation is a myth.

I think that "perfect" intonation does exist to some extent. I read about it in a book on intonation by Chris Leuba. A perfectly in tune major chord produces sum and difference tones that are harmonically related to the chord - no interferences. This is not true of minor chords, but there we are trying to express something different.
I believe that horns should slot loosely enough that we can get a strong resonance when playing in a section. In that case 1+1 is more than 2!
I get occasional oppertunities to play with Dave Tasa (solo tpt at the Frankfurt opera). He has a Monette Raja C and I used my Ajna2 Bb - I play second and really try to get each chord to ring. It is easier to do with him than any other people that I play with, we always have a reason to smile!
The reason is the similar sound concept, intonation and the "dense" sound with a lot of overtones.

Originally Posted by rowuk

I think that "perfect" intonation does exist to some extent.

As oxymoronic as that statement is, I agree with you completely! I totally forgot about resultant tones (playing with guitars and singers will do that to a guy, I guess), but yeah, great trumpets create great, loud and sometimes annoying resultant tones. It would be a curious test, and tough as all get-out to pull off, but to find which manufacturer's horns produced the best resultant tones would be interesting (by "best resultant tones" I mean those that are loud and annoying.), and then compare this data to their equal tempered intonation. My hypothesis is that Monette would win hands down, but that the "in-tune" trumpets would generally not fare as well in producing resultant tones.

Thanks for the thread Robin. I'd enjoy the references when you get the chance.

Particularly, does what you have there depict or discuss a measure of what's considered high harmonics and low? To my meaning; from left to right- nine representing the lowest response, to zero being the beginning of a considered reference of high? Low//Less/Dark 987654321 0 123456789 High/Greater/Bright

-I should mention too Robin, to that last post; hypothetical build formulas- to give the (depiction/discussion) i'm speaking to a name. Some notions of practically applied less/more harmonic response by design?

It's a lot to ask of a maths reference i know, but a line to such a meander of shop talk would be very cool.

Much grata-

Originally Posted by godchaser

-I should mention too Robin, to that last post; hypothetical build formulas- to give the (depiction/discussion) i'm speaking to a name. Some notions of practically applied less/more harmonic response by design?

It's a lot to ask of a maths reference i know, but a line to such a meander of shop talk would be very cool.

Much grata-

Chris,
My sincere apologies for a rude comment,but I think you should keep your posts a little less complicated,especially your writing.
It took me 10 minutes to understand exactly what you meant in your last question.
Keep things simple,you'll get further.

"It's a lot to ask of a maths reference i know, but a line to such a meander of shop talk would be very cool."

What does this mean?