A somewhat puzzling title, if you think about it. However, the way brass instruments sound is often described in such terms as "bright" and "dark". In this article I would like to discuss some of the variables that determine the "color" of sound. What follows represents my understanding of the subject at the present time. If you know differently, please do let me know. Especially the terminology is by necessity somewhat vague.
The terms "bright" and "dark" refer to the way overtones are produced. When a non-electronic instrument is played, there is the basic tone which is being played and a number of "overtones". These are tones that are higher than the basic tone being produced. The number and frequency of these overtones are a factor in the color of the sound. Sound which is called "bright" has mostly higher-frequency overtones, while "dark" means the overtones are more evenly spread across the frequency spectrum. When overtones are eliminated the sound is described as "dead", which shouldn't be confused with "dark". Another factor in the color of the sound is the shape of the sound wave (so I am told). In brass instruments, several variables determine this color, such as the size of the bore, the degree to which the bore is conical, the material the instrument is made of and the total weight of the instrument.
The bore size of an instrument is the diameter of the tubing. Since this diameter isn't constant throughout the instrument, the bore size is usually measured at the second valve (except on a slide trombone of course). The initial bore size at the mouthpiece is determined by the outer diameter of the mouthpiece, which is the same for all instruments of a certain type. That is, the outer diameter of (e.g.) a trumpet mouthpiece shank should be the same for all mouthpieces, which in turn means the bore of the mouthpiece receiver is the same on all trumpets. After the mouthpiece receiver, things vary considerably from one model (trumpet, etc.) to the next. What effect then does the bore size have on the sound of the instrument? When a playing an instrument, increasing the air pressure (playing louder) will cause a change in color; the sound becomes "brighter". Increasing the bore size causes an increase in the amount of air pressure the player needs to apply to the instrument to make the sound "brighter". The effect of this is that, e.g., a large bore trumpet will sound more mellow, almost flugelhorn like, when played softly than a trumpet with a smaller bore. A player of this large bore trumpet will have to apply much more air pressure (play louder) to achieve a bright, sparkling sound than a player on a medium-large bore trumpet. A small bore trumpet achieves the bright sound at relatively low volume.
Conical vs cylindrical
The degree to which an instrument is conical has a profound influence on the sound it produces. In a "cylindrical" instrument, the tubing has the same bore throughout. A "conical" instrument has tubing which starts with a small bore and widens out to a larger bore. Theoretically, trumpets and trombones are cylindrical bore instruments. In practical terms however, almost all instruments including trumpets and trombones are conical to some degree. The difference is in the degree. The effect of increasing the degree of conical-ness of an instrument can perhaps best be explained using an example: A trumpet is a (theoretically) cylindrical instrument. A cornet is a somewhat conical instrument. A flugelhorn is a very conical instrument. A trumpet sounds "penetrating", a cornet somewhat more mellow, a flugelhorn sounds very mellow. This difference is caused by a change in the shape of the sound wave, so I am told. I am also told that the change is not the same as occurs when increasing the bore, but apparently this is rather complicated. The difference in degree of conical-ness and the influence on the way it sounds is also the reason why several models of trombone have the tuning slide in the hand slide and not the bell crook: it allows the entire bell to be (smoothly) conical from the join with the hand slide to the end of the bell. When the tuning slide is in the bell, there needs to be a section of cylindrical tubing to allow for the tuning slide. Incidentally, it would appear that the more cylindrical the bore is the better an instrument "slots" and conversely, it is more difficult to "bend" notes.
Next, the material the instrument is made of. Different metals produce different overtones. Renold Schilke (the man behind the line of instruments carrying his name) did research into this some years ago, putting steel and lead bells on a trumpet and observing the results. Those results were somewhat surprising. The steel bell, when struck produced a beautiful "ping" sound, as you would expect. The lead bell, conversely, didn't "ring" at all. However, when played on a trumpet, the steel bell created so many overtones the results were chaotic when viewed on an oscilloscope. Not practical for musical purposes. The lead bell on the other hand produced almost no overtones at all, making the sound almost "mechanical". Both bells were useless for practical purposes. If you would like to read the entire paper Schilke wrote on this and other subjects, follow this link: Materials and their affect on the acoustics of brass instruments. More useful for our purposes is the comparison between brass and various metals such as aluminum, silver, copper, gold and nickel. Aluminum, silver and nickel make a tone "brighter" compared to brass. Gold and copper on the other hand "darken" the tone. The more copper in the brass alloy, the darker the sound is. Hence coprion, and such alloys as "red/rose brass". The cause of these differences lies is in the hardness or inflexibility of the metals. The harder or more inflexible a metal is, the brighter the sound will be, and vice versa.
Weight has a distinct influence on sound and the way it is produced. These days many manufacturers have both "heavy weight" models and "light weight" models. It is my understanding that the thicker the brass on an instrument is, the "darker" the tone is. Conversely, a light weight instrument with thin brass sounds "tinny" (as in "tin can" and not "small"). This difference in thickness of the brass is sometimes also described as "heavy walled" and "thin walled". One side-effect as far as the color of the sound goes is that adding weight increases the "slotting" of the tones. The term "slotting" refers to how well a note when played finds the "center" of the tone. Another way of putting it is the ease with which a note can be bent up or down. Increasing the "slotting" (adding weight, such as with heavyweight valve caps) makes it more difficult to bend notes. Ever notice how Maynard Ferguson in the 1970's frequently produced huge "shakes", while he rarely did so in the 1960's? Perhaps one reason is that in the 1960's he used a heavy Conn 38B Connstellation, while in the 1970's he played a much lighter Holton.
The 38B Connstellation
With all of this information it is possible to form a hypothesis on what makes the 38B Connstellation work the way it does. First, it has a small 0.433" bore. This brightens the tone at lower volumes. However, the small bore is offset by the fact that the 38B, for a trumpet, is a pretty conical instrument. The conical-ness "mellows" the tone a bit, and also means the 38B accepts a large volume of air (believe me, the 38B is very free-blowing). The nickel plating brightens the tone. The 38B is certainly also not one of the lighter weight instruments you are liable to come across. This "darkens" ("enriches"?) the tone quite a bit. All of these factors are combined to form the unique sound of the 38B Connstellation.