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Every resource I've seen and person I've talked to has said that putting low voices, usually trombones, in close spacing anywhere below C4 is to be avoided at all costs, due to muddiness. As I arrange, though, this rule is causing me some grief, as it forces me to treat the 2nd trombone as a chord-root machine, or to put the 1st trombone up into the higher part of its practical range, crossing higher than the alto voices. Not only that, but in band arrangements, making the baritone double the tuba at the octave would result in very close spacing anyway, and often between the two trombones!

Furthermore, I've recently seen band arrangements of considerable age and popularity (as in, played week in and week out every school year for no less than 80 years) that do use close voicing below C4. It's never long chords or extended passages, but they're there: Bb3 and G3, C4 and Ab4, and even (I think I saw it) Bb3 and G3!

This leads me to question: Is close voicing really so bad? If not, where's the limit? I'd never make a chord at F2 and A2, for example, and that for any instrument. If it is to be avoided like the plague, how am I supposed to handle voice leading?

There are acoustical reasons for not wanting close voicing in the lower register; in short, the upper harmonics muddy each other up and fog up the sound.

But in my experience, C4 is a really high limit; I can think of tons of scores with thirds below C4.

Every musical environment is different, and sometimes you might want that slightly muddy sound. But if I had to come up with a hard rule, I would be inclined to use C3 as your upper limit instead of C4.

Below C3, composers often just stick with octaves, but occasionally you'll find some perfect fifths between tuba and bass trombone, or split between two tuba parts, etc.

Edit: As I mention in a comment to mkingsbu's answer, Mahler 3 has consecutive thirds of D2–F2–A2 at m. 209 of the first movement. These tight spacings do happen, but typically they're written to create a very specific effect.

Closed vocings aren't bad, but you need to be aware of the register you are in no matter what you compose. In lower registers, having notes close together isn't always what you want. Specifically intervals that are supposed to have color like 3rds and 6ths both will sound "muddied" to most. Perfect internals typically don't observe this problem. This is also the reason in most counterpoint people are taught to keep the tenor high. It's not necessarily a bad sound, but expected harmonies may not turn out the way you want to due to this property.

Like with anything else in music listen to what you are writing. You should be able to hear a difference in clarity from the low register closed chords to a higher register open. The muddiness may even be something you desire for your piece.

Human pitch discrimination is frequency dependent. There is a concept of critical bands. You can read about it in a text on Physics and music by Rigden. I keep promoting that text because I've taught out of it as several universities. There are probably many good texts on the subject. In short, there is a critical minimum frequency difference at which people will not likely be able to hear the difference between two tones. This also has an impact on the perception of consonance and dissonance in an interval. It is a fact that small intervals will be "muddy", more dissonant, and perhaps indistinguishable at low frequencies (in the low registers). That doesn't mean you can't do it. At the end of the day you need to be happy with your arrangement. If you're just looking to arrange a piece of music and trying to find work for each section I'd adhere to the rule (guide line) but it you're composing you have freedom to break the rules. It will produce an effect and as long as that effect is what you want it works. But I'd be careful and try it out during a rehearsal in an auditorium and see if it sounds the way you think it does. The "muddiness" has nothing to do with acoustics and acoustic scattering and interference will make the effect worse. If you find yourself with limited options for notes in lower registers you can always rearrange a piece to have different harmony, chord inversion etc.

As a trombonist, I've used D3 as the cutoff though I make context dependent exceptions.

When you say:

or to put the 1st trombone up into the higher part of its practical range, crossing higher than the alto voices

That this isn't as big of a deal as you might think for trombonists, depending upon the difficulty level you are writing for. If it is a professional ensemble, C5 is absolutely expected range for a tenor player. Alto parts slightly higher, up to the Eb above it, really. So having each member of the trombone section belonging to a different 'voice' in an overall voicing in an orchestration is perfectly okay.

If you would like a snapshot of some writing that is largely considered idiomatic to the trombone, you can check out a resource such as http://www.tromboneexcerpts.org. That is a collection of resources that are used in auditioning, which is why I suggest everything can be considered 'idiomatic'... because if it isn't, people are still treating it as if it is! Perhaps a better way of putting it would be that it's in the 'standard repertoire' that a trombonist would be expected to play.

Each excerpt has a recording from several orchestras that demonstrate the written passage, so you can hear how it might sound on the trombone, in the context of the full orchestra. In most cases it has all of the trombone parts so you can see the voicings for that part of the passage. The exception would be solos within a larger work, such as Mahler 3. Incidentally, that is a good example of a 2nd inversion, at least in the trombone part with a fairly tight D minor chord starting that particular excerpt, which would violate closed intervals or other voicings in the trombone part below C4.

Muddiness depends on other considerations as well, such as volume and tuning. Just thirds (i.e., in a harmonic ratio of 6/5 or 5/4) will sound clearer than equal-temperament thirds. Check out some renaissance counterpoint, which generally works very well with trombones playing the lower voices. I'm thinking of Schütz Die mit Tränen säen, SWV 42, and Selig sind die Toten, SWV 391. There are also some great pieces by Thomas Tallis usually sung by men's voices that have close spacing in the lower register in certain sections.

You may also be interested in a page I have found from the Ohio State University School of Music (by means of a web search employing heavy use of the - operator), called Spacing of Chords. To summarize, the page notes that Walter Piston called into question the historical rule about chord spacing matching the harmonic series, since actual practice showed that acceptable spacing depended among other things on register. The page then goes on to describe psychoacoustic work on chord spacing that has been done since the 1960s.