One can find several slide position charts online. There is some variance among them. This Slide Position Chart is mathematically generated – it is just a guide, but it should get you started. However, in my experience, while low C teeters on the very end of the slide, on many (if not most) modern horns, it is completely off the end! Some older horns had longer slides (and we lipped ’em down for years – even some low Bs). Additionally, this chart by Dr. Micah Everett, is pretty good (note: looks like Bb/F/D bass – the D postions are further in than the chart above – perhaps due to D tuned as a just major third in Bb).

Also, despite what some slide position charts show, low Db is usually a little past 6th position (if you tune F in 1st – more below) as George Roberts and Paul Tanner showed in the chart in Let’s Play Bass Trombone (sadly out of print). And in Alan Ostrander’s Method for Bass Trombone, he writes, that with low F in tune in first, low Db “is an inch or so beyond sixth” (emphasis added). YMMV.

Putting the slide in the right place is very important. But it’s entirely possible to play an in-tune pitch with the slide in the wrong place. (See Tuning Slide Anecdotes) Right place is better than wrong place! If the slide position’s off, the tone won’t really center, it won’t fully resonate, and it’s tough on the chops! In the low register, particularly below the staff, there is more “room” to get in trouble between harmonics.

However, slide placement is less critical in fast passages. Edward Kleinhammer wrote in The Art of Trombone Playing, “Eventually, the tempo will become such that stopping [the slide] at each tone will become impossible. At this point keep the slide in motion, playing each tone as you go by its respective position. . . . there is a degree of ‘faking’ in this procedure” (see Slide Technique and Swindlesmanship). My friend, Bob McChesney (who has amazing facility), demonstrates this cleverly. His explanation is, to my mind, half right; perception is part of it, but physics is involved. (See Tone Production.)

In Fundamentals of Musical Acoustics, Arthur Benade explains the primary reason: “The reflected wave, upon returning to the mouthpiece, ‘tells’ the lips how and when they must reopen to admit the next puff of air in the sequence of puffs that sustain the tone after everything has settled down. Until the first reflections begin to come back, the lips are on their own. The air column has not yet expressed its preference for one or another of the frequencies with which it is able to collaborate. . . . Several more round trips are required before the regime of oscillation has set itself up completely. In a fast running passage, there is barely time for one regime of oscillation to be set up before it must give way to the next.” This is why it’s difficult to play really fast and really loud – the horn isn’t helping. (More on acoustics and intonation, here, standing waves, here and here.)

There is also a variety of dogma about how to tune the F valve. Some folks tune 2nd space C to the same position as low Bb – this yields a flat low F in 1st but makes low C in 7th a little more accessible (still gotta lip it down). Some tune low F in 1st very flat, so low C is VERY accessible –  and never play F in 1st. Phil Teele used to tune his single valve Williams to E. I tune the low F to the same position as low Bb so an in-tune low F is available in 1st. Some folks tell me, “the F in sixth sounds better” – nonsense – whatever you practice the most will sound the best (the whole masterclass is great).

I play dependent valves; independent offers more possibilities. For a long time, I eschewed upper harmonics on the valves, for example D in the staff in 1st with both valves. Over the years, I have learned to use them effectively. With practice – and with modern valves – they sound fine. Don’t be mislead by the fact that they feel different. It doesn’t matter what they feel like, only how they sound. You’ll get used to how they feel. (I should point out that not everyones agrees. Try for yourself.)

Different trombonists describe F (and other) valve slide positions differently. My thought is relate them to the Bb positions: E in “2.2,” Eb in “3.6,” D in “4.9,” Db in “6.125,” C in “7.999,” and so on.

NOTE: slide position charts are, at best, just guides. Horns and people are variable. You need to find where to put your slide on your horn. Use both a tuner (do NOT take it to work) and drone tracks to learn your – and your horn’s – tendencies – and LISTEN! Benjamin Coy’s tuningdrones.com is a great tool.

The ear, coordinated (see “Ear-Hand Coordination”) with a little “muscle memory” should place the slide, not the eye!

Also, the trombone is far from a perfect harmonic series. For example, the F above the staff is frequently sharper than the F in the staff. This chart is a pretty good example of a “real-world” Bb trombone (however, there are some missing pitches and one error up top). This page has a fairly simple explanation of the intonation tendencies of the harmonic/overtone series – relative to tempered intonation (but high C is usually a little sharp). This chart spells out those tendencies in cents. These tendencies can vary noticeably with different instruments and different players. Chicago trombonist and professor emeritus at De Paul University, Mark McDunn, once published a chart titled The 51 Positions of the Slide Trombone illustrating this – for his horn – a grain of salt . . .

Learn your tendencies on your instrument(s) and listen and tune carefully. Slow practice and good slide technique help. Long Tone Duets for Trombone: Ralph Sauer Edition! is a GREAT resource – and – it can be “a lesson with Ralph” every day! “This edition not only captures Mr. Sauer’s sound on an included CD, but also reflects some of his teaching ideas embedded in the duets. By playing along with the CD, you can match Mr. Sauer’s clear tone, exquisite intonation, and superb articulation.”

NOTE: the harmonic series is approximated on a brass instrument due the “bell and mouthpiece effects” so intonation tendencies can be a little (or a lot) different from pure harmonics. “. . . the typical brass instrument will have several resonant frequencies that fall approximately along a harmonic series.”*

*White, Harvey  E.; White, Donald H.. Physics and Music: The Science of Musical Sound (Dover Books on Physics) (p. 252). Dover Publications. Kindle Edition (a great book)