Bass trombone and the 2nd valve

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Kbiggs
Posts: 1768
Joined: Mar 24, 2018

by Kbiggs »

One of the difficulties in playing bass trombone is getting the 2nd valve notes to sound and feel “the same as” the open horn. In my limited experience, this is true for independent and dependent basses, although dependent basses have a longer neckpipe which helps mitigate this effect. A lot of recent history in design and manufacture has worked on this situation, e.g., open wraps, boring out traditional rotor valves, Thayer valves, improved rotor valves, Lindberg valves, etc.

I think part of this is due to the second valve being the same bore size as the 1st valve. Some tubas and euphoniums address this by increasing the bore size of their 4th or 5th valve (i.e., valves that adjust the pitch by lowering a P4 like the trombone’s F valve, or that lower the pitch by either a sharp or flat M2).

Has anyone (a) developed and (b) successfully marketed and sold a trombone where the second valve is a slightly increased size to help reduce compression when using the second valve? What have been the results?
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tbonesullivan
Posts: 1959
Joined: Jul 02, 2019

by tbonesullivan »

Using two valve together is always going to have a different feel due to the increased length of tubing, going through the valves 2 more times, etc. I don't know if there is any real way to mitigate that. There have been various different thoughts on the bore of the valve attachment with relation to the regular bore. I also definitely seem to remember some talk of a progressive bore with a larger diameter second valve.

The problem I would see then is that if you use the valve independently a lot, there would be less parity between the F and Gb (or G) valve.
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Burgerbob
Posts: 6327
Joined: Apr 23, 2018

by Burgerbob »

Yes, the B&S Sarastro bass has progressive bore valves. Each port is successively larger, I think the final port on the Gb valve is above .620 something- I haven't checked for a while.

It's a very particular instrument- I love it (I own one!), but it's the strangest bass I own to just pick up and play. The blow through the valves is not, shall we say, "even." It's very good when you're doing it just right- the sound is amazing, but it's not intuitive. Maybe that's just because I'm used to "normal" basses.
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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

My memory is a little fuzzy, but I think we did an experimental rotary valve section this way at Shires. I did not like it, and I don't think anybody else thought it was worth pursuing any further either.

Contrary to your experience, with all other components the same (literally the same, not just same specs), I find independent rotary valves to respond more evenly than dependent rotors as I move between the open horn, one valve, two valves, and the pedal register. Not necessarily better and definitely not bigger, but more even.

The same thing is not true of axial flow valves.
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Finetales
Posts: 1482
Joined: Mar 23, 2018

by Finetales »

I would think if you were going to do a progressive bore on a bass trombone, you would put the Gb valve first and then make the F valve a little bigger. The other way around feels backwards, as the Gb valve is shorter.
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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

[quote="Finetales"]I would think if you were going to do a progressive bore on a bass trombone, you would put the Gb valve first and then make the F valve a little bigger. The other way around feels backwards, as the Gb valve is shorter.[/quote]

Now that's an interesting idea...
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harrisonreed
Posts: 6479
Joined: Aug 17, 2018

by harrisonreed »

[quote="Finetales"]I would think if you were going to do a progressive bore on a bass trombone, you would put the Gb valve first and then make the F valve a little bigger. The other way around feels backwards, as the Gb valve is shorter.[/quote]

If that was the concern I think you'd have to also have the Gb valve located first in the chain. Like, you would have the triggers operating the valves second they normal do (no difference to the operator), but the valve sections would be physically reversed from normal. Otherwise the valve would step down to a choke point after the F valve on the open horn.

[Edit] duh, you literally said that.... Having the Gb valve first. My bad!

Wouldn't you be effectively *adding* a choke point as you descend with to the C, this way? Most times you would be adding the Gb valve on after the F is already depressed, just because you are adding a shorter length of tubing, you are still adding tubing. I would think, based on the OP comment, that you'd want the second valve added (given that it's operated like a dependent setup) to be more open.

I think it just matters that the valves step up in the order they are on the open horn, adding cylindrical tubing on after shouldn't really be a big deal, since the valves are not always (or even often) going to be operated Gb first, then F or combined.

Just spit balling here. I play the bass as if it were dependent.
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JonTheCadet
Posts: 72
Joined: May 28, 2018

by JonTheCadet »

Having the Gb valve placed in front of the F valve is how Throja build their horns. Not sure if they use progressive rotor sizes
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Kevbach33
Posts: 295
Joined: May 29, 2018

by Kevbach33 »

[quote="Finetales"]I would think if you were going to do a progressive bore on a bass trombone, you would put the Gb valve first and then make the F valve a little bigger. The other way around feels backwards, as the Gb valve is shorter.[/quote]

This would be in line with the traditional German way of making contrabass trombones, where the D (or Eb) valve is before the Bb valve. While I don't know if many (any?) contrabass trombone valves are progressive bore (I think the Kanstul was, but in American configuration, C/Db/A, and even then each valve and loop were different bores), other than the B & S mentioned, there aren't any basses I can think of that have progressive bore valves (ports all different sizes) or valve sections (each valve and loop a different bore).

Is Shires missing out by not scaling their dual bore valve to bass trombone sizes, I wonder? (Not that I know if it'll happen or not, especially since they have access to Rotax valves after Eastman bought Willson...) I'd like to try the concept, but the B & S is tangential to my sound concept.
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muschem
Posts: 372
Joined: Jan 17, 2021

by muschem »

The more I try different combinations of things, the less I think that larger bores through the valves and valve wrap tubing solves the problem I've always thought it did. Or, maybe it used to (sort of) solve a problem that doesn't exist in modern valve designs. In any case, I've had much better experience in response, intonation, and "open" blow when the handslide bore and the valve bore match.

I don't have enough (well, ok... "zero" is a more accurate way to frame it) technical background in acoustic design to speak to exactly why that might be from a theoretical standpoint. But, the way I conceptualize it (and this may be completely incorrect), we don't "push" pressurized air through the horn very far at all... certainly not (in my mind) as deep as the valve(s) sit in the sound path. Rather, we excite the air column into a standing wave in a tube that is essentially closed at one end. Our lip reed embouchure creates movement (vibration) in the horizontal plane, with higher pressure on the oral cavity side and lower pressure on the mouthpiece side. This horizontal motion (yes, there would be vertical motion as well, but for this mental model, I'm mostly concerned with the horizontal plane) of the lips can send kinetic energy either direction, but pressure drop across the lips means that more goes forward than comes back. But, what I think we often experience as "stuffiness", partials with bad response and intonation, and other related issues, would seem to be artifacts not of a bore constriction problem, but rather an interference problem when there are sharp changes to the bore size, unintentional chambers acting as Helmholtz Resonators, or other discontinuities in the sound path, which send reflections back toward the embouchure, rather than efficiently out the open end of the tube. Maybe that sounds like a bunch of nonsense, but I promise AI didn't write it... it is just how I think about it :)

Anyway, back to the bore size - I don't design instruments, nor am I an acoustic engineer, but I think a progressive bore *might* work ok, if the sound path was smooth (as smooth as it can be) along that increase. But, I would include the handslide in the equation, because in my own limited experience, it matters. Having smooth bore increase through the valves wouldn't help too much (just speculation) if there is still a sharp change between the handslide bore and the valve bore, as is common for most designs. If you match the bore size through the valve and wrap to the handslide, I think the need for progressive bore increase through the 2nd valve goes away (or is drastically reduced). I think Jay Friedman was onto something here - pairing a .562 bore handslide with a large tenor bell section, where the valve bore is also at or very close to .562, actually plays *easier* rather than *harder* (for me - your mileage may vary). I've always assumed it would be harder... larger bore = more work, seems like a natural and intuitive equation. But, I don't find that to be the case in practice - if you match bore sizes throughout with tapered/smooth increases. I don't mean to imply that Jay isn't an absolute monster player, or that I'm anywhere near that league (I can't even see it from where I stand). Just that I was relatively shocked to find how well that setup works when I actually tried it. Do I think bass handslide should expand bore to match the currently used valve bore? Perhaps not. Maybe traditional rotor designs were trying to compensate for sub-optimal flows and restrictions by increasing the nominal bore size... and *maybe* modern, improved valves with better designed paths through the valve cores don't *need* to compensate for those restrictions. So, maybe (counterintuitively, I'll admit), valve bore and wrap tubing bore should downsize to match common handslide bores? I don't know... maybe that's crazy talk - I need to do more testing...
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MStarke
Posts: 1031
Joined: Jan 01, 2019

by MStarke »

[quote="JonTheCadet"]Having the Gb valve placed in front of the F valve is how Throja build their horns. Not sure if they use progressive rotor sizes[/quote]

Pretty sure yes.

I sold my Throja bass 2 or 3 years ago. I think today he is building them with bigger rotors, but even the "old" one had a fantastic valve range. Overall a very good instrument, but didn't fit my needs anymore.
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brassmedic
Posts: 1447
Joined: Dec 14, 2018

by brassmedic »

[quote="Kevbach33"]<QUOTE author="Finetales" post_id="291968" time="1767722642" user_id="136">
I would think if you were going to do a progressive bore on a bass trombone, you would put the Gb valve first and then make the F valve a little bigger. The other way around feels backwards, as the Gb valve is shorter.[/quote]

This would be in line with the traditional German way of making contrabass trombones, where the D (or Eb) valve is before the Bb valve. While I don't know if many (any?) contrabass trombone valves are progressive bore (I think the Kanstul was, but in American configuration, C/Db/A, and even then each valve and loop were different bores), other than the B & S mentioned, there aren't any basses I can think of that have progressive bore valves (ports all different sizes) or valve sections (each valve and loop a different bore).

Is Shires missing out by not scaling their dual bore valve to bass trombone sizes, I wonder? (Not that I know if it'll happen or not, especially since they have access to Rotax valves after Eastman bought Willson...) I'd like to try the concept, but the B & S is tangential to my sound concept.
</QUOTE>

But the idea of older German contrabass trombones was to have a dual instrument. It could be played in either Eb or Bb. They weren't thinking in terms of combining the valves. American bass trombones started out as the opposite. The second valve was only there to add length to the first valve. They were designed with the idea that the second valve would only be used together with the first valve (in fact a necessity on dependent setups). The idea of using the second valve by itself didn't come around until later.

I think whether you wanted to have the Gb be the larger of the two valves would depend how you approach playing. The traditional way stems from single valve basses with F attachment. F is your "default" valve, and Gb extends the length for low C and B. Personally, I choose to play E, Eb, D, Db on the F valve rather than reaching further to get those notes on the Gb valve (all other things being equal, of course), but I know many players like their Gb valve to be the "default" valve. So I don't think there would be a single "correct" way to do it.
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brassmedic
Posts: 1447
Joined: Dec 14, 2018

by brassmedic »

[quote="muschem"]The more I try different combinations of things, the less I think that larger bores through the valves and valve wrap tubing solves the problem I've always thought it did. Or, maybe it used to (sort of) solve a problem that doesn't exist in modern valve designs. In any case, I've had much better experience in response, intonation, and "open" blow when the handslide bore and the valve bore match.[/quote]
Consider this, though: The further you extend the slide, the more open the bore is. In 7th position, you are putting air through the entire outer slide. IIRC, the bore of the outer slide is actually bigger than the bore of the valve, although I might need to check that again. So if you "match" the bore of the inner slide to the valve bore, it's actually a choke from the outer slide to the lower branch of the inner slide, which continues through the valve section. So F with the valve is actually a much tighter air passage than F in 6th position.
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JohnL
Posts: 2529
Joined: Mar 23, 2018

by JohnL »

[quote="brassmedic"]Consider this, though: The further you extend the slide, the more open the bore is. In 7th position, you are putting air through the entire outer slide. IIRC, the bore of the outer slide is actually bigger than the bore of the valve, although I might need to check that again. So if you "match" the bore of the inner slide to the valve bore, it's actually a choke from the outer slide to the lower branch of the inner slide, which continues through the valve section. So F with the valve is actually a much tighter air passage than F in 6th position.[/quote]

Are we looking at things from a fluid dynamics standpoint or an acoustics standpoint?
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JTeagarden
Posts: 625
Joined: Feb 24, 2025

by JTeagarden »

I'm pretty sure "Bass Trombone and the 2nd Valve" is a Roald Dahl children's book.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

[quote="JohnL"]

Are we looking at things from a fluid dynamics standpoint or an acoustics standpoint?[/quote]

That is the appropriate question. Presumably, we are talking about acoustic impedance—shown by the shape of peaks and valleys of acoustic pressure as a function of frequency—not flow resistance (the static end-to-end pressure drop of air flow without sound). Ideally, the frequency spectra of different notes should be similar in shape (meaning continuity of tone quality) as we direct the sound-path through various sets of tubes using valves.

The subtitle of Blair Bollinger’s book (for inline geometry) is:

“You’ve Got Two Valves — Use Both”.

Since the valves can be used independently or in combination, this might suggest that both attachments should have the same bore. The question then becomes: how should the (valve and) attachment bore compare with that of the hand-slide?

It has been suggested that, since an actuated attachment represents an extension of the slide to effectively longer (“8th”, “9th”, . . .) positions, the attachment bore should be close to that of the outer tubes of the slide. Indeed, most commercial tenor and bass trombones use this conventional “oversized” attachment bore design. But that would only make sense if the attachment(s) were inserted into the bow at the end of the outer slide. [Obviously, not ergonomically feasible.] In fact, they are (usually) inserted at the upstream end of the tapered gooseneck, where the bore size matches that of the inner slide tubing—so as to guarantee continuity (of cross-sectional area) at that point between slide and gooseneck when neither valve is actuated. This strongly suggests that the valve(s) and attachment(s) should have a bore size that matches that of the inner slides (or the larger inner slide of a dual-bore hand-slide).

In fact, this question was (supposedly definitively) put to rest twenty-seven years ago (at least for tenor trombones with an attachment)—in an article published in the ITA Journal, Vol 27, No 2, Spring 1999, entitled:

Improving Attachment Intonation, Tone Quality & Attack Response

In that article, the author describes theoretical analyses and prototype testing carried out in coordination with René Hagmann in the mid-1990s in an attempt to investigate and (hopefully) correct the well-known “problems” associated with attachment alternates in the low-tenor register: flat and “stuffy” (second harmonic) F2, sharp and uncentered (third harmonic) C3, unreliable attack response. It is because of these “problems” that professional players mostly prefer slide-alone positions for exposed sustained tones involving F2 and C3 (in 6th position) and E2 and B2 (in 7th position). And why there is not more interest in different attachment tunings (other than P4 as the default) offering many more attachment alternates in the otherwise awkward low-tenor register, the philosophy being: “Why would I want to play many more sub-quality attachment alternates?”

The ITA Journal article describes the author’s prototypes designed by (i) replacing the attachment tubing with a smaller bore that matches that of the standard slide, and (ii) replacing the standard slide with a dual-bore slide, where the larger bore matches that of the standard attachment. This involved both medium- and large-bore Bb tenor trombones with G-natural attachments (the optimal tuning for offering many attachment alternates). With either type of matched bore, all of the usual attachment “problems” magically disappeared—attachment alternates were the full equivalents of their slide-alone counterparts (of the same sound-path length). Longer sound-path attachment notes were a “natural” sounding extension in terms of tone quality.

By contrast, Mr Hagmann’s main prototype involved simply placing a Bach 50 (“bass”) slide on a Bach 42B bell (with, of course, a Hagmann valve), with conventional Bb/F tuning. Again, all the usual attachment problems magically disappeared. Low-tenor and sub-tenor notes had a more “robust” and “darker” tone quality—and, perhaps surprisingly, the larger-bore slide did not seem to detract from high-register brightness. When tested by Andrea Bandini of Orchestre de la Suisse Romande, he remarked, emphatically that: “Il est plus ouvert et offer une meilleure projection!” Coincidentally (and unbeknownst to René), this was (except for the valve) exactly the same combination that Jay Friedman was exploring within roughly the same time period. And Jay prefers that combination because, as he has said: “it’s more open and with better projection!”

Of course, this confirms the earlier observation that an attachment represents an extension of the region near the upstream end of the gooseneck—the bore of which indeed matches that of the incoming arm of the slide. This is also appropriate for inline dual-valve designs using compact rotary valves. For “bulkier” valves, like the Hagmann or Thayer, the valves themselves take up more space along (what would be) the gooseneck. So it’s appropriate that the downstream valve and attachment might be of slightly larger bore, and this is the basis of Mr Hagmann’s “progressive bore” design—using tapered ducts inside the valve (only feasible with his three-duct design).

With inline dual-valve designs, it doesn’t matter at all which attachment comes “first” (i.e. upstream). The “European” tuning of F contras, F/D-Bb-Ab, is entirely appropriate for this big trombone—much (much!) more so than the transposition of the popular Bb/F-Gb-D bass trombone to: F/C-Db-A. [I can demonstrate this with ETSP Charts, if anyone is interested.] The European tuning of the contra transposes to Bb/G-Eb-Db, which is an excellent combination. Even better is Bb/G-E-D, which is my preferred tuning for bass and continuously chromatic tenor. [I attach a picture of a Willson bass customized to this tuning with 14.3 mm tubing throughout slide, both valves, and both attachments (taken from the compendium of Tiffany Johns). The thumb trigger operates the (downstream) G attachment.]

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Kbiggs
Posts: 1768
Joined: Mar 24, 2018

by Kbiggs »

Adding to/clarifying my initial post:

Adding a second valve seems to create the largest difference in response, whether you’re going from the open horn to two valves, or adding a second valve while already playing a valved note. Adding extra tubing means the lips have to vibrate and create a wave to excite an additional chunk of static air/space in order to create a pitch.

I suppose this is the Holy Grail for bass trombonists: a bass trombone that minimizes the feeling/response between open, one valve, and two valve combinations.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

[quote="Kbiggs"]

I suppose this is the Holy Grail for bass trombonists: a bass trombone that minimizes the feeling/response between open, one valve, and two valve combinations.[/quote]

Referring to the Bb/G-E-D Willson bass mentioned earlier, with valves and attachments bores matched to the standard 14.3 mm slide, the E attachment is 20¢ sharp, which guarantees an exactly in-tune D double-valve combination. The harmonics of the G attachment with the slide closed are indistinguishable (in all respects) from those in slide-alone 4th position. Similarly, the E-attachment harmonics in its "first" position (about 16 millimetres extended) are indistinguishable (in all respects) from those in slide-alone 7th position. Of course, we don't have a slide-alone "9th" position for comparing the double-attachment D harmonics. But we can compare these with G-attachment 6th position and E-attachment 3rd position—and, as expected, these are all indistinguishable in terms of intonation, tone-quality and attack response.

By the way, the (slightly sharp) E attachment is very easy to get used to: E-attachment 3rd position (for the D fundamental) lines up (exactly) with the slide-alone 4th position (for the G fundamental)—as it must (of course), according to the basic design.
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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

OK, the bass trombone is fundamentally not a particularly well-designed instrument...the question is what to do about it?

Maybe the answer is to radically redesign it, as Sesquitone has done for himself. I'd be really intrigued to try his instrument! It's hard to see that happening on a large scale though - certainly not anytime soon.

So with the instruments and mouthpieces available to us - which are much, much, much, much better than what was easily available even 30 years ago - the answer is in how we practice, and I have very specific recommendations.

I speak from experience. I was not a natural fit to the bass trombone. I'm an average-sized guy, not a great big person with air to spare, and I did not have a naturally great low register. What I did have was a good ear and an affinity for bass lines and the bottom of the ensemble.

I spent many years - well into my professional career - as a bass trombone player with a better than average high register and worse than average low register. When I started graduate school I played an ensemble placement audition in which I did not manage to center a single low C, and there were several. The auditions I won happened to prioritize my strengths - high register and clarity of articulation and pitch.

I tried many things over the years, including the Phil Teele long tones (until a trumpet player friend who hired me for many gigs offered me $10 to warm up ANY OTHER WAY), which helped but were detrimental to other important aspects of my playing.

What finally helped the most was extending my lip slurs all the way through the single and double valve registers. I now do daily lip slurs covering more than two octaves while holding down both valves, either single valve, and the open horn. I do them slow and fast.

Start with the connection between 2nd and 3rd partials. Assuming Bb/F/D tuning, find the A in long first position with both valves down (remember, the tuning adjustments for the different partials are bigger with the longer tubing); match the pitch to the open A and make it sound as good as you can, and then slur down to the D. Make that slur as smooth as you can get it. Look in a mirror and make sure your corners are staying engaged, not collapsing in the transition and then re-forming. Then expand up to the 4th partial and spend a lot of time with various 3-note slurs. When you're feeling pretty good about the D and the double valve notes in general, start there and go up through the partials to the 5th and back down, to the 6th and back down, etc.

Note how much air this takes, and I don't mean blowing lots of fast, hard air, I mean air in your body behind and underneath the sound. Stand or sit up straight; extend the crown of your head towards the ceiling as if it's suspended from a big helium balloon. Imagine your chest cavity as a big vessel that you are simply pouring air into with every breath. Keep your body in position to be ready for that air, so that no part of the inhale is wasted correcting your posture.

You might find that your slide migrates to a different position than you thought the double valve notes were in. Good! If you're getting the slurs to be smooth, then you've found the right place. If you've been lipping them down (or up, though I think that's more rare), that will not work when doing these slurs. With the slide in the right place, your articulations on those notes will improve TREMENDOUSLY.

I'll note again that the partials are not in tune with each other, and you will help yourself tremendously by making the adjustments at the slide. Start with the standard adjustments, though your particular instrument might be a little different. The center of the position area is 2nd and 4th partial; 3rd partial is probably a little sharp and needs to be adjusted out; 5th partial is probably a little flat and needs to come in (except on some instruments on the open horn in 3rd, 2nd, and 1st positions - 5th partial is weird that way); 6th partial is like 3rd but might need to go out slightly farther.

Happy practicing!
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brassmedic
Posts: 1447
Joined: Dec 14, 2018

by brassmedic »

I am skeptical of any claims that a single design modification "magically solved" all response problems.
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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

[quote="brassmedic"]I am skeptical of any claims that a single design modification "magically solved" all response problems.[/quote]

Oh yeah...remember when we thought the Thayer valve was going to solve all our low register problems? I got them. They didn't.

Though I still wouldn't want to play a stock closed-wrap 50B3.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

[quote="brassmedic"]I am skeptical of any claims that a single design modification "magically solved" all response problems.[/quote]

Okay, so if you (i.e. anyone reading this) want to "experience the magic", and you have access to a "large-bore" tenor trombone (Bb/F) with conventional "oversized" attachment—this usually means 13.9 mm slide with a 14.3 mm attachment (and "reasonably good" valve)—and a "bass" trombone (e.g. 14.3 mm) slide with compatible slide receiver, try the following exercise. [And this is relevant to the theme of this thread, i.e. the so-called "second" valve.]

Start with the conventional Bb/F tenor. With the slide locked, tune the F attachment to match the pitch of (attachment fourth harmonic) F3 to (slide-alone third harmonic) F3. Wiggle the trigger back-and-forth to make sure the pitches are the same. [The tone quality will differ a bit because they're different harmonics.]

Now, with the attachment actuated, and slide still locked, lip-slur (in a relaxed way) down to F2. Do not try to use "embouchure compensation" to adjust the pitch of the F2—just let it sit wherever it wants to. Lip-slur back-and-forth the octave until the F2 feels very "relaxed". Listen to the two pitches on sustained tones. The pitch of the F2 will (most likely) be significantly flat compared with the upper octave. [Check with a tuner, if you wish.] And its tone quality a little "stuffy" (i.e. lacking energy in higher overtones.] If you try to compensate for the flatness—by "lipping" it up—it will get even more "stuffy". Also try (with relaxed lip slurs), with slide still locked: Bb2 -> F2 -> Bb1 -> F2 -> Bb2 . . . and so on. The Bb octaves should be well in tune with each other, but the F2 will be flat (and a bit stuffy). You might continue on down to the pedal F1, back and forth. The first-harmonic pedal F will typically be better in tune than the second harmonic F2.

Also, in a relaxed way, lip-slur, back-and-forth, with the trigger held down (slide still locked): F2 -> C3 -> F1 -> C3 -> F2 . . . . The C3 will be noticeably sharp and "uncentered" (i.e. easily lipped in either direction). The F2 still flat and stuffy.

Unlock the slide and play some etudes and exercises involving F2 and C3 played with the attachment. You will probably have to lip up the F2 and play the C3 well away from the bumpers. Tone quality will not be as "pure" as it would be if these notes were played in 6th position— which you should also check, for comparison. Also, for later comparison, play some etudes, arpeggios and scales in the upper tenor register. Also into the sub-tenor register.

*************

Now, switch to the "bass" trombone slide—and start over with all these exercises (using the same relaxed lip slurs). What do you immediately notice? Any "magic". No change? Slightly better? Noticeably worse in any way? It takes a lot more "air"? Or not? What about the upper register? It's "more open with better projection" over the entire range? Low-tenor and sub-tenor notes are "fuller" and "darker" without loss of "brightness" in the upper register?
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brassmedic
Posts: 1447
Joined: Dec 14, 2018

by brassmedic »

[quote="Sesquitone"]<QUOTE author="brassmedic" post_id="292048" time="1767809058" user_id="4102">
I am skeptical of any claims that a single design modification "magically solved" all response problems.[/quote]

Okay, so if you (i.e. anyone reading this) want to "experience the magic", and you have access to a "large-bore" tenor trombone (Bb/F) with conventional "oversized" attachment—this usually means 13.9 mm slide with a 14.3 mm attachment (and "reasonably good" valve)—and a "bass" trombone (e.g. 14.3 mm) slide with compatible slide receiver, try the following exercise. [And this is relevant to the theme of this thread, i.e. the so-called "second" valve.]

Start with the conventional Bb/F tenor. With the slide locked, tune the F attachment to match the pitch of (attachment fourth harmonic) F3 to (slide-alone third harmonic) F3. Wiggle the trigger back-and-forth to make sure the pitches are the same. [The tone quality will differ a bit because they're different harmonics.]

Now, with the attachment actuated, and slide still locked, lip-slur (in a relaxed way) down to F2. Do not try to use "embouchure compensation" to adjust the pitch of the F2—just let it sit wherever it wants to. Lip-slur back-and-forth the octave until the F2 feels very "relaxed". Listen to the two pitches on sustained tones. The pitch of the F2 will (most likely) be significantly flat compared with the upper octave. [Check with a tuner, if you wish.] And its tone quality a little "stuffy" (i.e. lacking energy in higher overtones.] If you try to compensate for the flatness—by "lipping" it up—it will get even more "stuffy". Also try (with relaxed lip slurs), with slide still locked: Bb2 -> F2 -> Bb1 -> F2 -> Bb2 . . . and so on. The Bb octaves should be well in tune with each other, but the F2 will be flat (and a bit stuffy). You might continue on down to the pedal F1, back and forth. The first-harmonic pedal F will typically be better in tune than the second harmonic F2.

Also, in a relaxed way, lip-slur, back-and-forth, with the trigger held down (slide still locked): F2 -> C3 -> F1 -> C3 -> F2 . . . . The C3 will be noticeably sharp and "uncentered" (i.e. easily lipped in either direction). The F2 still flat and stuffy.

Unlock the slide and play some etudes and exercises involving F2 and C3 played with the attachment. You will probably have to lip up the F2 and play the C3 well away from the bumpers. Tone quality will not be as "pure" as it would be if these notes were played in 6th position— which you should also check, for comparison. Also, for later comparison, play some etudes, arpeggios and scales in the upper tenor register. Also into the sub-tenor register.

*************

Now, switch to the "bass" trombone slide—and start over with all these exercises (using the same relaxed lip slurs). What do you immediately notice? Any "magic". No change? Slightly better? Noticeably worse in any way? It takes a lot more "air"? Or not? What about the upper register? It's "more open with better projection" over the entire range? Low-tenor and sub-tenor notes are "fuller" and "darker" without loss of "brightness" in the upper register?
</QUOTE>
My tenor is Bach 42 with Thayer valve. My bass slide is Shires. Middle Bb on a Bach 42 is flat compared to the other partials, so F in the staff has to be played quite a bit out from first position. If you tune the valve so that the F in the staff matches, that puts the low F all the way in, about where the middle Bb lies, so yes, quite a bit flatter than the middle F. With the bass slide it is exactly the same difference between the 2 F's. The middle F is even further out on the slide, but the low F has the same degree of flatness compared to the middle F. So no, bass slide does not magically make partials line up (and really there is no such thing as a trombone where the different partials are in tune with each other; that's why we have to adjust every note with the slide).

Response is very good on C and B with the valve, and using the bass slide doesn't seem to improve it. I will say that the response and tone quality with the .547 slide are better for me in 6th and 7th, and I would attribute that to the fact that the outer slide is approx. .580 bore, whereas the valve tubing is only .562. :bassclef: :line4: This partial is sharper than :bassclef: :space5: (Bb) this partial, so by the time you get down to E vs. B, there is a considerable difference. That's why you have to play C and B so far out on the slide when using the valve. It's not a bore mismatch issue.
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muschem
Posts: 372
Joined: Jan 17, 2021

by muschem »

[quote="brassmedic"]<QUOTE author="Sesquitone" post_id="292075" time="1767820175" user_id="15151">

Okay, so if you (i.e. anyone reading this) want to "experience the magic", and you have access to a "large-bore" tenor trombone (Bb/F) with conventional "oversized" attachment—this usually means 13.9 mm slide with a 14.3 mm attachment (and "reasonably good" valve)—and a "bass" trombone (e.g. 14.3 mm) slide with compatible slide receiver, try the following exercise.[/quote]
My tenor is Bach 42 with Thayer valve. My bass slide is Shires. Middle Bb on a Bach 42 is flat compared to the other partials, so F in the staff has to be played quite a bit out from first position. If you tune the valve so that the F in the staff matches, that puts the low F all the way in, about where the middle Bb lies, so yes, quite a bit flatter than the middle F. With the bass slide it is exactly the same difference between the 2 F's. The middle F is even further out on the slide, but the low F has the same degree of flatness compared to the middle F. So no, bass slide does not magically make partials line up (and really there is no such thing as a trombone where the different partials are in tune with each other; that's why we have to adjust every note with the slide).

Response is very good on C and B with the valve, and using the bass slide doesn't seem to improve it. I will say that the response and tone quality with the .547 slide are better for me in 6th and 7th, and I would attribute that to the fact that the outer slide is approx. .580 bore, whereas the valve tubing is only .562. :bassclef: :line4: This partial is sharper than :bassclef: :space5: (Bb) this partial, so by the time you get down to E vs. B, there is a considerable difference. That's why you have to play C and B so far out on the slide when using the valve. It's not a bore mismatch issue.
</QUOTE>

One of the things that fascinates me about playing an instrument is how our individual experiences can be so similar in some ways and nearly opposite in others. I've tried Sesquitone's experiment on various combinations of three different tenor bells (8" flare & 8.5" flare, 3 different materials), two different valve sections (one rotor & one axial), and four different slides (.525, .547 [x2], and .562/.578), and for me, there is a significant difference in both response and partial intonation that is consistent moving from tenor slides to a bass slide.

How we perceive "response" is fairly subjective, but intonation is more quantitative, and that part intrigues me. Of course, we can adjust intonation to compensate in a number of ways (many of which don't involve changing the slide position), and those adjustments might not always be a result of conscious decisions on our part. Is intonation on F2 and C3 better for me on a bass slide because I expect it to be? That is entirely possible. Is intonation on those notes unchanged when brassmedic plays them on a bass slide, because that aligns with his experience and expectations? Also maybe? My experimenting so far has involved an "oversized" bass slide (.562/.578 - so the lower leg is larger than the valve bore on tenor) because it is what I had readily available (I'm working on getting other bass bore combinations to try). I also didn't try Sesquitone's experiment with a tuner until I had already spent a couple of weeks playing tenor bell sections with my bass slide. By that time, I had already formed a subjective impression of how the setup played, and that may have contributed to some confirmation bias that skewed my results on the tuner.

I can easily accept that I may be doing something different when I use a bass slide... maybe my horn angle changes, or I play more open/closed, or... a number of possibilities exist. The interesting part (to me) is how consistent my results are, going back and forth between tenor slides and a bass slide on different valves and bells. I think that's interesting in large part because, while I'd love to be a more consistent player, I know that I'm not. I do long tones in front of a tuner every day as part of my warmup session, so I see the variation day-to-day even when my equipment remains constant. But, so far, every time I've checked it, F2 and C3 with the valve align nearly perfectly on a bass slide and the same notes are much different on my tenor slides. If it's confirmation bias, and I cannot discount that it may be, it is a very strong effect indeed to produce more consistent results than I believe myself to be capable of.

Whether the cause for the difference is entirely pyschosomatic on my part or rooted in actual physics, I plan to continue testing this and aiming for a closer matched-bore setup, since my initial results have been so good. Maybe this will eventually all wear off, like the honeymoon period for a shiny new mouthpiece. Or, maybe something about my approach just works better in this setup. Whatever it is, I'll take it for as long as it lasts :)
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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

Mike, you're moving towards an essential point here, which is that different players access the low register in different ways, and not always in the way that is ideal to their embouchure type.

Doug Elliott and Dave Wilken can speak better on this than I can, but I think many players who jut their jaw out and tilt the horn up to play low would be better off leaving their jaw in place and tilting the horn down. Not all, but many. These motions affect the pitch, and specifically how well the octave between 2nd and 4th partial matches.

I also think Sesquitone's experiment with a larger bore slide says more about the bore of the slide than the bore of the valve tubing.
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brassmedic
Posts: 1447
Joined: Dec 14, 2018

by brassmedic »

[quote="muschem"]

One of the things that fascinates me about playing an instrument is how our individual experiences can be so similar in some ways and nearly opposite in others. I've tried Sesquitone's experiment on various combinations of three different tenor bells (8" flare & 8.5" flare, 3 different materials), two different valve sections (one rotor & one axial), and four different slides (.525, .547 [x2], and .562/.578), and for me, there is a significant difference in both response and partial intonation that is consistent moving from tenor slides to a bass slide.[/quote]
But Benny said the slide bore needs to match the valve and valve tubing. Your lower leg is .578 and the valve tubing is .562, so you're not actually doing his experiment.
How we perceive "response" is fairly subjective, but intonation is more quantitative, and that part intrigues me. Of course, we can adjust intonation to compensate in a number of ways (many of which don't involve changing the slide position), and those adjustments might not always be a result of conscious decisions on our part. Is intonation on F2 and C3 better for me on a bass slide because I expect it to be? That is entirely possible. Is intonation on those notes unchanged when brassmedic plays them on a bass slide, because that aligns with his experience and expectations? Also maybe? My experimenting so far has involved an "oversized" bass slide (.562/.578 - so the lower leg is larger than the valve bore on tenor) because it is what I had readily available (I'm working on getting other bass bore combinations to try). I also didn't try Sesquitone's experiment with a tuner until I had already spent a couple of weeks playing tenor bell sections with my bass slide. By that time, I had already formed a subjective impression of how the setup played, and that may have contributed to some confirmation bias that skewed my results on the tuner.

Very possible. Also very possible that the players who tried Benny's "experiment" and proclaimed that it magically solved every problem just thought that because they wanted it to do that. I couldn't even tell you how many times I've tried a mouthpiece that felt like a panacea at first, but turned out to be disappointing on further use. One time I was with a tuba player, trying out a baritone horn. I remarked that the low Bb was very flat. He picked up the horn and to my ear clearly lipped it up until it was in tune, and then said, "You have to find the center of the pitch". He thought I was subconsciously lipping it down because I "expected" it to be flat, but I think he was subconsciously lipping it up.

Am I subconsciously lipping the pitch to be where I "expect" it to be? Maybe, but when I play my Shires bass trombone, the middle Bb is not flat. When I play my Bach tenor, the middle Bb is flat (something I have to remind myself every time I switch horns). Am I subconsciously lipping it down? I suppose that's possible, but why would I expect the tuning note to be flat?
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harrisonreed
Posts: 6479
Joined: Aug 17, 2018

by harrisonreed »

[quote="GabrielRice"]

Doug Elliott and Dave Wilken can speak better on this than I can, but I think many players who jut their jaw out and tilt the horn up to play low would be better off leaving their jaw in place and tilting the horn down. Not all, but many. These motions affect the pitch, and specifically how well the octave between 2nd and 4th partial matches.
[/quote]

I've heard about this embouchure type I think, but this would be disastrous for my low range. I have to tilt up, especially for pedals. I think I actually switch to upstream for pedals, but it might just be in my head like some here have said. Might be Dave who said it wasn't likely. Not trying to make a scene, but just point out just how variable everyone is with how they play.
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tbonesullivan
Posts: 1959
Joined: Jul 02, 2019

by tbonesullivan »

The quartventil was first invented back in the 19th century. Has the bore of the attachment always been greater than the bore of the inner slide? I know that some earlier designs had the valve much farther "downstream" after the gooseneck. Sometimes part of a tuning slide. I will say that I also do prefer to use 6th position for sustained C3 and / or F2. I also don't use both valves unless I need to, as I would prefer to play D2 in F valve position 4.

Definitely some very interesting food for thought in this thread, even if much of it goes WAY over my head.
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PhilG
Posts: 15
Joined: Apr 09, 2018

by PhilG »

[quote="JTeagarden"]I'm pretty sure "Bass Trombone and the 2nd Valve" is a Roald Dahl children's book.[/quote]

:lol:
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Digidog
Posts: 483
Joined: Dec 13, 2018

by Digidog »

[quote="brassmedic"]I couldn't even tell you how many times I've tried a mouthpiece that felt like a panacea at first, but turned out to be disappointing on further use.[/quote]

It seems to me that every mouthpiece I try is a miracle come true on the first, brief play-around. I feel like I’ve never been better.

The real trick is to discern and distinguish the sensation from something new, from a change and from something fresh, from that deeper knowing of what I really feel and percieve when I’m into the regular, every-day playing.
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Kbiggs
Posts: 1768
Joined: Mar 24, 2018

by Kbiggs »

[quote="GabrielRice"]Mike, you're moving towards an essential point here, which is that different players access the low register in different ways, and not always in the way that is ideal to their embouchure type.

Doug Elliott and Dave Wilken can speak better on this than I can, but I think many players who jut their jaw out and tilt the horn up to play low would be better off leaving their jaw in place and tilting the horn down. Not all, but many. These motions affect the pitch, and specifically how well the octave between 2nd and 4th partial matches.
[/quote]

This describes my playing. After my last lesson with Doug, I’ve made progress into the double-valve pedal register keeping the jaw as neutral as possible, using appropriate embouchure motion (not a shift), and adjusting the horn angle down slightly. It’ll take more practice to increase my muscle memory.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone » (edited 2026-01-10 12:24 p.m.)

[quote="Kbiggs"]Has anyone (a) developed and (b) successfully marketed and sold a trombone where the second valve is a slightly increased size to help reduce compression when using the second valve? What have been the results?[/quote]

Since this discussion is about the "second" valve—i.e. that operated by the finger trigger and (usually) downstream of the thumb-trigger-operated valve—I would encourage everyone to to view the YouTube presentation (of several years ago) by Denson Paul Pollard: "Explanation of G valve tuning with musical examples". Mr Pollard's bass trombone has two Hagmann valves, featuring Mr Hagmann's "progressive bore" principle, where the bore through the valves starts off matching that of the slide and slowly increases through the interior tubing of the valves in order to mimic the expansion of the gooseneck that would otherwise occur (without the valves). The bore through each of the individual wraps is constant, but when the valves are not engaged, the bore "progressively" increases through the tapered tubes inside each valve. The "clarity" of the G-natural valve demonstrated by Mr Pollard is due to the (discontinuity-free) progressive bore—and has absolutely nothing to do with the fact that the G-natural wrap length is (209 mm) shorter than the (now more popular) G-flat tuning. Watch Mr Pollard's thumb and finger action; and note the naturally flowing and (mostly) short-positioned slide manipulation. Of course, progressive-bore can be used with any combination of valve tunings. But it is limited to the Hagmann valve geometry because of the three-tube design, featuring slightly tapered tubes inside the rotor cage. With very compact rotaries, it is not needed—because not much length is taken up along the gooseneck. In this case, the "standard" match-bore principle can be used to advantage.
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Burgerbob
Posts: 6327
Joined: Apr 23, 2018

by Burgerbob »

My Bach 36 plays very well (and in tune) despite the valve section being TWO sizes too large for the slide bore (or, tellingly, about the same size as the outer slide).
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

[quote="Burgerbob"]My Bach 36 plays very well (and in tune) despite the valve section being TWO sizes too large for the slide bore (or, tellingly, about the same size as the outer slide).[/quote]

When you say "plays very well (and in tune)", does that mean that, for tenor repertoire (i.e. E2 and above), you are as completely comfortable playing second and third harmonics in attachment positions 1 an 2 as you are in slide-alone positions 6 and 7, respectively—depending on which combinations provide the most facile slide motion? What about third-harmonic Bb2 in attachment position 3, that has a longer sound-path? Any other handy tenor-range attachment alternates? [This is still relevant to the "2nd valve" question.]
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

It’s probably fair to say that the “2nd valve” here (usually) refers to that for the finger-trigger-operated Gb attachment, in line on the gooseneck, downstream of the “1st valve”, which is for the thumb-trigger-operated F attachment on a bass trombone, where the double combination produces a D fundamental—i.e. Bb/F+Gb=D. This seems to have “evolved” to be the most common tuning combination, much more so than the other inline independent valve combination using the G-natural 2nd valve: Bb/F+G=“Eb”, where the “Eb” is too flat to be useful, so D2 is the shortest-position available double-valve (equitempered) note. And where the dependent geometry seems to (now) be far less popular.

This raises the question: “is ‘evolution’ in instrument design the best strategy, or is there a more rational approach based on optimal design, given desirable attributes?”

Blair Bollinger states: “You have two [independent] valves, use both”. But, given the two independent attachments, are they tuned in an optimal way? Mr Bollinger addresses this question. It is a (demonstrable) fact that the harmonics of the F and Gb attachments are too close together compared with the distribution of the Bb harmonics. So the Bollinger tuning is an attempt to spread the two sets of attachment harmonics apart. The alternative of a G-natural tuning of the second valve achieves this nicely, but this puts the slide position for B1 a long way out. Halfway between G-natural and G-flat for the “second-valve” Bollinger tuning is a “reasonable” compromise—but it takes for granted that the “first-valve” tuning must remain at F, presumably to be compatible with the ubiquitous P4 tuning of single-valve tenor trombones.

An optimal design approach would state: “You have two independent valves available. How should the respective attachments be tuned to achieve desirable attributes?” And the accompanying question: “What are the desirable attributes (i.e. design criteria)?”

Regarding the latter, since this is a bass trombone, we would like to fill in the “tenor gap” (using a seven-position slide in Bb), i.e. the missing notes: Eb2, D2, Db2, C2, and B1, between the first and second Bb harmonics. If that’s the only criterion, you don’t need two valves. The single valve P5 tuning, Bb/Eb, provides exactly those five notes in the available (only) five positions from the Eb-attachment’s second harmonic, extending the range down to pedals continuously. Slide manipulation is no more awkward than with a (non-attachment) Bb tenor trombone. Other higher Eb-attachment harmonics are not useful because they mostly “duplicate” (different) Bb harmonics.

But bass-trombone repertoire, by definition, is in the lower register. And, with the Bb/Eb combination, this will involve a lot of fully extended slide positions. We know that, for a single-valve tenor (without regard to necessarily extending the lower register), the (thumb-trigger) minor-third attachment is (demonstrably) optimal for the given design criterion of providing the most handy attachment alternates in the otherwise awkward low-tenor register. With a seven-position slide in Bb, the lowest (non-pedal) G-attachment note is D2. So, with two (independent) valves available for the bass-trombone design, perhaps we can achieve compatibility with that by keeping the thumb-trigger G-attachment and choosing a second-valve (finger-trigger) attachment tuning to provide (at least) the missing Db2, C2, and B1 using the second harmonic of that attachment and of the double-attachment combination—and maybe even provide a non-pedal Bb1, nicely rounding out a continuous (non-pedal) range. And check to see if higher second-valve harmonics provide any other handy attachment alternates. It doesn't matter which valve is upstream on the gooseneck. We will use matched-bore, of course, making sure there is smooth continuity through the inside of the slide receiver.

[I will leave the discovery of that second-valve tuning as an “exercise for the reader”. Since the tuning of the double combination is determined by the individual tunings of the independent attachments, you might want to choose the double tuning first, and "work backwards" to find the necessary tuning of the second valve. Some options worth trying for the double: D2, Db2, C2. Hint: transposition (up a P4) of the European tuning of the F contra, F/D+Bb=Ab, provides a “close second” optimal solution for these design criteria. European tuning is optimal for the big contra. The obvious "problem" with the American tuning, F/C+Db=A, is that, again, the two sets of independent-attachment harmonics are too close together. Also, the Gb1 is much further out than with the Ab double.]]

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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

[quote="Sesquitone"]This raises the question: “is ‘evolution’ in instrument design the best strategy, or is there a more rational approach based on optimal design, given desirable attributes?”[/quote]

Fair question.

Blair Bollinger states: “You have two [independent] valves, use both”. But, given the two independent attachments, are they tuned in an optimal way? Mr Bollinger addresses this question. It is a (demonstrable) fact that the harmonics of the F and Gb attachments are too close together compared with the distribution of the Bb harmonics.


Demonstrable fact? No. Valid opinion, sure.

So the Bollinger tuning is an attempt to spread the two sets of attachment harmonics apart. The alternative of a G-natural tuning of the second valve achieves this nicely, but this puts the slide position for B1 a long way out. Halfway between G-natural and G-flat for the “second-valve” Bollinger tuning is a “reasonable” compromise—but it takes for granted that the “first-valve” tuning must remain at F, presumably to be compatible with the ubiquitous P4 tuning of single-valve tenor trombones.


Actually, the Bollinger tuning was an accident that turned out to be happy for him and useful for many others after his advocacy and explanation of its benefits. It was an "attempt" at Bb/F/Gb/D tuning. The tech who installed the Thayer valves on his Bach 50 got the length of the second valve tubing wrong.

An optimal design approach would state: “You have two independent valves available. How should the respective attachments be tuned to achieve desirable attributes?” And the accompanying question: “What are the desirable attributes (i.e. design criteria)?”


Sure.

We know that, for a single-valve tenor (without regard to necessarily extending the lower register), the (thumb-trigger) minor-third attachment is (demonstrably) optimal for the given design criterion of providing the most handy attachment alternates in the otherwise awkward low-tenor register.


We do? Again, opinion, not demonstrable fact.

With a seven-position slide in Bb, the lowest (non-pedal) G-attachment note is D2.


Is it? The C on an F attachment is not particularly useful unless you give up the F in 1st. Maybe it's a little better with the shorter tubing of a G attachment. And the B2 ends up somewhere in no-mans-land...I mean 5th position. Ish.

-------------------

I'm going to leave your argument there...

A lot of useful things on the planet Earth have occurred through evolution, and for myself I count the Bb/F/D bass trombone tuning as one of them. It give a Bb Major arpeggio in first position, and it puts the low C and B - the notes where tenors fear to tread and that really distinguish us as bass trombonists - in pretty reasonable slide positions. I see the close alternates between the F and Gb valves as a feature, not a bug.

I can understand the utility of Blair's tuning as he demonstrates it. He's got a lot of notes lined up in 3rd position rather than first, and he LOVES to use them that way. He also says "There are slide guys and buttons guys...I'm a buttons guy." That's as close to a direct quote as I can remember. He might use non-gendered language now...that was years ago.

I can also understand the utility of Paul Pollard's Bb/F/G/Eb-ish tuning, but he has the trade-off of a B1 that's all the way at the end of the slide. I like my C1 near fourth position G and my B1 near 5th position F#. Different strokes.

I'm a slide person, not a buttons person. I played a dependent for years, and I play a single valve bass trombone if I can.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone » (edited 2026-01-16 3:50 p.m.)

Yes, thanks Gabe, for your close reading. Of course you are right. I threw in the "demonstrable facts" to see who was paying attention. I was not aware of Mr Bollinger's tech's mistake—although I do know that something similar happened with early versions of the adoption of Hagmann valves by B&H for their inline bass.

A slide length that has seven available positions in Bb has six positions with the G (natural) attachment engaged (that's a mathematical/geometrical fact). So the lowest (equitempered) fundamental is indeed D. [With the Gb valve, the sixth position (Db) is a tad beyond slide-alone seventh.]

By the way, there are a lot of nice arpeggios available with the minor-third tuning: a minor-seventh (or major-sixth) in a single position across the bass clef—easily modified to other (four-note) chords within one or two slide-position shifts. Very much like the upper register of the slide-alone harmonics. Similarly, with the Bb/G+E=D tuning in the sub-tenor register. The basic single-position chord between the first and second slide-alone harmonics is a minor-sixth (or half-diminished).

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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone » (edited 2026-01-17 1:27 a.m.)

[quote="GabrielRice"]Actually, the Bollinger tuning was an accident that turned out to be happy for him and useful for many others after his advocacy and explanation of its benefits. It was an "attempt" at Bb/F/Gb/D tuning. The tech who installed the Thayer valves on his Bach 50 got the length of the second valve tubing wrong.

I can understand the utility of Blair's tuning as he demonstrates it. He's got a lot of notes lined up in 3rd position rather than first, and he LOVES to use them that way. He also says "There are slide guys and buttons guys...I'm a buttons guy." That's as close to a direct quote as I can remember. He might use non-gendered language now...that was years ago.

I can also understand the utility of Paul Pollard's Bb/F/G/Eb-ish tuning, but he has the trade-off of a B1 that's all the way at the end of the slide. I like my C2 near fourth position G and my B1 near 5th position F#. Different strokes.

I'm a slide person, not a buttons person. I played a dependent for years, and I play a single valve bass trombone if I can.[/quote]

The following might be called: "Finger-wagging arpeggios using the 2nd valve".

With the G-natural 2nd-valve tuning, you have a Gm7 arpeggio (with the root of G2) available in first position (slide closed)—mimicking the slide-alone Gm7 an octave higher, also (mostly) fixed in first position. [The top G4 is the "first" available equitempered note along the seventh harmonic.] As you descend chromatically, the "almost-fixed-position" is retained for F#m7 and Fm7. The Em7 and Ebm7 are still within about half a position increment throughout the two octaves. And the lowest Dm7 positions deviate by about two-thirds of a position. Note that G-natural 2nd-valve tones have the same sound-path lengths as their slide-alone counterparts for the first four attachment positions. The point being that a lot of other arpeggios of four-note chord types (or their inversions) on different roots are available usually within one position increment either side of the minor-seventh arpeggio.

With the G-flat (F-sharp) 2nd-valve tuning, the opposite is true. Here, the deviations in the highest available arpeggio, F#m7, are wide, and they get narrower as you descend: the two-octave Dm7 is close to (slide-alone) sixth position all the way. With the G-flat tuning, only the first three attachment positions have the same sound-path lengths as their slide-alone counterparts.

With the G-half-flat (Bollinger) tuning of the 2nd valve. The "straight-up" fixed-position arpeggio is Em7 sitting right on slide-alone fourth position (attachment third position) in the middle of the slide extension. The higher and lower arpeggios have slide deviations of less than half a position increment. Again, with this tuning, only the first three attachment positions have tones with the same sound-path length as the corresponding slide-alone tones. A rapid "finger-wagging" up-and-down lip-slurred E-minor-seventh in the middle of the slide—<B>alternating</B> between attachment and slide-alone harmonics—is one of Mr Bollinger's favourite demonstrations of this tuning. [The same demonstration could be made for the G-minor-seventh in first position for the G-natural tuning.]

All of the above can be seen <I>at a glance</I> from the ETSP Charts shown below. These are plots of Equitempered Tones (vertical axis) versus Slide Position (horizontal axis). The black dots represent slide-alone equitempered tones. The "asterisks" represent available "2nd-valve" tones for the respective second, third, and fourth attachment harmonics. [For clarity, the "1st-valve" (F-attachment) tones are not shown. Nor are attachment pedals. However, the second harmonic of the double-attachment tones is sketched in (pink) for reference.] The slightly curved lines sloping down to the right represent <I>all </I>tones along individual harmonics.

Finally, note the (slight) difference in the double-valve position of the B1 in the three cases. Also note the available non-pedal Bb1 for the G-flat tuning: it's this B-flat that's "all the way at the end of the slide". The B-natural for the G-natural tuning is just beyond slide-alone sixth position; as Mr Pollard says: "Still there!" Whereas the Bollinger B1 is just short of sixth. For the G-flat tuning (D double), the B1 is about half-way between slide-alone fifth and sixth.

PS [In case anyone wants to know] The Bb/G+E=D tuning (ETSP Chart not shown) has all the advantages of the (closer-positioned) minor-sixth arpeggios, plus the advantage of the (closer-positioned) double-attachment tones—with the triggers switched: G(thumb), E(finger), D(double). As you can see (also at a glance), the uniform <I>interleaving </I>of the B-flat and G-natural harmonics closely duplicates (an octave lower) the natural harmonics of the Bb instrument in the upper register—providing the possibility of facile slide motion all the way down into the sub-tenor range.

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Kbiggs
Posts: 1768
Joined: Mar 24, 2018

by Kbiggs »

My apologies if this appears to be a reductionist argument, but any discrepancies in intonation—regardless of the length of tubing on the respective valves—can be adjusted by use of the main handslide, no?

Different systems of valve tunings then become a matter of education, training, and habit, no?

While different systems of valve tunings have their advantages and disadvantages, choice of valve tunings then becomes a matter of preference.

Chacun à son goût, non?
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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

Bingo
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hornbuilder
Posts: 1384
Joined: May 02, 2018

by hornbuilder »

Nailed Kenneth
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

[quote="Kbiggs"]Different systems of valve tunings then become a matter of education, training, and habit, no?

While different systems of valve tunings have their advantages and disadvantages, choice of valve tunings then becomes a matter of preference.

Chacun à son goût, non?[/quote]

A combination of education, training, and habit seems to favour a taste for the single quart valve as the default. Then, for the Bb/F combination, in order to fill in the missing B1, a variety of other tunings for a second dependent or independent valve become a matter of preference. Given a range of choices for the double-valve tuning (Eb, D, Db, C), it's perhaps a bit surprising, then, that for a continuously chromatic bass trombone, there seems to be so little interest in a <B>single</B> quint valve. This is a unique "solution": with a "tenor"-length hand-slide, the second harmonic tones of the five fundamentals available with the valve just exactly fill in the five missing tones in the tenor gap, blending seamlessly into pedals. With a Bb/Eb combination, slide manipulation is no more awkward than with the (non-attachment) Bb tenor. The single-valve instrument is significantly lighter than typical dual-valve arrangements.
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brassmedic
Posts: 1447
Joined: Dec 14, 2018

by brassmedic »

[quote="Sesquitone"]The single-valve instrument is significantly lighter than typical dual-valve arrangements.[/quote]
Absolute weight isn't the issue. Balance is much more important. Why do tenor trombones have counterweights? If absolute weight were the only issue, then counterweights would make the instrument harder to hold. They don't. Valves on bass trombones are behind the fulcrum point, so they counterbalance the slide section.
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Burgerbob
Posts: 6327
Joined: Apr 23, 2018

by Burgerbob »

a Bb/Eb instrument makes sense in so many ways, until you actually try to play music on one.
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hornbuilder
Posts: 1384
Joined: May 02, 2018

by hornbuilder »

[quote="Burgerbob"]a Bb/Eb instrument makes sense in so many ways, until you actually try to play music on one.[/quote]

<EMOJI seq="2764" tseq="2764">❤️</EMOJI> <EMOJI seq="1f609" tseq="1f609">😉</EMOJI>
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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

I have a colleague here in the Boston area - primarily a tenor trombonist - who used to do a lot of bass trombone doubling in theaters on a Mt. Vernon Bach 50B tuned Bb/flat E. I subbed for him on The Producers and was astounded to watch him navigate that book that way when I went in to audit.
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tbonesullivan
Posts: 1959
Joined: Jul 02, 2019

by tbonesullivan »

[quote="GabrielRice"]I have a colleague here in the Boston area - primarily a tenor trombonist - who used to do a lot of bass trombone doubling in theaters on a Mt. Vernon Bach 50B tuned Bb/flat E. I subbed for him on The Producers and was astounded to watch him navigate that book that way when I went in to audit.[/quote] oh wow, that must have required a longer tuning slide, correct? I have sometimes been curious about the areas in the Ostrander books for learning Flat F and other tunings for single valve instruments.
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GabrielRice
Posts: 1496
Joined: Mar 23, 2018

by GabrielRice »

Yes, it had a custom open wrap and a longer valve slide.

Ray Premru would pull his F slide about 2 inches to play great low Cs in 7th position. When I practice a single valve bass I always spend some time in that tuning. If you put low Eb in normal third it all lines up pretty well.

In fact, that's another independent valve tuning strategy I've seen: long F slide so that you can play a really solid low C in normal 7th, and then use the 2nd valve for all Fs and Cs in the staff.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

[quote="GabrielRice"]Ray Premru would pull his F slide about 2 inches to play great low Cs in 7th position. When I practice a single valve bass I always spend some time in that tuning. If you put low Eb in normal third it all lines up pretty well.

In fact, that's another independent valve tuning strategy I've seen: long F slide so that you can play a really solid low C in normal 7th, and then use the 2nd valve for all Fs and Cs in the staff.[/quote]

Ray would also play an "authentic sounding" B1 in the same position just by "embouchure adjustment" alone. You could see his cheeks puff out (just a little).

And if the valve is tuned to "sharp E" rather than "long F"—specifically, 19.7¢ sharp E (so that D2 sits exactly at slide-alone fourth position), the single-valve C2 is about a third of a position increment short of (slide-alone) seventh position. See blue highlighted stars on the accompanying ETSP Chart.

Then, if the "other" valve is tuned to G-natural, you have (by design) a perfectly in-tune double-valve D2 with the slide closed, and another C2 essentially at (slide-alone) fourth position. The B1 is about halfway between (slide-alone) fifth and sixth. And you have a non-pedal Bb1 at the end of the slide. See pink circled tones. [Repeated an octave below in pedals.]

This is my preferred tuning—but with the triggers reversed: Bb/G(thumb)+E(finger)=D(double). Compatible with the single-trigger minor-third-attachment tenor (Bb/G or C/A) and alto (Eb/C).

PS The dashed lines show whole-tone increments between adjacent harmonics. [This is a good "slide facility" diagnostic: the more uniform the slope, the more "natural" feeling the slide manipulation—mimicking the very facile slide-alone upper register. Note that between-adjacent-harmonic whole-tone runs are "against-the-grain" below the ninth harmonic, but reverse direction above that.] Curves sloping down to the right connect all tones along individual harmonics. Black dots are equitempered slide-alone tones. Open circles represent G-attachment equitempered tones (on the first five harmonics). Stars are E-attachment equitempered tones (first three harmonics). And cartwheels are for the double combination.

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Finetales
Posts: 1482
Joined: Mar 23, 2018

by Finetales » (edited 2026-01-19 11:06 a.m.)

I own a bass trombone in F/Gb (typical oversized valves) and one of Benny's experimental bass trombones in G/E (matched bore) valves. I play them both a lot.

Long story short: they are both great instruments that do everything well. For me, the F/Gb and G/E each have a lot of advantages and some disadvantages, in about equal measure. They are just in different places! Some technical licks lay more naturally in F/Gb, and others lay more naturally in G/E. At some point I might do a video demonstrating passages that take advantage of each system.

For what it's worth, I never liked F/G. Like others in this thread, I don't like that the combination is Eb and not D. But it works great for some people. With G/E, the E is tuned slightly sharp so that the D combination is exactly where you would expect. This works out great for me because I like my Gb valve sharp as well.

I also find that putting the G valve in the thumb makes much more sense to my brain. Every time I've tried an F/G, it was a struggle not playing Gb positions on the second valve. But F vs. G on the thumb comes naturally.

I have my own theory that the best dependent valve setup, e.g. for a single tenor or bass with a removable slot-in valve, would be G/Eb, which would allow you a lot of the flexibility of G/E/D and much more than dependent F/D. It would be fun to try this setup on alto or soprano, where there's not room for two independent valves...but now I'm getting into dangerous territory!
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MStarke
Posts: 1031
Joined: Jan 01, 2019

by MStarke »

For me the keypoint of F/G or Gb/D or F/D (for a dependent system) is that the first valve has the same tuning as most tenors with valve. Of course it can be discussed if the latter is a good choice.

But generally speaking it is certainly practical not only for doublers, but also for people switching and sometimes for section playing to have the same logic at least on the first valve.

If the above were not the case, and it could be viewed completely isolated, E/G/D or G/E/D sounds like a good idea.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

[quote="MStarke"]For me the keypoint of F/G or Gb/D or F/D (for a dependent system) is that<I> the first valve has the same tuning as most tenors </I>with valve. Of course it can be discussed if the latter is a good choice.

But generally speaking it is certainly practical not only for doublers, but also for people switching and sometimes for section playing to have the same logic at least on the first valve.

If the above were not the case, and it could be viewed completely isolated, E/G/D or G/E/D sounds like a good idea.[/quote]

Yes, this is exactly the point that I have been trying to make: the difference between sub-optimal evolution (SOE) and starting over, trying to be as close as possible to globally optimal design. On an inline (Bb) dual-valve setup, the "first" (i.e. thumb-trigger actuated) valve (whether upstream or downstream) is taken for granted to be F: to be compatible with the single (thumb-trigger actuated) valve on (most) tenors, which is taken for granted to be F (with slight variations such as "E-pull"). [This is the "conventional" single-valve tuning: ever since C F Sattler invented the quick-change mechanism using a return spring (instead of a static valve) in 1839.] Then we can discuss the virtues of various tuning choices for the "second valve", as has occurred here.

If you have one valve on a tenor, what is it to be used for? Primarily for extending the sub-tenor range down towards pedals (in which case, there might be a few handy attachment alternates offering more facile slide manipulation)? Or primarily for offering more attachment alternates—e.g. mimicking the facile natural harmonics of the slide-alone upper register—(in which case there might be a few notes available below the usual tenor range, E2)? The Bb/F tuning happens to (sort of) do both—in a sub-optimal way: offering (only) four attachment alternates in closer slide positions, and (more-or-less) four of the five missing notes in the tenor gap (with the frustrating absence of the B1). A "reasonable" compromise over the last one-hundred-and eighty-seven years (and likely to continue).

For extending the range down to pedals with a single-valve bass trombone (with a 7-position slide in Bb), there is a unique choice: the quint valve, Bb/Eb. Slide manipulation is no more "awkward" than with the non-attachment Bb tenor. The "problem", already alluded to, is that the bass-trombone repertoire will require many more "near-end-of-slide" notes to be played; and this is awkward. [Actually, C/F is a less awkward possibility.] So we should look at dual-valve possibilities, both dependent and independent.

But first, we should look at the "best" (thumb-trigger) single-valve tuning for the tenor to optimise low-tenor-range slide facility—without concern for added sub-tenor notes. Once we've decided on that, we can use this for the <I>compatible</I> thumb-trigger valve on the bass. There are three viable (descending-valve) candidates: major-second, minor-third, and major-third. It turns out that the minor-third provides attachment harmonics that interleave with the slide-alone harmonics in such a way that the combination is amazingly similar to the (slide-alone) natural harmonics in upper register—offering very "smooth" slide facility all the way down throughout the (otherwise awkward) bass clef. We could do Bb/G. We could also do C/A: with seven positions in C, we have six positions in A—taking us down to E2, the bottom of the standard (non-pedal) tenor range. [There are also two additional "bonus" pedals. For those following all this detail, I will leave identifying those as a "homework" exercise.]

So now, for the bass, we use the minor-third for the compatible thumb-trigger valve, and look at criteria for designing the second valve: dependent or independent. [For those favouring the major-third single-valve tenor, there is an interesting dependent dual-valve tuning for bass: Bb/F#/D. The augmented triad (with the slide closed) evenly fills in the octave gap between the Bb fundamental and first harmonic.] For independent tunings, we again look for combinations that provide <I>uniform interleaving</I> of the available lower harmonics of the (finger-trigger) valve with those of the thumb-trigger valve and slide-alone harmonics. I will skip the dirty details, but it turns out that the two most uniform interleavings are:

Bb/G(thumb)+E(finger)=D(double) and Bb/G(thumb)+Eb(finger)=Db(double).

Note that the latter is (perhaps not surprisingly) a transposition (up a P4) of the European tuning of the F contra.

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timothy42b
Posts: 1812
Joined: Mar 27, 2018

by timothy42b »

Very logical.

A C/A tenor would give you the missing low B as a pedal. I think you have a tenor set up that way, do you find that pedal a useful note? Better than the false tone on trigger third with an F attachment?
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Finetales
Posts: 1482
Joined: Mar 23, 2018

by Finetales »

[quote="MStarke"]For me the keypoint of F/G or Gb/D or F/D (for a dependent system) is that the first valve has the same tuning as most tenors with valve. Of course it can be discussed if the latter is a good choice.[/quote]

That's the overarching point, that F is not the only solution for a single valve instrument. And I would argue it's worse overall than a G valve, but that's probably a discussion for the many other threads we've done on that.

[quote="timothy42b"]A C/A tenor would give you the missing low B as a pedal. I think you have a tenor set up that way, do you find that pedal a useful note? Better than the false tone on trigger third with an F attachment?[/quote]

Yes, the low C and B are great notes on the C tenor, and the A valve makes the lowest valve note E, allowing you to play anything for straight Bb tenor on it. The low C and B are great on the Yamaha YSL-350C as well, though that horn doesn't have the low E.
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MahlerMusic
Posts: 158
Joined: May 07, 2019

by MahlerMusic »

Trumpet and Tuba players seems to love their C or CC setups. I wish there was a Professional C option for tenor Orchestra work.

On a side note I love using my G Contra on Bass stuff and again wish there was a G Bass option but this is not as usefully as many 3rd/Bass trombone parts are in the tenor range and if you get petals most are just Bb and A which are deep into the valves on a G.
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Finetales
Posts: 1482
Joined: Mar 23, 2018

by Finetales »

[quote="MahlerMusic"]Trumpet and Tuba players seems to love their C or CC setups. I wish there was a Professional C option for tenor Orchestra work.[/quote]

Lars Gerdt makes one now (with a G attachment), the model 316. It's a .500" bore, so probably only appropriate for certain lighter rep in the orchestra.

On a side note I love using my G Contra on Bass stuff and again wish there was a G Bass option but this is not as usefully as many 3rd/Bass trombone parts are in the tenor range and if you get petals most are just Bb and A which are deep into the valves on a G.


I have a wonderful German large bore G bass with a valve. I haven't used it in the wild yet, but I think it would be great for a lot of orchestral rep.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

[quote="timothy42b"]Very logical.

A C/A tenor would give you the missing low B as a pedal. I think you have a tenor set up that way, do you find that pedal a useful note? Better than the false tone on trigger third with an F attachment?[/quote]

Yes, the "bonus" pedals are C2 and B1—both very robust tones. But the C/A tenor (with 7 positions in C and 6 in A) is <I>not </I>continuously chromatic: Eb2, D2, and Db2 are missing—as seen in the ETSP Chart, below (extracted from a long-expired patent). [Roman numerals indicate harmonics.] Again, note the evenly distributed <B>interleaving</B> of slide-alone (black dots) and attachment (open circle) harmonics, closely mimicking the facile natural harmonics of the upper register.

You could keep the longer slide, picking up the Eb, but this would defeat an important attribute: the scaled-down slide of the C/A tenor, being 12% shorter than the Bb tenor, has proportionally less mass (i.e. both inertia and weight) and friction area, and is thereby very "fast" and well balanced.

And yes, this instrument parallels the C trumpet often used in orchestras and small brass ensembles. It has great carrying power.

[Some might say that "middle-C" on this trombone is "explosive". Handle with care!!!]

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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone » (edited 2026-01-21 2:17 p.m.)

[quote="MahlerMusic"]I wish there was a Professional C option for tenor Orchestra work.

On a side note I love using my G Contra on Bass stuff and again wish there was a G Bass option.[/quote]

The Yamaha YSL-350C has a dual-bore slide, 12.7 mm/13.3 mm (0.500''/0.525''), and a 204 mm (8'') bell. This is marketed as a "beginning" instrument for young students, nominally tuned to Bb with an ascending valve to C: 7 positions in C, but only 6 in Bb (missing E2). But it can be easily modified for professional use as a C/A instrument. The ascending-valve rotor can be simply reset 90º, making it descending. And the (then Bb) crook can be easily extended to A by a brass tech.

I, too, wish there was a commercially available "real bass trombone" option—tuned: G/E+C=Bb, i.e. up a major-second from the European tuning of the F contra. See comparative ETSP Charts. Note the significantly shorter slide for the G bass. [The coloured shading is bounded by chromatic scales of shortest (red) and longest (blue) slide positions; the wider the unshaded portion on any given horizontal line, the more available alternates there are. Where the coloured regions touch, there are no alternates. Open circles are thumb-trigger attachment tones, stars are for the independent finger trigger, and cartwheels for the double combination.]

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MahlerMusic
Posts: 158
Joined: May 07, 2019

by MahlerMusic »

[quote="Sesquitone"]<QUOTE author="MahlerMusic" post_id="292903" time="1768930667" user_id="6405">
I wish there was a Professional C option for tenor Orchestra work.

On a side note I love using my G Contra on Bass stuff and again wish there was a G Bass option.[/quote]

I, too, wish there was a commercially available "real bass trombone" option—tuned: G/E+C=Bb, i.e. up a major-second from the European tuning of the F contra.

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</QUOTE>

Why use the European Tuning? My G is G/D+E = Sharp B or G/D+Eb = Sharp BBb, this way the Thump Trigger is 6th position and the Finger Trigger is 4th or 5th position just like a "Bass"
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone » (edited 2026-01-21 11:04 a.m.)

One advantage of an inline, dual-valve contra in F is that (given appropriate valve tunings) the slide needs to be no longer than a 7-position slide in Bb—i.e. a "handle-free" slide. The two commercially available tunings for the F contra are the "European" (F/D+Bb=Ab) and the "American" (F/C+Db=A), the latter being a transposition down by a P4 of the most common inline dual-valve bass-trombone tuning, Bb/F+Gb=D. The other (now, not so common) bass-trombone tuning is Bb/F+G="flat-Eb" (the "Eb" is too flat to be useful). This has the advantage of the G-natural 2nd valve. The main disadvantage of this tuning is (only) that the B1 is at a somewhat longer slide position. If this is transposed down by a P4, the corresponding note, F#1, is beyond the length of the "handle-free" slide.

Both Bb bass-trombone tunings can be transposed down a minor-third for a bass in G. Alternatively, both the F-contra tunings can be transposed up a major-second. The transposed "American" tuning being common to both strategies. All of these strategies—keeping the same <B>relative</B> tunings of both valves—amount to Sub-Optimal Evolution (SOE).

The alternative strategy is to appeal to Globally Optimal Design: "You have two (independent) valves available. Tune each in order to make slide manipulation as facile as possible throughout the whole register". Without going into details—or a discussion of appropriate TLAs (Three-Letter Acronyms)—let me just say that two tunings for the G bass trombone handed down by Globally Optimal Design are definitely worth exploring: G/E+C=Bb and G/E+C#=B.

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timothy42b
Posts: 1812
Joined: Mar 27, 2018

by timothy42b »

I am intrigued, but there don't seem to be reasonably priced used 350C's around.

There is a John Packer copy. hmm.
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AtomicClock
Posts: 1094
Joined: Oct 19, 2023

by AtomicClock »

[quote="timothy42b"]There is a John Packer copy. hmm.[/quote]

Also Schiller: <LINK_TEXT text="https://www.schillerinstruments.com/sto ... -trombone/">https://www.schillerinstruments.com/store/studio-bb-c-tenor-trombone/</LINK_TEXT>

I wish someone would review it.
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Sesquitone
Posts: 291
Joined: Apr 25, 2022

by Sesquitone »

Another way to look at 2nd-valve tuning on inline designs is to use a kind of "slide-rule". For example, if we start with Jonathan Harker's precise "Universal Trombone Slide" and lay out horizontally the positions in staff notation, the increments between successive notes will be shown to increase geometrically (each about 6% longer than the previous increment). For F and Gb valves, we add the length representing the increment between Bb and Gb to the position representing F. Then see where that "lands" back on the universal slide. In this case, just slightly beyond D (by a few cents). Then we lay out underneath that a 7-position tenor slide and see where the end of the slide brings us back to on the universal slide, showing the lowest possible note available.

The first cut-and-taped sketch shows how that turns out. In particular, we see that the (non-pedal) Bb1 is captured at the end of the slide. The B1 is seen to be about halfway between slide-alone 5th and 6th.

The second sketch shows the same idea for the 2nd valve tuned to G-natural. In this case, the combination "lands" back on the universal slide at almost a third of a semitone beyond Eb. So the highest available (equitempered) double-valve combination is D2. The B1 is well on the slide ("still there!"). But the non-pedal Bb1 is not captured.

The next pair of tape-ups show the two commercial F-contra tunings, first the European tuning (F/D+Bb=Ab), and, finally, the American tuning (F/C+Db=A). With a slight stretch (of the Bb-tenor-length slide), the European tuning captures the low (non-pedal) F1. Also shown (by the dashed lines) is why the second valve tuned to D-natural does not reach the Gb1 (without an extension handle)—and so is not fully chromatic.

Of course, the same "slide-rule" idea can be used for designing, analysing, or tweaking any combination of base tuning and the respective tunings of both valves.

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