Why is a 5th valve a 'long 1st valve'??

[roweenie]

Actually, the "long1st valve" is a fairly recent invention, i.e. only about 50 years old. If you are interested you can find more than you might want about it here: http://www.galvanizedjazz.com/tuba/History.html

Unless I'm mistaken, doesn't the CSO York (built around 1930?) feature a "flat-whole-step" 5th valve? I believe there was a theory floating around that it was actually designed as a change valve to BBb.....

I guess my explanation is for all the stupid tuba players out there, heh, heh…

You and me, both - - -

[Donn]

Let’s check. The added length is always 5.88% of the previous length. So we get Ab is 614 needing an extra 202 cms. Now if I use 1,3 and 5 valves for Ab I get 50 + 82 + 82 = 214. 214 + 412 = 626 cms. This is 12 flat. If I use 12+4 I get 50+24+136 = 210 being an acceptable 7 flat.

The 1,2+4 tuning would be even flatter if you tune v4 flat, as I think you had better for 2+4 A. At least 139cm. But that's immaterial, if we're looking for a correct value for v5. If you're basing v5 on that 1,3+5 Ab, why not tune it so you're close to in tune on that note? Say 62cm. You can tune v3 longer, too, if you like, to 84cm, for a 1+3 alternate for Bb.

With those adjustments, your fingering chart is less than 2% off on any note, and until you get down to A the worst is 0.5% flat on B. F is 1.5% sharp, 1,2+3 alternate A is 1.6% sharp. 62cm is probably within reach on a typical "long 1st" valve.

It's about as good as anything I have for the "BBb 1st" long 1st, where Ab is 4+5, but not so much better as to make a compelling case.

By the way, I'm using a value closer to 1.0595 for half step: exp ((log 2) / 12). Initial basic tuning is flat enough on 1st and 2nd to make C 0.2% sharp, and 3rd to make Bb 0.2% sharp; 4th is Bb 0.3% or 0.4% flat.

[2ba4t]

Thank you all again. Now I understand!!

I must have had a faulty calculator - or something(!!!) So I have corrected the maths. The amount missing is 74cms. A 5th valve of 74 cms produces excellent results but many are slightly sharp. And, yes, you are right of course, make the 4th valve longer by 2 cms and you have almost perfect tuning semitone by semitone right down.

The 4th valve BBb is not noticeably flat – 0.5%
The pesky AA is only 1% sharp with 2+4.
The rest are perfect (less a 0.5% out).

BUT – the 5th valve is still not a ‘long 1st valve’!!! It is a short 3rd valve.

Importantly, this also means that the 5th valve is useful constantly and not just in rare very low passages. It is a very useful extra 3rd valve. Valves 1+2 = 71.6 cms; 3rd alone is 76.6 cms and 5th is nicely between them at 74 cms. This is a wonderful cure for fingering gymnastics in the four valve line up especially heavy pistons. The left hand 5th valve makes life easy.

The weight is a fraction of the compensating system AND the tuning is actually better. Comps’ low GGb, FF are EEE are progressively sharper.

Thanks again.

[windshieldbug]

OK, I’ll troll in...
Equal temperament only means that everything is equally out of tune.
Use your ears!

[Donn]

I know this kind of thing can be kind of disturbing to the typical artist types, but as I see it, the object is a tuning system. Do you make v5 on Eb as long as a BBb v1, and play Ab 5+4? What if v5 were longer, and you used a different fingering for Ab?

I'm not sure I can answer a question like that empirically, because I'm reluctant to solder on new valve tubing, and even if I don't need to do that, it's tricky to test tuning because it isn't the only factor in the pitch that comes out. With some computation, I can see how the valves interact at various lengths, and that gives me the ability to test 2ba4t's assertion that the 5th valve should be 74cm, where the BBb-1st version would be more like 59cm.

Here's what that looks like to me: (note that these may require scrolling to see the parts that matter)

Code: Select all

    ideal          result pct off valves
Eb  410.09: -----  410.09    0.00  ( )
D   434.47: --2--  434.88   -0.09  ( 24.8 )
Db  460.31: -1---  461.95   -0.36  ( 51.9 )
C   487.68: -12--  486.74    0.19  ( 51.9 24.8 )
B   516.68: --23-  516.89   -0.04  ( 24.8 82.0 )
Bb  547.40: -1-3-  543.96    0.63  ( 51.9 82.0 )
Bb  547.40: ----4  549.21   -0.33  ( 139.1 )
A   579.95: -123-  568.75    1.93  ( 51.9 24.8 82.0 )
A   579.95: --2-4  574.00    1.03  ( 24.8 139.1 )
Ab  614.44: 51-3-  617.97   -0.57  ( 51.9 82.0 74.0 )
G   650.97: --234  656.01   -0.77  ( 24.8 82.0 139.1 )
Gb  689.68: 512-4  699.87   -1.48  ( 51.9 24.8 139.1 74.0 )
F   730.69: 5-234  730.02    0.09  ( 24.8 82.0 139.1 74.0 )
E   774.14: 51234  781.88   -1.00  ( 51.9 24.8 82.0 139.1 74.0 )

But is 74cm really the optimal v5 length, for this system? What if it's 68cm? (And here I move v3 out some, because the alternate fingers I show here are useful for me.)

Code: Select all

    ideal          result pct off valves
Eb  410.09: -----  410.09    0.00  ( )
D   434.47: --2--  434.88   -0.09  ( 24.8 )
Db  460.31: -1---  461.95   -0.36  ( 51.9 )
C   487.68: -12--  486.74    0.19  ( 51.9 24.8 )
B   516.68: --23-  517.88   -0.23  ( 24.8 83.0 )
Bb  547.40: -1-3-  544.94    0.45  ( 51.9 83.0 )
Bb  547.40: ----4  549.21   -0.33  ( 139.1 )
A   579.95: -123-  569.74    1.76  ( 51.9 24.8 83.0 )
A   579.95: --2-4  574.00    1.03  ( 24.8 139.1 )
Ab  614.44: 51-3-  612.96    0.24  ( 51.9 83.0 68.0 )
G   650.97: --234  656.99   -0.92  ( 24.8 83.0 139.1 )
Gb  689.68: 512-4  693.88   -0.61  ( 51.9 24.8 139.1 68.0 )
F   730.69: 5-234  725.01    0.78  ( 24.8 83.0 139.1 68.0 )
E   774.14: 51234  776.88   -0.35  ( 51.9 24.8 83.0 139.1 68.0 )

At any rate, it's arguably an improvement on the traditional long 1st. If Ab is 5+4, G runs pretty flat as 5,1+4, and a 2,3+4 isn't much better.

Code: Select all

    ideal          result pct off   valves
Eb  410.09: -----  410.09    0.00  ( )
D   434.47: --2--  434.88   -0.09  ( 24.8 )
Db  460.31: -1---  461.95   -0.36  ( 51.9 )
C   487.68: -12--  486.74    0.19  ( 51.9 24.8 )
B   516.68: --23-  518.70   -0.39  ( 24.8 83.8 )
Bb  547.40: -1-3-  545.76    0.30  ( 51.9 83.8 )
Bb  547.40: ----4  549.86   -0.45  ( 139.8 )
A   579.95: -123-  570.56    1.62  ( 51.9 24.8 83.8 )
A   579.95: --2-4  574.66    0.91  ( 24.8 139.8 )
Ab  614.44: 5---4  608.29    1.00  ( 139.8 58.4 )
G   650.97: 51--4  660.15   -1.41  ( 51.9 139.8 58.4 )
G   650.97: --234  658.47   -1.15  ( 24.8 83.8 139.8 )
Gb  689.68: 512-4  684.94    0.69  ( 51.9 24.8 139.8 58.4 )
F   730.69: 5-234  716.90    1.89  ( 24.8 83.8 139.8 58.4 )
E   774.14: 51234  768.76    0.70  ( 51.9 24.8 83.8 139.8 58.4 )

So ... sure, pull it out some for Ab 1,3+5 if you like. How far, depends on how the other valves are tuned - might not be anywhere close to the length of the 3rd valve, but that all relates to some unspecified alternate fingerings where v5 substitutes for v3?

And for sure, this isn't like tuning a piano. We aren't going to get the pitches implied by these charts, and we might not want the exact pitch as derived from logarithmic intervals anyway, that's just an approximation.

[roweenie]

[roweenie]

LOL

[iiipopes]

It's really handy to know the 12th root of 2 math - for a starting point - when building an instrument, but it's not much good (as infinitely-varying bugles distort the theoretical) without extensive testing as a build progresses.

Further, even when some pitch may be playable in-tune at the theoretically-correct length, it may (again: due to all sorts of variables) lie not-quite in the center of the "lip-able" range (from flat to sharp) of that frequency...thus it a pitch could be slightly more resonant (in tune, whether equal temperament or harmonized) with the slide length slightly "off".

Exactly. But...the OP asked how long the 5th valve "should" be. Hence my mathematical answer.

[2ba4t]

Wasn't trolling, honest Injun.

I had just put on - onto a 4th slide - a dependant 5th which was a BBb 2nd valve. My strange mind then began wondering why? How much do I really need to get low EE never mind just an AA. This ended up as, eventually, 74cms. Now, he thinks, how can the 5 valves [with a 74 cms 5th valve] combine to give the right lengths? If I could post my chart - it has on it all the details with a 74cms; a tritone [168.5] and a 2+3 [105.5]. But I have not the IT skills to do it. I got as far as joining Onedrive uploaded the chart then it went bang.

However, you all have been through all this stuff already. I am just 100 years late to the party. Anyway, we see that the 'optimal' 5th valve is not a 'long 1st' unless one means a BBb first valve [66cms] or are happy to pull slides.

I am now gearing up to a project of adding 5th valves to several horns - as I have several reasonable rotaries I have salvaged to use up. Trouble is adding within the 4th slide is easier but gives less fingering options.

Frankentubas unite!!

Thanks to all for your generosity and knowledge.

Webster - troll - a dwarf or giant in Scandinavian folklore inhabiting caves or hills. I presume you meant that definition because some of the others are a little rude.

[2ba4t]

Donn, Thanks very much.

Bloke:
1] No. It was a non-comp Eb Hawkes from 1920s. I put a BBb 2nd valve in the 4th valve tuning slide like the Yamaha euphonium set up of years back (I now discover.) Now I am going to replace that length with 74cms to test my chart. It will need some nifty right angle switches. As it is a 3 + 1 layout having an independent 5th valve is less important for easier fingerings.

2] Extended 3rd comp slide - Great minds… – at least yours – I extended my 983 3rd comp slide when I converted it to a CC. Then I made a shorter extension loop for the EEb’s 17cms sharp F. Then, again too late, I thought why not go the whole hog [like your Roweenie photos]. So I added enough [36cms] as the best compromise being that 5cms is impossible to notice.

G 12+4 3cms flat
Gb 23+4 6cms flat
F 13+4 6cms flat
E 123+4 6 cms sharp
Now THAT is a compensating system.

The Blaikley 24cms 3rd comp slide produces the following;

G 3 +4 00cms flat
Gb 23+4 10cms flat
F 13+4 17cms flat
E 123+4 28 cms sharp

Philosophically I can’t see why a sharp F and very sharp E a la Blaikley is better than negligible discrepancies with Gb and F and E – except that the longer slide looks like a duodenal growth. It needs two kinks in it and still looks stupid. [Am still working on uploading photos. I hate smartphones and have an ancient Nokia.]

Note that this is in practice no better than a light weight non-comp non-dependant 74cms 5th valve
A 2+4 8 cms sharp
Ab 13+5 1cms sharp
G 24+5 4 cms sharp
Gb 124+5 7 cms flat
F 234+5 6 cms sharp
E 1234+5 1 cms flat.

A dependent 5th within the 4th means that not only must A be 8cms sharp but Ab must be 12+4 and not 13+4 and therefore 8 cms flat. This can be tweaked of course and is only 1.5% either way.

In conclusion, however, if a 74cms 5th valve [and importantly the equivalent on F, CC and BBb brethren], solves all problems – why have the comp system at all?? I suppose weight doesn’t matter to guardsmen and keeping the same fingerings was deemed important.

Da capo my post ‘Why so many valves?’Tue Jul 23, 2019 12:59 pm. Why do all serious non-comp tubas not have only 5 valves? What does a sixth or seventh add? All things come full circle,

[Donn]

Sure, but the other obvious side of it is that we make choices that benefit from simple mathematical analysis - like the "BBb 1st" valve logic advanced above, which is every bit as mechanical as 2ba4t's pursuit of a long 5th valve alternative. They're both science, if you like, that we use in its appropriate place to find a sensible way to use a 5th valve. Or we might take another road to the same end with compensating systems. No artists harmed.

[2ba4t]

Thanks again. I was searching for a lightweight AND non-slide pulling route. Comps are very, very heavy even though [supposedly] non-slide pulling. More than 5 valves non-comp seems illogical.

Where brass instruments meet physics there are innumerable complex subtleties and thousands of important details - but it must be scientifically possible to decide on the optimum for a desired effect provided we know our priorities. We cannot conflate playing with the science of manufacture. Factors such as cost, weight, intonation, range, carrying power, sweetness of tone, strengths in high or low ranges, ease of handling etc etc are for us to tell the manufacturer and establish in order of priority. Then the scientist works out the best specs and tries empirically if those specs produce the goods. Of course, there will compromises essential to balance the priorities. Usually the market controls this.

Unfortunately we are ruled by manufacturers and fads and a huge stinking heap of misinformation from snake oil experts. The world should be run by tuba players and tuba techs - then all would be well.

[iiipopes]

It's really handy to know the 12th root of 2 math - for a starting point - when building an instrument, but it's not much good (as infinitely-varying bugles distort the theoretical) without extensive testing as a build progresses.

Further, even when some pitch may be playable in-tune at the theoretically-correct length, it may (again: due to all sorts of variables) lie not-quite in the center of the "lip-able" range (from flat to sharp) of that frequency...thus it a pitch could be slightly more resonant (in tune, whether equal temperament or harmonized) with the slide length slightly "off".

Yes, indeed. Now, how much of that is the horn, with the various braces and bends altering the resonances nodes and anti-nodes, or especially as we get used to playing a particular tuba, we subconsciously (as we should) buzz the required pitch instead of something that roughly resonates to that valve combination and partial series, is another item of debate.

[geomiklas]

All of my college and professional tuba life, I've played Miraphone 186 5UCC with long 5th valve (major 3rd, a.k.a. 2&3 configuration). I bought a Schiller clone 186/188 with short 5th and hated playing it!