The "what key is this" question

[windshieldbug]

Kenton Scott is working on a way to answer this reliably as part of his Horn-u-copia project. I think he'd like input and try-outs.

His efforts are at http://www.horn-u-copia.net/cgi-bin/yab ... 1144682523

[iiipopes]

OK, here's how I helped a guy on brass-forum.co.uk figure out the pitch of an unknown horn. But you have to know your algebra and your semitone constant for it to work:

Measure the third valve slide, if possible, and if not, any slide where you can get a reasonably close measurement as to its actual length. The slide must be fully pushed in.

A note one semitone lower than another requires @ 1.0594631 times the length of the open tubing, as this number is the 12th root of 2, the multiplier needed to get 12 equal semitones in equal temperament out of an octave, which is, of course, double the pitch, and therefore double the length. The length of the entire horn is then determined from the function of multiplication of the proportions derived from the known valve slide lengths, which are geometric and not linear in nature.

If you know the length of the second valve slide, one semitone, the you use 1.0594631. If you know the length of the first valve slide, two semitones, then you use 1.0594631^2. If you have the length of the third valve slide, three semitones, you use 1.0594631^3. (1.0594631^12, which = @2, is the octave)

So, if you have the total length of the third valve slide, as y, then x, the length of the horn is as the following equasion:

x + y = x(1.0594631^3)

If you have the total length of the first valve slide, the equations is:

x + y = x(1.0594631^2)

And if you have the length of the second slide, the equation is:

x + y = x(1.0594631)

For academic sake, if by chance you have the length of the 4th valve slide, 5 semitones lower, then the equation is:

x + y = x(1.0594631^5)

The long whole step of a thumb valve won't work, as it is made to be used in conjuntion with the 4th valve, so it can't be used to determine the length of the open horn.

Solve for x, and you have the pitch of the horn:
BBb = @18 feet, or @216 inches
CC = @16 feet, or @192 inches
Eb = @13.5 feet, or @162 inches
F = @12 feet, or 144 inches

Of course, your result will always be a little off, as it is very hard to measure the exact curves of the valve slides into the valve casings, but you will be close enough that it will be apparent which it is.

Now, to go register and post this on Horn-u-copia....

[MartyNeilan]

I thought thios was a tuba BBS. What's with all the math?

I didn't know there was going to be MATH!

Tuba math is different:
Example:
A 4+1 can equal 4/4, 5/4, or 6/4
but 3+1 usually equals 4/4

A 4+2 is usually 5/4 or sometimes 4/4

Try explaining that to a math prof!

[Chuck(G)]

I wouldn't use the 3rd valve slide--some old French and Belgian instruments have the 3rd valve lowering the pitch of the instrument by 4 semitones, not 3 (the so-called "Ministerial" system).

Perhaps the 1st slide is a little better?

[iiipopes]

Hey, Chuck(G) -- using the 3d valve slide on the old French system that takes the pitch down four semitones is easy. You just alter the equation like this:

x + y = x(1.0594631^4)

And you can go to Horn-u-Copia to see how the equation is altered for high pitch horns, as well.

[Chuck(G)]

Hey, Chuck(G) -- using the 3d valve slide on the old French system that takes the pitch down four semitones is easy.

Yeah, my point was that not knowing that you had a 4 semitone 3rd slide can lead to some "interesting" results.

To determine the approximate pitch of an instrument, it's only necessary to measure the first slide. That way, you don't need to know what system the 3rd valve uses.

[Donn]

Am I missing something here? I think of a slide as the part of a tuba that has a variable length, by design. I would expect it to have the prescribed acoustical length at some intermediate adjustment point. All the way in, it should play sharp, and how sharp is an arbitrary design decision; likewise for all the way out. So it seems to me, not only is there no way to determine, <i>a priori</i> from a photograph, what tuning the slide is designed to support, neither can you determine whether the slide is actually extended to an appropriate length for that tuning.

[windshieldbug]

The key here is probability. For that matter, if you are studying the horn through an image, you are taking someone else's word for the overall length. The point is to determine key within a reasonable probability.

On eBay, for example, non-players may have no idea what a key is, let alone the key of an instrument, but they can measure the length of things.

And how many times do you see there an alto advertised as a "tuba horn"?

[Donn]

Sure, I'm not really hoping for great accuracy here, I'm just saying it's odd, to pick the part of the instrument that is by design wildly variable.

For example, there was one recently that looked a lot like an ordinary old silver plated top action Eb, but which the seller claimed was in F. Since he said it checked out on the tuner, that probably trumps any half baked dimensional analysis on the photo, but his account of it was somewhat ambiguous and anyway, this is just an example. I think the difference between F and Eb is 9:10 or less, and I'm pretty sure 1v or 3v tubes can vary by a good deal more than that. I will have to check this evening if my F and Eb Czech helicons even have different valve tubing - I believe they don't.

Why not use the complete length? Some sellers have been asked so many times they routinely post this information on their own. It's obviously more difficult to describe the complete circuit of a brass instrument from a photograph, but with a simple plotting application it might not be too hard in most cases.

[windshieldbug]

To make things even harder, try comparing high pitch (A=~452) to modern A=440. It may well be that the seller in the case you mentioned tried [any old mouthpiece on] the horn, and came up with an E fundamental, or, as you say, given the play in slides, a very flat F.

I don't know if what he is trying to do can make a good distinction between an F and Eb, or CC and BBb.

Where someone can provide a total length, pitch is not an issue. What Kenton is working on is a simple methodology to work out key from an image only. He is very computer savy. I know he is looking for input, so I'm sure he would appreciate it if you would give him your thoughts.

[iiipopes]

As for high pitch and some other variables, please see my extended post on Horn-u-Copia about using observations of other details and features of instruments to also help with identification. I only give one example, but the bottom line is to learn about as many horns by as many makers as you can, so when an unknown comes up, you can do some extrapolation by the actual physical details apparent in the picture, as well as by estimating lengths and proportions to come up with the key of the instrument.