Stupid French Horn Tricks a.k.a Why I Hate Transposing Instruments
Weird thing I saw today (well okay, actually this was several days ago, because these take me a while to write): A horn player using the 3rd valve all by itself, a fingering I was taught never to use. And then I started noticing other WTFery.
Granted, all of my horn playing was in middle school and high school, and I never actually got to the Advanced Private Lessons stage, this being merely the instrument I played so that I could be in the band (as opposed to piano which is what I cared about, but is kind of useless in a band), so maybe they would have covered these sorts of fingering nuances if I'd gotten that far. But I didn't.
And wikipedia is no help. They seem to think the '3' and '12' fingerings are equivalent, which they aren't, but that's wikipedia for you. It's also quite possible these are questions that simply don't have answers beyond, "It sounds better that way." (File under: Why Music Theory Isn't a Science). But I think there's room to beat on some things, so …
You can see what I'm talking about here (in which Radek Baborák does Richard Strauss's 2nd horn concerto, which is apparently the most popular version on YouTube at the moment. You should, of course, listen to the whole thing, but for this you can go 8m26s in, if the t= parameter isn't working for you).
The sequence of pitches up to the point where everything resolves is as follows (note that even just to say what the pitches are I have to digress on pretty much everything that is screwed up about the French Horn … and me):
Concert PitchCB♭BCC♯DFB♭ (high)E♭ "Concert" meaning these are the Actual Pitches, what you'd see if you hooked up an oscilloscope and tried to infer the notes from the frequencies -- or, if you're me, since my particular cross to bear is that I'm one of the 0.003% of the population that has a sense of absolute pitch, this also happens to be what I hear.
Unfortunately, if you're an actual horn player, you'd know that the horn is a transposing instrument, typically notated in F (i.e., meaning a 'C' on the page is actually a concert F, and so on), which means the notes you see on the page would actually be: Notated (F Horn) PitchGFF♯GG♯ACF (high)B♭ But it gets better, because even though the horn is traditionally an F instrument, modern players actually use a double horn, which is an F instrument and a B♭ instrument mashed together with a thumb valve switching between the two. The B♭ instrument is the shorter/higher one and hence the one you typically want to be using if you're playing in the upper register, as will often be the case if you're soloing or doing a horn concerto like this. Meaning you're going to be spending most of your time on the B♭ side of the horn. Meaning what really matters for the purposes of fingering is how we'd notate it for a B♭ instrument: Mechanical (B♭ Horn) PitchDCC♯DD♯EGCF Fingering13O123132312OO1 at which point I should launch into a quick review of how brass fingerings work:
- 'O'(open) is all valves off, so you just get the basic tube, i.e., the fundamental tone, which for a normal transposing instrument would be denoted as C, and all of its various harmonics (next C an octave up, G, higher C, E, G, stupidly-flat B♭, next higher C, D, E, at which point you're in Maynard Ferguson territory...).
- Valves are numbered 1,2,3, moving away from the mouthpiece (if you're trying to match things up with what you see in the video and have never played a horn before)
- The '2' valve is the shortest. It drops you a half step down from what the basic tube gives you;
- The '1' valve is longer; it drops you a whole step. Which then means '12' (i.e., both valves down) is (sort of, keep reading) 1½ steps down.
- And '3' is the longest, lengthed just right so that '23' is two whole steps down, with '13' and '123' being (sort of) the next two half steps further down, and we really don't use '3' by itself (or so I thought).
And just to be clear exactly how the other fingerings fail:
- in order to change a pitch by a given interval, you have to multiply the tube length by a given ratio, e.g., doubling the tube takes you down an octave, mutiplying the tube by 3/2 takes you down a fifth (e.g., from C to F). So, to combine intervals you have to multiply the ratios, meaning if, say, you wanted to go down an octave plus a fifth (C to low F), you're having to multiply the basic tube length by 2 × 3/2 = 3.
- But, combining valves adds tube lengths, i.e., to continue the example, if we were to have a Go-Down-An-Octave valve, it would need to be the same length as the basic tube (so that pressing it doubles our length); if we were to have a Go-Down-A-Fifth valve, it would need to be half the basic tube (so that adding it in would give us 3/2), and pressing both valves together would then give us 2½ basic tubes, not 3, i.e., putting us down an octave+a-third (i.e., from C to low A♭, missing the low F by quite a bit)
At which point I can reveal my (first) lie, which is that what I've given you above are actually B♭ trumpet fingerings.
Which you might not think would be any different from B♭ horn fingerings. However, the B♭ horn's basic tube is twice as long as the trumpet's. Meaning that, on the horn, the same notes are effectively the next octave up, the range where E is now one of the harmonics of the basic tube; meaning if you can use 'O' (open) to get you an 'E', then '2','1', and '12' should likewise work for D♯, D, and C♯, and then we can (at least) dispense with the '13' and '123' fingerings that really suck.
Which is all why, if this were me in high school, I'd be using these fingerings instead: Mechanical (B♭ Horn) PitchDCC♯DD♯EGCF B♭ Horn Fingerings1O1212312OO1 There are two problems here. One is that the E harmonic, the natural major third above the C harmonic is, due to math, flatter than than the even-tempered third that you might be used to hearing from a correctly-tuned piano. TL;DR: 5/4 (natural major third) < ∛2 (equal-tempered major third) < 81/64 (pythagorean third you get from the circle of fifths).
The second problem is that the flatter E is not necessarily wrong. In fact, if it's an E that's part of the usual C major triad (C-E-G) the flatter 5/4 interval is the E you want, the one that a good vocalist will head immediately for without even thinking about it. But if it's playing some other role, then maybe not, which is why I'm not automatically using 'O' for E or '2' for D♯, even if '1' for D and '12' for C♯ are still going to be huge wins over '13' and '123', which are so horribly sharp that even trumpet players have their own extraordinary measures to cope --- nothing quite as stupid as a double trumpet, but you will often see this extra little-tiny-trombone slide on the 3rd valve which is indeed used to artificially lengthen it to make '13' and '123' not be sharp anymore.
Which finally brings us to this performance. Keep in mind that what we have here is a slow passage with long, sustained tones. That is, intonation is going to matter here, and so you need to use every last trick in the book to get it right. And luckily for us, the camera zooms in so we can see what Baborák actually does with it: Baborák Fingerings1O[T]2[T]O233OO1 The black outlined stuff is actually relatively easy to explain. [T] means he's released the thumb valve putting us back on the F side of the double horn, which is actually a better way of dealing with the orneriness of the '123' and '13' fingerings. To understand this you need to refer back to the "Notation" line to see that, on the F horn, Notated (F Horn) PitchGFF♯GG♯ACF (high)B♭ these notes are F♯ and G, G being one of the harmonics of the basic F horn tube, and F♯ being the reliable '2' fingering, keeping in mind that the F side of the double horn has almost all distinct tubing (only the mouthpiece and bell are shared), including a completely separate set of valve slides, meaning they can all be adjusted independently of however the B♭ side is set up, so there are no worries about those adjustments interfering with each other.
(And I actually knew about this much in high school; the only reason I never made use of it it is this weird consequence of absolute pitch: I associated fingerings with sounds not notes on a page, which meant I could only keep technique for one set of fingerings in my head and thus had to actually forget the F fingerings in order to learn the B♭ ones, and once I did that, I could only play with the thumb valve permanently stuck down the whole time. Presumably, if I'd ever gone on to become a professional horn player, I'd have found a way around that, but I never did, so...)
The real WTFs are those red boxes. The first and fourth notes are actually the same note and yet he's using two different fingerings. And the passage is slow enough that we don't have the, "Well, it's just easier on my fingers" excuse.
And then we have the original question of why he's using '3'. Again, wikipedia tells you '3' and '12' are equivalent fingerings for both E and A. But, in this recording, I have observed that Baborák pretty much exclusively uses '3' for E while at the same time pretty much exclusively using '12' for A (by which I mean the E and A on the B♭ horn, i.e., concert D and G in case that wasn't clear -- hm, I should have started this two notes earlier so that you could actually see him doing an A. Rewind if you care).
So there's something going on there.
And since this is getting progressively longer, I'm going to stop here for now, but not without dropping some clues.
First is an actual score (t=8m8s, we're in the last four measures on this page; soloist is 4th line from the top [switches to 8th line on the next page]),
which, because we're not fucking with you enough, is notated for an E♭ Horn, not an F Horn (which means those B♭ horn E's and A's whose fingerings I'm having issues with, which are concert D and G, respectively, are actually denoted B and E in the horn part in the score; are you confused yet?).
which is actually less surprising given that the piece itself is in the key of E♭ (because back in the bad old days before they had double horns and valves, you would typically use a (valveless) natural horn pitched in the key of the piece you were playing and then using lip+hand tricks pretty much everywhere -- even if I'm pretty sure this piece, written by Richard Strauss in the 1940s, would be completely insane to attempt on a natural horn) Notated (E♭ Horn) PitchAGG♯AA♯BDG (high)C meaning we might want to give some thought to what roles the notes are playing. At which point Emma (
emmacrew) would tell me I should really be using Solfège to talk about this: SolfègeLaSolSiLaLiTiReSol (high)Do Underlying HarmonyI⁶V⁷I
which gets extra fun because because I never really learned Solfège...
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