re: instruments and pitches

Cecil's Columns/Staff Reports
1

Regarding Cecil’s answer about why instruments come in different pitches (http://www.straightdope.com/classics/a1_319b.html)

I think he’s a bit off the mark here. As a classically trained trumpet player, I have a whole kit full of trumpets in different pitches. The reason why trumpets – and French Horns for that matter – come in different pitches has to do with the fact that they started out without valves. The pitches that early trumpets (Baroque and Classical periods) were able to produce was determined by the natural harmonic series that occurs when a column of air in a tube is set vibrating. Early trumpeters used their lips to select which pitches would be played, but there was no way to sound notes that did not occur within the harmonic series. This meant that they had to have trumpets in various pitches (i.e. various lengths) to play pieces in different keys. For example, you had a “C trumpet” to play works in C, a “D trumpet” to play works in D, etc. etc.

The invention of valves and keys changed this because it allowed trumpets and other instruments to play chromatically – i.e. in any key - without having to change instruments. This would seem to suggest that the invention of valves would have led to the use of a single instrument – pitched in C for example – which would be suitable for all music in all keys. That didn’t happen for a variety of reasons, but the one which I believe is relevant to the saxophone example has to do with pitch center and instrument range.

Cecil alludes to this when he writes “…if you think a tenor (B-flat) sax is too low for a given tune, you can get an alto (E-flat) sax instead.” But this explanation does not address why B-flat and E-flat were chosen as the pitch centers for these instrument (why not B natural and E natural?)

Every instrument has a limit as to the number of notes – it’s range – that can be played on it. The range is centered on the pitch the instrument naturally sounds (i.e. what pitch the instrument is “in” – C, B flat, E flat, D etc.) In the case of saxophones, I believe that the pitches of the different kinds were selected to provide the maximum possible range within a given voicing. For example, a baritone sax is able to play a certain range of notes centered in the “baritone” voice register. Some of these notes overlap with the lower end of the tenor sax range, but the tenor can play higher, overlapping with the lower range of the soprano sax which can play higher still. Altogether, the saxophone family – from contrabass to sopranino - pretty much covers the entire range of the piano, which pretty much covers the “useful” range of pitches used in music.

A final note: Cecil wrote: “Changing keys would mean having to completely rethink your fingering” Not exactly, at least in the trumpet world. The are two ways to solve this problem. The easiest is to re-write the music – transpose it up or down - so that the pitches sounded correspond to the notes desired. In this case, your changing the written notes, not the fingerings (i.e. C is still fingered C, but you write a D instead of C and the musician plays a D, but it sounds at the pitch you want to hear).

The more complicated way – something that trumpet players do all the time – is to play a note different from what you see written (called transposing). We don’t think of it as “re-thinking the fingerings”. Instead, we play notes above or below the notes that are written. For example, you have a B-flat trumpet in hand but your music is for trumpet in C. You have to transpose every note up a whole step. You see a C but you play a D (different fingering). You could argue that the trumpet player has changed the fingering of the note C, but most trumpet players would tell you that they really haven’t. They’re just playing different notes. C is still C, but although I’m seeing a C on the page, I’m not playing C, I’m playing D. See?

2

The real reason trumpet players use different pitched instruments is because they get paid extra for doubling.:wink:

3

The natural-harmonic point is more important to brass, but the fingering point is more important to woodwinds, which saxophones are, despite the fact that they are made of brass. Brass players have three, four, maybe six valves to worry about; woodwind players have 15 to 30 keys, holes, pads, and/or rings, and perhaps a half-hole or two.

Another historical factor is that the clarinet was first introduced to the orchestra in the Classical period (in the technical sense of after the Baroque and before the Romantic) in order to play Baroque trumpet parts, the art of playing which had been lost. (Hence the name: “clarionette”, in its earliest form.) The saxophone, of course, is the bastard child of the clarinet and the ophicleide (an obsolete keyed-brass instrument replaced long ago by the tuba family).

There is an error in the original column. Saxophones ain’t got no valves (except for the spit valve found in the baritone and larger instruments). Saxophones have keys.

The current family, by the way, is:
Bb Subcontrabass (major 23rd–three octaves and a tone–lower than written). *
Eb Contrabass (major 20th–two octaves and a major sixth–lower than written). *
Bb Bass (major 16th–two octaves and a tone–lower than written).
Eb Baritone (major 13th–one octave and a major sixth–lower than written).
Bb Tenor (major 9th–one octave and a tone–lower than written).
Eb Alto (major 6th lower than written).
Bb Soprano (major 2nd lower than written).
Eb Sopranino (minor 3rd higher than written). *
Bb Soprillo (minor 7th higher than written). *

  • Rare.

Obsolete members include:
C Melody (one octave lower than written).
F Mezzo-soprano (major 5th lower than written).
C Soprano (as written).

4

I’m not sure if anyone has spelled out exactly the benefit of transposing instruments: you learn one set of fingerings*

If I’m a trumpet player, I’ll sometimes have a C trumpet, a D trumpet for Bach and an Bb trumpet for the marching band. When I see the notes C-D-E on the score, I always use the same fingering. The sounds that come out will be different, but that’s a problem for the person writing the score - he will adjust for me.

*byankee is correct - you do tend to learn transposing fingerings over time, but in theory you shouldn’t have to.

5

I’ve always heard that the definition of a gentleman is someone who can play the saxaphone, but doesn’t.

6

No, no…you’ve spelled “bagpipes” wrong…

jay(former bari sax player)jay

7

In other words, you’re not a professional trumpet player.

Classical scores (real ones, not the editions printed for high schools) have trumpet parts written all over the place.

8

As a pianist/saxopohonist/brass player/band director/composer (if that gives me any credibility), I believe that the reason various instruments are in different keys has to do with intonation–that is, the ability of an instrument to play “in tune” with itself.

If the tubing of brass instruments were unwound, a Bb trumpet would be about 4-1/2 feet long, a trombone or euphonium (sounding an octave lower) 9 feet, and a tuba (an additional octave lower) 18 feet. (These are rough estimates, not inch-precise.) The French horn, in the key of F, is about 12 feet long. For reasons of acoustics, bore size, etc., the horn usually plays in the range between the trombone and trumpet, not below the trombone as one might expect based on the length of tubing alone.

These “open horns,” as we call them when no valves are depressed, can play certain notes. Notes lower in the range are separated by fairly wide gaps; as the instrument plays higher in its range, the notes get closer together. (There’s a somewhat mathematical formula to this “overtone series,” as it’s called.)

In order to fill in these gaps to play the “missing” notes, additional tubing must be added to the instrument. The largest gaps, down low in the range, are 7 half-steps wide, so six additional “lengths” of tubing must somehow be added to the horn. The trombone does this by moving the slide to one of six other positions (besides the closed one, also called “first position”). The valved instruments use six combinations of valves besides the “open” one (no valves down).

Since each combination of valves, i.e., each different length of tubing, can produce a whole “overtone series” of notes (from low to very high, each combination having “gaps” in the same relative places as the open horn), as a player plays higher in the instrument’s range, he finds notes that can be played with different combinations of valves. We call these “alternate fingerings,” but on brass instruments they are not used except in special cases (baroque solos with lots of trills, for example). Most high school players know and use only one fingering for each note.

We teach players the overtone series, then tell them to use the shortest length of tubing possible for any given note. This will produce the most “in-tune” pitch in most cases. (Actually, since we start kids in band in the 5th grade, we just teach them the proper fingerings–it’s later that they learn the overtone series. But they can see the point.)

Here we come to the answer (finally!): Instruments are a certain length because they play better “in tune” (with themselves) than instruments of other lengths. A C trumpet is commonly used in orchestras (this allows for easier key signatures while playing with the strings), but a C trumpet does not play in tune as well as a Bb trumpet; since the trumpet has a much larger role in concert and jazz bands than it does in the orchestra, the Bb trumpet–the one that’s more “in tune,”–is by far the most common member of the trumpet family.

A Bb trumpet is a transposing instrument; to sound an actual C it must play a D. The music is already transposed in almost all cases, so the player reads and plays D.

The Bb trombone and Bb tuba, however, are not transposing instruments; despite their names, they are in the key of C. To sound an actual C, they read and play a C.

By the way, to make a note sound a half-step lower, the tubing of an instrument must be lengthened by approximately 5.9%. Each valve combination lengthens the tubing by that amount; there are, however, some notes, low in the range, where the tubing available is not long enough, so some players manually add tubing by pulling slides out while playing certain notes. Watch a tuba soloist sometime–see how busy his left hand is!

9

Not quite. The largest gap is a full octave wide, from (say) low b flat (or whatever the low open note in your scale is) to the note a full octave below that, with the same fingering. But both because that’s an inconveniently big gap and because it takes a heck of a lot of air to sound that note, one usually doesn’t bother with it and just adds tubing. I did once manage to sound the fundamental tone on a tuba in all-closed fingering, but only for a fraction of a second, and it completely emptied my lungs to do so.

I also learned all of the alternate fingerings in high school, but that was mostly because the valves on my tuba were in terrible shape, and you could usually only count on two out of the three working for any given song.

10

That’s because jazz has led to a popular style of saxophone playing that is sloppy, sentimental, and mostly out of tune, which sounds OK for 32-bar solos against a solid band, but is extremely grating in extended unaccompanied performance. The instrument can be played otherwise, typically in late French Romantic music (the obvious example being Ravel’s “Bolero”) and in British military bands.

As to the choice of instrument size, sometimes fashion can be destructive. For example, few people play the F trumpet anymore, but after being backstage conductor at an original-instrument performance of Beethoven’s “Fidelio” some years back, I’m never again going to find the famous Act-II solo tolerable played on an itty-bitty jazz-voiced modern Bb trumpet.

11

Chronos is correct, but I wasn’t counting the fundamental pitch (also called the “pedal tone”) as a true note because it’s not usually considered a playable, musical tone. It’s never written in trumpet parts (except perhaps in a virtuostic solo), and only very rarely in trombone or tuba parts. It’s a pretty nasty sounding note on the trumpet unless one practices it every day, but it’s fairly easy to produce on the trombone, and it sounds pretty good. And it takes LOTS of air on the tuba! Kudos, Chronos!

Generally, though, the pedal tone isn’t considered to be a “normal” part of the instrument’s range, as a glance at a fingering chart will attest.

Chronos did well to broach the subject, however. About half of that bottom octave gap is filled by adding more tubing (pressing the valves or extending the slide). To complete the rest of the octave, some instruments have a fourth valve whose length equals that of the 1st and 3rd valves (the two longest) combined. When used in conjunction with the other three valves, one is able to play the rest of the chromatic scale, using the pedal tone as the bottom note.

The same thing is accomplished on the trombone with the use of a “trigger,” played by the left thumb, which opens an additional length of tubing (located by the player’s head) equal in length to 6th position. To avoid offending all the professional trombonists among the teeming millions, I will add that, when using the trigger, there are really only 6 useful, in-tune positions available (instead of the usual 7) because the extra tubing added by the trigger means you’re playing a longer instrument; the slide positions necessary to create the half-steps must therefore be farther apart from each other (5.9% of an 11.7’-long horn is bigger than 5.9% of a 9’-long horn). This leaves a gap of a single note, which can be “faked” by playing a false 7th position, but as this note is B natural (even rarer in this range than it is in the “real” range), it’s no big deal. Trombonists who have to play these notes in real life play an actual bass trombone, which has TWO triggers!

Because of the same out-of-tune problems that occur in the bottom octave with the trombone/trigger combination (easily brought in tune by moving the slide to a slightly different position), there exist what are called “compensating” euphoniums (euphonia?) and tubas. Invented, I think, by the F. Besson brass company and now available from other manufacturers, this system engages more tubing on the three “regular” valves when the fourth valve is depressed, forcing the air through the proper lengths of tubing required to play the bottom octave more accurately in tune.

Most professional tubists play an instrument pitched slightly higher, in C, or even higher, in F. To play the lowest notes these horns have FIVE valves–like a bass trombone with two triggers. Just to brag that they use all five fingers, I guess! Even so, you’ll still see good tubists adjusting slides with the left hand.

Tubas and euphoniums with four valves are common–even expected–at the high school level, as are trombones with the so-called “F attachment.” Four-valve trumpets are almost non-existent, however; trumpets are rarely called upon to play low in the range. One will find four-valve flugelhorns though (basically a trumpet with a more conical bore, including a roughly 6-1/2" bell [compared to a trumpet’s 5" bell] used mostly in jazz for its extra-mellow sound).

As for the saxophones, they are in Bb and Eb because those lengths of tubing play best in tune with themselves (realizing, of course, that the placement of the tone holes is a compromise allowing the instrument to play in tune in as many different keys as possible. This is true for all the woodwinds, but that’s another story). The C melody sax (only slightly smaller than a Bb tenor, but occasionally still available on eBay) was an absolute dog when it came to intonation. Buy one, then hang it on the wall–it’s really not good for anything else!

12

As a not-very-good trumpeter who had a little experience 20+ years ago with the tenor horn (or “tenor saxhorn” if you prefer), I found the pedals not too hard to hit on the tenor, but if I ever have to hit 'em on the trumpet to save my life, please notify my next of kin. :slight_smile:

13

It’s not hard to hit them; the trick is doing it without sounding like a fart!

14

I thought that was the trick to playing any note on any brass instrument… :stuck_out_tongue:

jay (former woodwinder) jay

15

As a former, reasonably pathetic, HS trombone player and physicist, I’ve got to know, and this seems to be the time to ask. (Let’s face it, the spreadsheet I’m working on blows more than Chronos did. :smiley: ) On a trombone would what Chronos is talking about playing high and low b flat in first position? Or is it playing the b flat one octave lower than low b flat? I seem to recall using happyboy’s “false” seventh position to reach it, and mostly to see if I could do it. I never knew seventh was a false position, though. (I assume “cheating” means it just replicates first, but at a lower pitch?) I always thought they didn’t bother to teach it to us, because kids, and some adults, could not comfortably and repeatably reach it.

I played a trombone with an F attachment for a few years. There is a problem with them that other instruments do not have. Most bands make you wear white gloves. I never found white gloves in men’s sizes, only women’s. Now imagine playing on a cold December day, hanging onto a large, wind cooled, brass instrument, with tight gloves quite effective at cutting off all circulation to your thumb when placed in position to use the valve. The only way I kept my thumb was to use the valve more often than strictly warrented - movement helped.

16

I’m not sure if this has been mentioned, but one reason is that the diatonic scale is not the same as the corresponding notes on a chromatic scale.

Sure, the chromatic, equally-tempered scale is a pretty close approximation, and it’s fine for pianos (which have three differently-tuned strings for most notes) and guitars (which you can bend a little bit), but it isn’t exact.

So a C-note sax is never going to sound quite as good as a E-flat sax when playing in E-flat.

17

Sorry for the confusion. Chronos is referring to the pedal tone, an octave lower than low Bb, played in first position (same as “no valves down” on a tuba). Seventh position is not “false” except when using the extra tubing afforded by the F attachment–the extra length means there’s really only room for six positions to play notes in tune in the bottom half-octave, since each position has to be farther apart when the attachment is engaged. “Cheating” means putting the slide farther out than the true seventh position (there are little marks on the slide where seventh should be) in order to get enough tubing to play that one note in tune.

All the half-steps are there in theory, but with the F attachment engaged, the notes are all out of tune (sharp) if played with the slide in the “regular” positions. That’s why there are only six usable positions, each a little bit farther apart, when the F attachment is used. Which is why a player would have to “fake” that one note in seventh–he’s really on the verge of pulling the slide off completely, and air begins to leak out where the inner and outer slides meet.

Any trombone uses 7 positions to make the various notes, but seventh is required only to play low B natural (the note a half-step above low Bb) and low E natural (the lowest note without the F attachment or pedal tones, a half-step below sixth-position low F). Higher B’s and E’s are available with shorter lengths of tubing, so that’s what is used.

Most trombone players at the high school level rarely have to play low B natural or low E natural, for two reasons: almost all band music is written in keys containing at least one flat (which is always Bb; the second is Eb–and we’ve just all but eliminated the need for trombonists to play B and E natural!); and even when it’s not, trombone parts are written mostly in the tenor range (we have tubas to cover the bass part) and don’t often have to play in the extreme low range. Bass trombone parts do use the extended range, however.

I’ll bet, SlowMindThinking, you were playing low E natural (in seventh position) and that’s what you’re thinking of. It also could have been a pedal E (below pedal Bb), but I doubt it. There are pedal notes available in all positions, but the longer the tubing gets, the more difficult it becomes to make the note come out.

You probably also remember playing low F and low C in sixth position, and “high B natural” in fourth, and meybe even middle and high E natural in second position. Seventh is there, and usable–it’s just that the two notes that can be played only in seventh aren’t required very much. It’s the same in the trumpet world: how often is a trumpet player called upon to play low F# (all three valves, the lowest non-pedal note on the horn)? Hardly ever!

By the way, as a band director, I can tell you that the wrong notes that come out of the trombone section (and flute section, for that matter) are almost always B and/or E naturals, being played as flats. We play so much music using those two notes that kids will automatically play Bb and Eb, even when the key signature says otherwise! (Ab is also common for both instruments.)

18

No.

Your faith in the precise intonation of saxophones is touching.

19

Thank you! My trombone had raised marks on the inside of the slide near 7th position. I always figured they were just there to keep me from pulling the slide off when screwing around. Shows you how serious I was. :rolleyes: (I generally just found the positions by memory and ear, except for first and third.)

BTW, I mostly used the F-attachment to bail out the baritone players, and occassionally the French Horns. I recall an arrangement for “The Enertainer” (“That’s Enertainment”?) for which the slide alone was too slow, and most of our baritonists and french horns too weak, but I could play with the attachment. I actually got to play a duet with a french horn. She was supposed to solo, but stumbled early so I picked it up for her. I’m guessing that history records very few french horn - trombone duets. And the recording industry records even fewer.

I’m sure you are right. I played distressingly long ago.

Seems to me my wrong notes were probably way more common than that, although b’s and e’s (flats) were the most common notes, so I’m sure I made those mistake, too.

20

You obviously listened to my brother.