On my trombone (a regular B

^{b}bone) there's a harmonic series of notes I can (notionally !) play purely by changing my

*embouchure*:

^{}

Partial | Fundamental [1st partial] | 2 ^{nd} | 3 ^{rd} | 4 ^{th} | 5 ^{th} | 6 ^{th} | 7 ^{th} | 8 ^{th} | 9 ^{th} | 10 ^{th} |
---|---|---|---|---|---|---|---|---|---|---|

Note | B ^{b} | B ^{b} | F | B ^{b} | D | F | A ^{b}- | B ^{b} | C | D |

Currently my range is from the B

^{b}2nd partial (I can get the pedal B

^{b}not-very-reliably after I've been practising for a while and my lips are loosened up) up to about the 6

^{th}partial, sometimes 7

^{th}, again once my lips have warmed up a bit, but not very reliably.

Interestingly the intervals of the harmonic series (of partials) form a pretty curve when you write them up on a stave, here's the B

^{b}series:

It turns out that the reason for this curve is rooted in physics (as you'd expect), but, curiously, also has to do with our perception of sound; the fundamental pitch of my trombone is the pedal B

^{b}(at 58.27Hz), it transpires that each partial up is a

*multiple of the fundamental frequency*, so the next partial up from the fundamental is 2 * 58.27Hz. More details below for the curious.

That's the physics bit, now the perception bit: what we hear as an octave interval is really the doubling of a note's frequency.

So from 58.27Hz to 2*58.27Hz explains the octave interval from Fundamental B

^{b}(58.27Hz) to 1st partial B

^{b}(116Hz).

The next partial is 3*58.27Hz = 174.81Hz which is an F (there's a table of frequencies here), and so on:

4 * 58.27Hz = 232.08Hz : B

^{b}

5 * 58.27Hz = 291.25Hz : D

6 * 58.27Hz = 349.65Hz : F

7 * 58.27Hz = 407.89Hz : A

^{b }(this one's a bit flat, A

^{b}is more like 415Hz - another weird perceptional thing?)

8 * 58.27Hz = 466.16Hz : Bb

9 * 58.27Hz = 524.43Hz : C

...

Now you know :)

**More on the physics**

Open cylindrical tubes resonate at the approximate frequencies:

*f = nv / 2L*

where

*n*is a positive integer,*L*is the length of the tube, and*v*is the speed of sound in air (~343m/s).A trombone with slide closed is about 2.8m, and has a bore of about 1.4cm so the fundamental resonant frequency is:

*f = (1 * 343) / (2 * 2.8)*

*= 343 / 5.6*

*= 61Hz*

Near enough, the formula is an approximation since the anti-node reflection point is a little past the end of the tube.

Solving for the other partials gives:

*f=2: 122*

*f=3: 183*

*f=4: 245*

*f=5: 306*

etc.

More details here: http://en.wikipedia.org/wiki/Acoustic_resonance#Resonance_of_a_tube_of_air

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