Horn Harmonic Series

Last week I looked at using the harmonics of the horn when playing Nielsen's Wind Quintet. This week I'll pay attention to the number of harmonics playable on the horn and start showing how pitches from the different lengths of tube in the horn can interact with each other.

Here's a short paragraph about the instrument. Horn parts are almost always written a perfect 5th higher than they sound. The standard instrument from the middle of the 19th century was the F horn with valves so most music for valve horn is written for horn in F. Nowadays a large portion of players use a double horn in B♭and F with 3 valves plus thumb valve yet the music is still written in F. Each valve allows air to vibrate through another length of tube. The second valve slide lowers the pitch of either B♭or F horn by a semitone, 1st valve by a tone, 3rd (or 2 & 1) by a tone and a semitone, 2 & 3 together by two tones, 1 & 3 together by somewhat short of two tones and one semitone, all three by a quartertone short of 3 tones.

Harmonics. The easiest harmonics to play on the F horn are harmonics 3-12 (written G below the treble staff to the G at the top of the treble staff. The easiest harmonics to play on the B♭ horn are harmonics 2-9 (written F below the treble staff to the G at the top of the treble staff. In the same pitch range the low C horn (F horn plays valves 1 & 3) uses harmonics 4-16. These are not so easy to play as the overall tube length is long and narrow and the sound often a bit stuffy.

The short video here shows these harmonics. Horn in F, Horn in B♭ (high; short), horn in C (low; long). At the end of the video you can hear the F horn harmonics 1-19 to show how the extended range of the horn and the smaller and smaller intervals, progressively through the higher range.


Matching harmonics

It's easy to achieve a scale of just intonation intervals by matching the tuning of 2 harmonic series. The most obvious is to match the written Cs between the F and Bb horns. The middle C is F horn harmonic 4 and B♭horn harmonic 3. A nice F major scale can be played with just these two horns and is shown in staff notation below. The 4th degree is flatter than normal, for sure.

 This is how it sounds:


Other simple scales can be achieved by slightly adjusting a valve slide. For example, pushing the F horn 1st valve slide slightly in matches so that its harmonic 10 matches the F horn harmonic 9.

(For those interested the ratios of the written C scale are C=1:1, 0 cents  D=9:8, 204 cents  E=5:4, 386 cents  F=27:20, 520 cents  G=3:2, 702 cents  A♭=63:40, 787 cents  B♭=9:5, 1018 cents.)


Extending the F horn 1st valve slide slightly, so that its harmonic 9 matches the F horn harmonic 8.

(For those interested the ratios of the written C scale are C=1:1, 0 cents  D=10:9, 182 cents  E=5:4, 386 cents  F=4:3, 498 cents  G=3:2, 702 cents,  A♭=14:9, 765 cents  B♭=16:9, 996 cents.)

In an upcoming blog, I'll show the harmonic series matching of 5 tube lengths to the pitch concert A, as used in my trio You Were Never My Country for soprano, horn and piano. Greviilea Ensemble will perform this on October 22.

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