John D wondered
I commute an hour and 15 minutes each way to work every day. Recently,
I cut a piece of hose to be pitched in F. Now on my way to work I can
warm-up and do a series of slurring and tonguing exercises on the hose
horn. It has changed my life for the better.
I have a question for anyone who understands the physics of this. For
some reason, my hose is badly out of tune. The interval between the c's
(from the bass clef C to middle C and to the treble clef C) is very
badly out of tune. It is naturally closer to a minor ninth than an
octave without lipping it in tune (which is substantially more difficult
on the hose than my horn). Why would this be? I assumed that any pipe
would naturally play octaves that are in tune with themselves.
**********
A cylindrical tube sealed at one end (by your mouth) and open
at the other will produce playing notes which are odd multiples of
the lowest frequency. Since there is no way for one odd multiple
to be exactly twice another, there are actually no octaves possible.
The errors get smaller and smaller as you play higher notes. Here is
an explanation that involves a little math.
In an open natural horn, the playing frequencies are integer multiples of
the lowest frequency:
1 2 3 4 5 6 7 8 9 11 12
Middle C is the fourth of these; an octave higher is the eighth.
And 8 is twice 4, giving a true octave 2/1.
G is the third of these; an octave higher is the sixth. These are
also in a 2/1 ratio.
In your hose, the notes are thus:
1 3 5 7 9 11 13 15 17 19 21 23
The fourth of these and the eighth are in a 15/7 ratio, a little
larger than an octave.
The third of these and the sixth are in a 11/5 ratio.
Since 15/7 is closer to 2/1 than 11/5 is, we see that the
playing notes sound more in tune the higher we get. And since
a hose is such a low quality instrument, it is easier to bend the
notes. So a garden hose sounds a bit more in tune in the high
register than in the low register.
A funnel will change the frequencies a little, but not enough
to enhance the musical value of the instrument. Mainly, the
funnel makes the instrument sound louder. And if it falls
off the hose, it makes a charming hat to wear.
I'm surprised that the interval you report from low C to middle
C is as close to an octave as you indicate. I bet you are bending
the notes.
My opera "Fun with Dick and Jane" includes an aria for Jane
on the immortal words "See Spot run." There is an extensive obligato
part for garden hose in D. I actually find that it is easier to lip
notes in tune on the hose than on my horn. (Of course, it helps
that my horn is already in tune.) This is because the resonances
in the hose aren't very strong, so they tend to be spready.
Gotta go,
Cabbage
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