De site over het instrument alpenhoorn
Pipes and frequencies
 
Application to the alphorn
 
 
We will now investigate how useful the previous models are to explain the frequencies produced by an alphorn.
For this purpose I have chosen my own alphorn, in E, build by myself.
Specifications:
Length of the conical tube included the mouthpiece: 337 cm
Inner diameters of the conical tube: 1,3 cm and 5,5 cm.
Length of the bell: 60 cm.
Inner diameter at the end of the bell: 23 cm.
Anyhow, an alphorn is neither a complete cone nor a truncated cone! However, if we put aside the bell of the alphorn, then we get a truncated conical tube and this tube we can test.
Specifications of this truncated conical tube:
Length L: 337 cm
Diameters d1 and d2: 1,3 cm and 5,5 cm
a = d1L / (d2-d1) = 1,3 x 337 / (5,5 - 1,3) ≈ 104 (cm), so the apex a is not small and therefor we may expect that model 4 will better apply than model 3.
 
To keep the testing process simple, I made use of a chromatic tuner (SEIKO SAT500) to identify the produced notes.
This means that the measuring-unity is not hertz but semitone.
 
Results of this test:
 
 
Frequencies
according to model 4
 
L = 337
d1 = 1,3
d2 = 5,5
 
Notes according to
model 4
Frequencies
according to model 3
 
L= 337
d1 = 0
d2 = 5,5
 
f = 343 / 2L'
 
Notes
according to model 3
 
Produced
notes
 
f1 = 44 (Hz)
F1
f = 51 (Hz)
G#1
 
f2 = 86
F2
2f = 101
G#2
E2 / F2
f3 = 133
C3 +
3f = 152
D#3
C3 +
f4 = 182
F#3
4f = 202
G#3 -
F#3 -
f5 = 232
A#3
5f = 253
C4 -
A#3
f6 = 282
C#4 +
6f = 304
D#4 -
C#4
f7 = 332
E4 +
7f = 354
F4 / F#4
E4
f8 = 382
F#4 / G4
8f = 405
G4 / G#4
F#4
f9 = 432
A4 -
9f = 455
A#4
A4 --
f10 = 483
B4 -
10f = 506
B4 +
B4 --
f11 = 533
C5 / C#5
11f = 557
C#5
C5
f12 = 584
D5
12f = 607
D5 / D#5
D5
 
 
 
 
 
 
 
The results are clear. Model 4 gives a good prognosis for the produced notes. The frequencies of model 3 are to high.
 
This result enables us to conclude that model 4 will also give a good prognosis for the produced notes, is we should extend the tested truncated conical tube with length 337 cm to a truncated conical tube with length 397 cm.
After that we will be in the position to compare these notes with the real notes of our alphorn in E and to see what the effect of the bell is.
 
                                                                  
 
An easy calculation shows that the diameter at the end of the extended truncated cone is 6,25 cm.
 
Results of this comparison:
 
 
Extended
truncated cone
(no bell)
 
L = 397
d1 = 1,3
d= 6,25
 
Frequencies
according to
model 4
 
 
 
 
 
 
 
 
 
 
Notes
according to
model 4
Alphorn in E
(with bell)
 
 
L = 397
 
 
 
 
Produced
notes
 f1 = 40 (Hz)
 D#1 / E1
 
 f2 = 74
 D2
 D#2 / E2
 f3 = 114
 A#2 -
 B2
 f4 = 155
 D#3
 E3
 f5 = 197
 G3
 G#3
 f6 = 239
 A#3 / B3
 B3
 f7 = 282
 C#4 +
 D4 -
 f8 = 325
 E4 -
 E4
 f9 = 367
 F#4
 F#4
 f10 = 410
 G#4 -
 G#4
 f11 = 453
 A4 / A#4
 A4
 f12 = 496
 B4 
 B4 
 
 
 
 
 
The second and third column show the well-know effect of the bell:
the bell raises progressively the lower frequencies.
The result is a full harmonic series with the fundamental missing!
However, we may assume that there is a lower frequency, higher than the fundamental, but to low te be blown.
  
 
© 2007 J. de Ruiter