3B Scientific Acoustics Kit - Manual (Page 7)

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fold, four-fold, etc. As measured earlier, 1/4 of 5.5
is 1.4 (rounded up).
24. Wind instruments and the laws they obey
• Blow the whistle. You can change the effective
length of the whistle by moving the plunger.
When the length is short, the whistle produces a
high tone and when it is longer, it produces a lower
tone.
Reasons: when a weak air current passes through
the whistle, standing waves are produced. In this
case, the length of the whistle corresponds to a
quarter wave length. When a strong air current
passes through the whistle, overtones are produced
whose frequency is an odd multiple of the funda-
mental tone.
In the case of an open whistle, the first harmonic is
twice the frequency of that for a closed whistle.
25. C major scale and its intervals
• To determine the intervals, the higher fre-
quency is divided by the lower frequency.
For the interval D/C = 1188/1056, the common
divisor is 132. We thus get ratios of 9/8, 10/9,
16/15, 9/8, 10/9, 9/8 and 16/15.
Reasons: the intervals between the individual tones
of a musical scale are not equal. Intervals can be
distinguished into the major tone (9/8), minor tone
(10/9) and half-tone (16/15).
26. Harmony and dissonance
• Play all possible combinations on the reed
pipe.
Pleasing harmonies (consonances) are produced at
the octave, the fifth note, the fourth, the major
third and minor third. Discordant notes (disso-
nances) emerge between the second and seventh
notes. The combination of tones produced by two
neighbouring tones is also called dissonance.
27. G major triad
• Simultaneously blow notes G, B and D on the
reed pipe.
A highly melodious combination is heard. This
combination of notes is termed the G major triad.
Reasons: consonance is produced if several notes
produce a melodious combination of pairs. The G
major triad is formed as a combination of the ma-
jor third and the minor third. The frequencies of
the notes G, Band D have a very simple ratio to one
another, viz. 4:5:6.
In order to derive this ratio, the fundamental fre-
quencies specified on the reed pipe should each be
divided by 6.
(To obtain a physically correct frequency, the fun-
damental frequencies printed on the pipe need to
be multiplied by 33).
It is also possible for the tuning of the reed pipe
and metallophone to differ audibly due to manu-
facturing processes.
28. Four-part G major chord
• Add to the G major triad the G’ octave as well.
To achieve this, simultaneously play G, B, D
and G’.
The result is a full and melodious “four-part G
major chord”.
Reasons: a four-part major chord features the fol-
lowing consonances:
Octave 1:2
Fifth 2:3
Major third 4:5
Minor third 5:6
29. Major scales in an arbitrary key
• First play the C major scale on the metallo-
phone. Begin with C. Subsequently play a simi-
lar scale starting from G.
A C major scale from C’ to C’’ sounds pleasantly
consonant. If you try to play a similar scale starting
at G’, though, there is a definite dissonance at F’’.
The note is a semitone too low.
Reasons: according to experiment 25, the following
intervals must be exhibited in every scale:
9/8, 10/9 16/15, 9/8, 10/9, 9/8, 16/15
For the sequence of notes G’…G’’, however, the
following intervals are specified on the base plate
of the metallophone:
10/9, 9/8, 16/15, 9/8, 10/9, 16/15, 9/8
The underlined intervals are correct, the others are
incorrect in this sense.
The intervals 9/8 and 10/9 are so close to one an-
other that it is extremely difficult to distinguish
between them. Hence, the divergence from the
ideal between G’ and B’ is irrelevant. However, the
“imperfection’ between E’’ and F’’ is easily notice-
able. In this case, an interval of 16/15 occurs in-
stead of 9/8. The F’ note is therefore a semitone too
deep.
30. Producing half-tones
• On the reed pipe, play the scale from G’ to G’’
making sure that the A’ note of the reed pipe is
genuinely tuned to standard pitch. Use the
tuning fork to compare the pitch.
A G major scale on the reed pipe is pleasantly con-
sonant.
Reasons: instead of the F’ note, a completely new
note, F#, is introduced. The interval between F’