# Sound analysis extended

Sound analysis of the violin

The tone we hear consists of the root and various overtones. Together they determine the timbre.

• The strength of a tone, how loud it sounds, is called Loudness. The corresponding unit is decibel, abbreviated to dB. So a tone of 89 dB sounds stronger, louder than a tone of 85 dB. This scale is not directly proportional. Practically speaking, two violins of both 85 Hz, together sound like 88 Hz.
• The pitch is expressed in Hertz, abbreviated to Hz. This does work straight-proportional. 880 Hz sounds 2x as high as 440 Hz (one octave higher).
• The timbre of an instrument is determined by the strength ratio of the root and the different overtones.

In a measurement report we examine the sound of a violin by means of a number of questions:

1. How strong is the key- or root tone on a particular string in relation to the overtones? A strong root gives a full, warm sound.
2. How strong are the different overtones? A lot of sound in the area of human hearing (1000- 3000Hz) gives a full tone. Little sound between 1000 and 3000 Hz and a lot of treble gives a shrill sound.
3. How large is the range of the violin (in the treble)?
4. Does the violin sound about the same over all four strings?

Based on many measurements it appears that a good sounding violin has the following properties:

• The root is louder than the overtones.
• The strength -or loudness- of the overtones decreases regularly.
• The violin also produces sound in the area above 10,000 Hz.
• Over all 4 strings the sound is about the same strength (equal loudness).

Working method

With the help of the computer and a special computer program, recordings are made. Then the sound is analyzed per tone. This results in a graph that shows the loudness of the tone in dB as a function of the frequency in Hz.

Along the vertical axis, the Loudness is in decibels (dB). The higher the graph, the louder the tone. Along the horizontal axis is the frequency. The higher the frequency in Hertz (Hz), the higher the tone sounds. In this example a C4 (262 Hz) is played on the g-string of a violin. In the graph the highest peak is the root tone. To the right we see a number of overtones, of which the 1st and 2nd overtones are indicated by a black arrow. The overtones gradually decrease in loudness (loudness). The black line drawn here connects the peaks as much as possible. If the peak remains below the black line, the overtone is somewhat weaker. If the peak is above the line, then that peak is proportionally stronger (louder). The part to the left of the root is not important for the violin. These are the sounds of the computer.

Good sounding is not always the same as beautiful sounding. For example, some people prefer a sonorous sounding Guarneri del GesÃ¹. The other prefers a more clear Stradivarius sound.

Do all strings sound equally loud?

You can use a decibel meter (or app) to measure the loudness in decibels (dB) of the four strings. You can also measure the loudness by reading them from the audiograms.

In the example table below a violin is measured over the four different individual strings.

Loudness in dB Example
Violin and year of construction G string D string A string E string
Kessels 1904 91 dB 93 dB 93 dB 89 dB

The difference here is big. 93 decibels is experienced about twice as loud by the human ear as 89 dB. As mentioned above, doubling the strength gives an increase of 3 dB.

So much for the backgrounds of the sound analysis.