Abstract
The French word son (sound), as used here, expresses here the pitch of the vibrations. An acute sound differs from a grave sound by the greater (acute) or smaller (grave) number of vibrations that it executes in a given interval of time.
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Notes
- 1.
Chladni used the symbol ut for the first note in the musical scale, but we have replaced it by do regularly used in modern texts. We have left the seventh note as si, since both si and ti are used today in different countries.—RTB
- 2.
In the early mathematical studies of music, a debate existed between those who used the number of half oscillations (simple vibrations) per second, and those who used the number of full oscillations (double vibrations). The latter school won out.—RTB
- 3.
This “powers-of-two” scale is no longer used in music but is commonly employed in instruction in physics, and is sometimes called the physicists’ scale.—RTB
- 4.
What Chladni refers to is the second partial (often the second harmonic).—TDR
- 5.
Unlike Chladni, we do not assume that the modern reader readily understands Latin. The first line of this quote from Leibniz is a famous definition of music: “Music is a hidden arithmetic exercise of a soul that does not know it is counting.” Leibniz says that the pleasure we obtain from music comes from this unconscious counting.—CBH
- 6.
Most musicians now consider the perfect fourth to be consonant.—TDR
- 7.
Although \( \frac{3}{2}\times \frac{3}{2} \) does not appear to equal \( \frac{9}{8} \), this is the original text in both French and German versions of this work.—MAB
- 8.
It is popularly believed that Guido of Arezzo took the opening syllable letters from each line of a hymn to Saint John the Baptist to form the names of notes in the musical scale:
UTqueant laxis
REsonare fibris
MIra gestorum
FAmuli tuorum
SOLve polluti
LAbii reatum
Sancte Ioanne—RTB
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Chladni, E.F.F. (2015). Section 1: Primary Ratios. In: Treatise on Acoustics. Springer, Cham. https://doi.org/10.1007/978-3-319-20361-4_2
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