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harmonic number
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first three harmonic standing waves in a stretched string first 10 notes in the overtone series of G2
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harmonic number

physics
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first three harmonic standing waves in a stretched string
first three harmonic standing waves in a stretched string Figure 4: The first three harmonic standing waves in a stretched string. Nodes (N) and antinodes (A) are marked. The harmonic number (n) for each standing wave is given on the right (see text).

In physics, the term "harmonic number" refers to the integer n in the sequence of frequencies that can exist as standing waves in a system, such as a stretched string. These frequencies are integral multiples of the fundamental frequency. The fundamental frequency, also known as the first harmonic, is the lowest frequency at which a system can vibrate. For example, in a stretched string, additional standing waves can be created, and the frequency of these vibrations (fn) is related to the fundamental frequency (f1) by the equation fn = n f1, where n is the harmonic number. This concept is also applied in quantum mechanics, where a vibrational quantum number defines the energy state of a harmonic vibrating atomic system. The study of harmonic sequences in mathematics, dating back to the Pythagoreans, explored numerical intervals and their relation to musical harmony.1234

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4 Britannica Sources
  1. harmonic sequence
  2. number symbolism - Pythagoreanism
  3. sound - Fundamentals and harmonics
  4. vibrational quantum number

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