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Just like melodic sequences, harmonic sequences occur when a segment of chords is followed by the same progression of chords transposed up or down by some interval. For example, we may start with a I-V progression in Major, and then transpose this pattern of chords down a second, we end up with a viio-ii progression.
The harmonic mean is calculated as the reciprocal of the arithmetic mean of the reciprocals, a progression has a specific formula for computing its nth term, and the difference between a progression and a sequence will be discussed in this article.
In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression, which is also known as an arithmetic sequence. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.
E.g.,1/a, 1/(a+d), 1/(a + 2d), and so on are in HP as a, a + d, a + 2d are in AP. In other words, the inverse of a harmonic sequence follows the rule of an arithmetic progression. Example of harmonic progression is 1/2, 1/4, 1/6,
Example of harmonic progression is 1/2, 1/4, 1/6, If we take the reciprocal of each term of the above HP, the sequence will become 2, 4, 6, . which is an AP with common difference of 2. In order to solve a problem on Harmonic Progression, one should make the corresponding AP series and then solve the problem.
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Harmonic Sequence Definition It is an infinite series that never converges to a limit. For example, lets take an arithmetic sequence as 5, 10, 15, 20, 25, with the common difference of 5. Then its harmonic sequence is: 1/5, 1/10, 1/15,1/20,1/25.
A sequence of numbers is said to be in harmonic sequence if the reciprocals of all the elements/numbers/data of the sequence form an arithmetic sequence. Example of Harmonic Sequence: 13,16,19,112,115.

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