Why do we have inversions but not permutations?

1. Why do we have chord inversions?
2. How many inversions does a permutation have?
3. What is inversion in a permutation?
4. Are voicings and inversions the same thing?

Why do we have chord inversions?

The trick is to use inversions to keep notes that are common to both chords in the same position in each chord. If there are no common tones, then use the same inversion of each chord to keep the note movement to a minimum.

How many inversions does a permutation have?

The number of inversions in a permutation is equal to that of its inverse permutation (Skiena 1990, p. 29; Knuth 1998). If, from any permutation, another is formed by interchanging two elements, then the difference between the number of inversions in the two is always an odd number.

What is inversion in a permutation?

An inversion in a permutation is a pair of numbers such that the larger number appears to the left of the smaller one in the permutation. ... One way to help calculate the inversion number is to look at each position in the permutation and count how many smaller numbers are to the right, and then add those numbers up.

Are voicings and inversions the same thing?

The difference between the concept of inversion and that of voicing is in the goal of the concepts respectively. The goal of the concept of inversion is to have another bass note apart from the root note, while the goal of the concept of voicing is to rearrange the notes of a chord, considering them as voices.