Heptacircle chords: Difference between revisions

'''Heptacircle chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the heptacircle comma, [[2431/2430]].  

Heptacircle chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.5.11.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.  

For triads, there are three pairs of chords in inverse relationship:

* 1-11/9-18/13 with steps of 11/9-17/15-13/9 and its inverse 1-13/9-18/11 with steps of 13/9-17/15-11/9;

* 1-15/11-13/9 with steps of 15/11-18/17-18/13 and its inverse 1-18/17-13/9 with steps of 18/17-15/11-18/13;

* 1-15/13-11/9 with steps of 15/13-18/17-18/11 and its inverse 1-18/17-11/9 with steps of 18/17-15/13-18/11.

For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are:

The inversely related pairs of chords are:

* 1-11/9-18/13-17/9 with steps of 11/9-17/15-15/11-18/17 and its inverse 1-15/11-17/11-17/9 with steps of 15/11-17/15-11/9-18/17;

* 1-15/11-5/3-17/9 with steps of 15/11-11/9-17/15-18/17 and its inverse 1-17/15-18/13-17/9 with steps of 17/15-11/9-15/11-18/17;

* 1-18/13-18/11-17/9 with steps of 18/13-13/11-15/13-18/17 and its inverse 1-15/13-15/11-17/9 with steps of 15/13-13/11-18/13-18/17;

* 1-15/13-18/13-17/9 with steps of 15/13-6/5-15/11-18/17 and its inverse 1-15/11-18/11-17/9 with steps of 15/11-6/5-15/13-18/17;

* 1-17/15-18/11-17/9 with steps of 17/15-13/9-15/13-18/17 and its inverse 1-15/13-5/3-17/9 with steps of 15/13-13/9-17/15-18/17;

* 1-13/9-18/11-17/9 with steps of 13/9-17/15-15/13-18/17 and its inverse 1-15/13-17/13-17/9 with steps of 15/13-17/15-13/9-18/17.

For pentads, there are three pairs of chords in inverse relationship:

* 1-15/13-15/11-5/3-17/9 with steps of 15/13-13/11-11/9-17/15-18/17 and its inverse 1-17/15-18/13-18/11-17/9 with steps of 17/15-11/9-13/11-15/13-18/17;

* 1-15/11-13/9-18/13-17/9 with steps of 15/11-18/17-17/15-15/13-18/17 and its inverse 1-15/13-17/13-18/13-17/9 with steps of 15/13-17/15-18/17-15/11-18/17;

* 1-15/13-11/9-18/13-17/9 with steps of 15/13-18/17-17/15-15/11-18/17 and its inverse 1-15/11-17/11-18/11-17/9 with steps of 15/11-17/15-18/17-15/13-18/17.