Nicolic chords

Nicolic chords are essentially tempered chords tempered by the nicola, 1575/1573.

Nicolic chords are of pattern 1b in the 15-odd-limit. There are 3 triads, 6 tetrads and 2 pentads for a total of 11 distinct chord structures.

The nicolic triads include the following palindromic form since it identifies 13/7 by a stack of two 15/11's:

• 1–15/11–13/7 with steps of 15/11, 15/11, 14/13.

And a pair in inverse relationship:

• 1–15/11–11/7 with steps of 15/11, 15/13, 14/11, and its inverse
• 1–15/11–26/15 with steps of 15/11, 14/11, 15/13.

For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are

• 1–15/13–15/11–11/7 with steps of 15/13, 13/11, 15/13, 14/11;
• 1–15/13–22/15–11/7 with steps of 15/13, 14/11, 15/14, 14/11.

The inversely related pairs of chords are

• 1–15/11–11/7–13/7 with steps of 15/11, 15/13, 13/11, 14/13, and its inverse
• 1–15/11–22/15–26/15 with steps of 15/11, 14/13, 13/11, 15/13;
• 1–15/11–26/15–13/7 with steps of 15/11, 14/11, 15/14, 14/13, and its inverse
• 1–15/11–22/15–11/7 with steps of 15/11, 14/13, 15/14, 14/11.

They can be extended to pentads:

• 1–15/14–15/13–15/11–11/7 with steps of 15/14, 14/13, 13/11, 15/13, 14/11, and its inverse
• 1–15/13–15/11–22/15–11/7 with steps of 15/13, 13/11, 14/13, 15/14, 14/11.

Equal temperaments with nicolic chords include 29, 31, 43, 58, 72, 87, 94, 103, 121, 130, 159, 190, 217, 224, 311, 414, 441, 665 and 855.

Here is a listening sample, tempered to TE tuning of nicolic.

Ratio	1/1	15/13	15/11	11/7
Cents	0.000	247.099	536.086	783.185
Sound [info]