Nicolic chords

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

There are three triads, six tetrads and two pentads as 15-odd-limit essentially tempered chords.

The nicolic triads include the following palindromic form,

• 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
• 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]