Xenllium: Created page with "'''Heartlandismic chords''' are essentially tempered chords tempered by the heartlandisma, 3971/3969. There are three triads, six tetrads and two pentads..."

2023-08-14T13:25:32Z

Created page with "'''Heartlandismic chords''' are essentially tempered chords tempered by the heartlandisma, 3971/3969. There are three triads, six tetrads and two pentads..."

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'''Heartlandismic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the heartlandisma, [[3971/3969]].

There are three triads, six tetrads and two pentads as 2.3.7.11.19 [[subgroup]] 21-odd-limit essentially tempered chords.

For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is
* 1-21/19-11/9 chord with steps of 21/19-21/19-18/11.

The inversely related pair of chords is
* 1-19/18-21/19 with steps of 19/18-22/21-38/21 and its inverse 1-22/21-21/19 with steps of 22/21-19/18-38/21.

For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
* 1-19/18-21/19-7/6 chord with steps of 19/18-22/21-19/18-12/7;
* 1-22/21-21/19-22/19 chord with steps of 22/21-19/18-22/21-19/11.

The inversely related pairs of chords are
* 1-21/19-7/6-11/9 with steps of 21/19-19/18-22/21-18/11 and its inverse 1-22/21-21/19-11/9 with steps of 22/21-19/18-21/19-18/11;
* 1-21/19-22/19-11/9 with steps of 21/19-22/21-19/18-18/11 and its inverse 1-19/18-21/19-11/9 with steps of 19/18-22/21-21/19-18/11.

They can be extended to pentads:
* 1-19/18-21/19-7/6-11/9 with steps of 19/18-22/21-19/18-22/21-18/11 and its inverse 1-22/21-21/19-22/19-11/9 with steps of 22/21-19/18-22/21-19/18-18/11.

Equal temperaments with heartlandismic chords include {{Optimal ET sequence|14, 41, 48, 63, 77, 89, 104, 118, 152, 166, 193, 207, 270, 311, 359, 477 and 629}}.

[[Category:21-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Heartlandismic]]

Heartlandismic chords - Revision history

Xenllium: Created page with "'''Heartlandismic chords''' are essentially tempered chords tempered by the heartlandisma, 3971/3969. There are three triads, six tetrads and two pentads..."