Xenllium: Created page with "'''Dudon chords''' are essentially tempered dyadic chords tempered by the dudon comma, 361/360. There are two tetrads, four pentads and one hexad as 2.3...."

2023-09-06T04:11:52Z

Created page with "'''Dudon chords''' are essentially tempered dyadic chords tempered by the dudon comma, 361/360. There are two tetrads, four pentads and one hexad as 2.3...."

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'''Dudon chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the dudon comma, [[361/360]].

There are two tetrads, four pentads and one hexad as 2.3.5.19 subgroup [[19-odd-limit]] essentially tempered chords.

The two dudon tetrads are palindromic:
* 1-19/16-19/15-3/2 with steps of 19/16-16/15-19/16-4/3;
* 1-19/18-19/15-4/3 with steps of 19/18-6/5-19/18-3/2.

For pentads, there are two pairs of chords in inverse relationship:
* 1-19/15-3/2-8/5-19/10 with steps of 19/15-19/16-16/15-19/16-19/18 and its inverse 1-19/16-3/2-19/12-15/8 with steps of 19/16-19/15-19/18-19/16-16/15;
* 1-19/16-5/4-3/2-19/12 with steps of 19/16-19/18-6/5-19/18-19/15 and its inverse 1-6/5-19/15-3/2-19/10 with steps of 6/5-19/18-19/16-19/15-19/18.

Finally there is a palindromic hexad,
* 1-19/16-19/15-3/2-19/12-19/10 with steps of 19/16-16/15-19/16-19/18-6/5-19/18.

Equal temperaments with dudon chords include {{Optimal ET sequence|9, 12, 15, 26, 27, 29, 38, 41, 53, 65, 77, 118 and 171}}.

[[Category:19-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Dudon]]

Dudon chords - Revision history

Xenllium: Created page with "'''Dudon chords''' are essentially tempered dyadic chords tempered by the dudon comma, 361/360. There are two tetrads, four pentads and one hexad as 2.3...."