Xenllium at 01:40, 24 February 2025

2025-02-24T01:40:34Z

← Older revision		Revision as of 01:40, 24 February 2025
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	* 1–17/16–19/16–11/8–19/13 with steps of 17/16–19/17–22/19–17/16–26/19.		* 1–17/16–19/16–11/8–19/13 with steps of 17/16–19/17–22/19–17/16–26/19.

	Equal temperaments with Blumeyer chords include {{Optimal ET sequence\| 13, 20, 24, 33, 37, 46, 57, 67, 70, 80, 100, 104, 113 and ~~124~~ }}.		Equal temperaments with Blumeyer chords include {{Optimal ET sequence\| 13, 20, 24, 33, 37, 46, 57, 67, 70, 80, 100, 104, 113, 124, 137, 150, 170, 194 and 307 }}.

	[[Category:19-odd-limit]]		[[Category:19-odd-limit]]

Xenllium: Created page with "'''Blumeyer chords''' are essentially tempered chords tempered by the Blumeyer comma, 2432/2431. Blumeyer chords are of Dyadic chord/Pattern of essenti..."

2025-02-23T12:51:06Z

Created page with "'''Blumeyer chords''' are essentially tempered chords tempered by the Blumeyer comma, 2432/2431. Blumeyer chords are of Dyadic chord/Pattern of essenti..."

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'''Blumeyer chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the Blumeyer comma, [[2432/2431]].

Blumeyer chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.11.13.17.19 [[subgroup]] [[19-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:
* 1–26/19–16/11 with steps of 26/19–17/16–11/8, and its inverse
* 1–17/16–16/11 with steps of 17/16–26/19–11/8;
* 1–16/13–11/8 with steps of 16/13–19/17–16/11, and its inverse
* 1–19/17–11/8 with steps of 19/17–16/13–16/11;
* 1–22/19–16/13 with steps of 22/19–17/16–13/8, and its inverse
* 1–17/16–16/13 with steps of 17/16–22/19–13/8.

For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
* 1–13/11–16/11–13/8 with steps of 13/11–16/13–19/17–16/13;
* 1–17/16–11/8–19/13 with steps of 17/16–22/17–17/16–26/19;
* 1–17/16–16/13–17/13 with steps of 17/16–22/19–17/16–26/17.

The inversely related pairs of chords are
* 1–16/13–11/8–19/13 with steps of 16/13–19/17–17/16–26/19, and its inverse
* 1–17/16–19/16–19/13 with steps of 17/16–19/17–16/13–26/19;
* 1–19/16–11/8–19/13 with steps of 19/16–22/19–17/16–26/19, and its inverse
* 1–17/16–16/13–19/13 with steps of 17/16–22/19–19/16–26/19;
* 1–19/17–11/8–19/13 with steps of 19/17–16/13–17/16–26/19, and its inverse
* 1–17/16–17/13–19/13 with steps of 17/16–16/13–19/17–26/19;
* 1–13/11–26/19–16/11 with steps of 13/11–22/19–17/16–11/8, and its inverse
* 1–17/16–16/13–16/11 with steps of 17/16–22/19–13/11–11/8;
* 1–22/19–16/13–11/8 with steps of 22/19–17/16–19/17–16/11, and its inverse
* 1–19/17–19/16–11/8 with steps of 19/17–17/16–22/19–16/11;
* 1–19/17–22/17–11/8 with steps of 19/17–22/19–17/16–16/11, and its inverse
* 1–17/16–16/13–11/8 with steps of 17/16–22/19–19/17–16/11.

For pentads, there are three pairs of chords in inverse relationship:
* 1–13/11–26/19–16/11–13/8 with steps of 13/11–22/19–17/16–19/17–16/13, and its inverse
* 1–19/17–19/16–11/8–13/8 with steps of 19/17–17/16–22/19–13/11–16/13;
* 1–19/17–19/16–11/8–19/13 with steps of 19/17–17/16–22/19–17/16–26/19, and its inverse
* 1–17/16–16/13–17/13–19/13 with steps of 17/16–22/19–17/16–19/17–26/19;
* 1–17/16–16/13–11/8–19/13 with steps of 17/16–22/19–19/17–17/16–26/19, and its inverse
* 1–17/16–19/16–11/8–19/13 with steps of 17/16–19/17–22/19–17/16–26/19.

Equal temperaments with Blumeyer chords include {{Optimal ET sequence| 13, 20, 24, 33, 37, 46, 57, 67, 70, 80, 100, 104, 113 and 124 }}.

[[Category:19-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Blumeyer]]

Blumeyer chords - Revision history

Xenllium at 01:40, 24 February 2025

Xenllium: Created page with "'''Blumeyer chords''' are essentially tempered chords tempered by the Blumeyer comma, 2432/2431. Blumeyer chords are of Dyadic chord/Pattern of essenti..."