Ragismic chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Newer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled
4,516 edits
Created page with "'''Ragismic chords''' are essentially tempered chords tempered by the ragisma, 4375/4374. The ragismic temperament has 4 t..."
 
Xenllium (talk | contribs)
autopatrolled
4,516 edits
No edit summary
Line 5: Line 5:
For triads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
For triads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
* 1-25/18-36/25 chord with steps of 25/18-28/27-25/18.
* 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.


The inversely related pair of chords is
The inversely related pair of chords is
Line 11: Line 11:


For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
* 1-27/25-36/25-14/9 chord with steps of 27/25-4/3-27/25-9/7;
* 1-27/25-25/18-3/2 chord with steps of 27/25-9/7-27/25-4/3;
* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25.
* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25.
Line 18: Line 18:
* 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7 and its inverse 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;
* 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7 and its inverse 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;
* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
* 1-27/25-25/18-36/25 with steps of 27/25-9/7-28/27-25/18 and its inverse 1-25/18-36/25-50/27 with steps of 25/18-28/27-9/7-27/25;
* 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27 and its inverse 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7;
* 1-25/18-36/25-14/9 with steps of 25/18-28/27-27/25-9/7 and its inverse 1-9/7-25/18-36/25 with steps of 9/7-27/25-28/27-25/18.
* 1-27/25-25/18-27/14 with steps of 27/25-9/7-25/18-28/27 and its inverse 1-25/18-25/14-27/14 with steps of 25/18-9/7-27/25-28/27.


For pentads, there are one palindromic chord and four pairs of chords in inverse relationship. The palindromic chord is
For pentads, there are one palindromic chord and four pairs of chords in inverse relationship. The palindromic chord is
* 1-27/25-25/18-36/25-50/27 chord with steps of 27/25-9/7-28/27-9/7-27/25.
* 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7.


The inversely related pairs of chords are
The inversely related pairs of chords are
* 1-27/25-25/18-36/25-14/9 with steps of 27/25-9/7-28/27-27/25-9/7 and its inverse 1-9/7-25/18-36/25-50/27 with steps of 9/7-27/25-28/27-9/7-27/25;
* 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27 and its inverse 1-9/7-25/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27;
* 1-27/25-9/7-25/18-50/27 with steps of 27/25-25/21-27/25-4/3-27/25 and its inverse 1-27/25-36/25-14/9-50/27 with steps of 27/25-4/3-27/25-25/21-27/25;
* 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3 and its inverse 1-27/25-7/6-14/9-42/25 with steps of 27/25-27/25-4/3-27/25-25/21;
* 1-27/25-9/7-36/25-50/27 with steps of 27/25-25/21-28/25-9/7-27/25 and its inverse 1-27/25-25/18-14/9-50/27 with steps of 27/25-9/7-28/25-25/21-27/25;
* 1-27/25-7/6-25/18-14/9 with steps of 27/25-27/25-25/21-28/25-9/7 and its inverse 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
* 1-27/25-9/7-25/18-36/25 with steps of 27/25-25/21-27/25-28/27-25/18 and its inverse 1-25/18-36/25-14/9-50/27 with steps of 25/18-28/27-27/25-25/21-27/25.
* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27 and its inverse 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21.


They can be extended to hexads as
They can be extended to hexads as
* 1-27/25-9/7-25/18-36/25-50/27 with steps of 27/25-25/21-27/25-28/27-9/7-27/25 and its inverse 1-27/25-25/18-36/25-14/9-50/27 with steps of 27/25-9/7-28/27-27/25-25/21-27/25.
* 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7 and its inverse 1-27/25-7/6-3/2-14/9-42/25 with steps of 27/25-27/25-9/7-28/27-27/25-25/21.


Equal temperaments with ragismic chords include {{Optimal ET sequence|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.
Equal temperaments with ragismic chords include {{Optimal ET sequence|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.

Revision as of 03:50, 14 July 2023

Ragismic chords are essentially tempered chords tempered by the ragisma, 4375/4374.

The ragismic temperament has 4 triads, 11 tetrads, 9 pentads and 2 hexads as essentially tempered chords.

For triads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are

  • 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
  • 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.

The inversely related pair of chords is

  • 1-9/7-25/18 with steps of 9/7-27/25-36/25 and its inverse 1-27/25-25/18 with steps of 27/25-9/7-36/25.

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

  • 1-27/25-25/18-3/2 chord with steps of 27/25-9/7-27/25-4/3;
  • 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
  • 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25.

The inversely related pairs of chords are

  • 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7 and its inverse 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;
  • 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
  • 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27 and its inverse 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7;
  • 1-27/25-25/18-27/14 with steps of 27/25-9/7-25/18-28/27 and its inverse 1-25/18-25/14-27/14 with steps of 25/18-9/7-27/25-28/27.

For pentads, there are one palindromic chord and four pairs of chords in inverse relationship. The palindromic chord is

  • 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7.

The inversely related pairs of chords are

  • 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27 and its inverse 1-9/7-25/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27;
  • 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3 and its inverse 1-27/25-7/6-14/9-42/25 with steps of 27/25-27/25-4/3-27/25-25/21;
  • 1-27/25-7/6-25/18-14/9 with steps of 27/25-27/25-25/21-28/25-9/7 and its inverse 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
  • 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27 and its inverse 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21.

They can be extended to hexads as

  • 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7 and its inverse 1-27/25-7/6-3/2-14/9-42/25 with steps of 27/25-27/25-9/7-28/27-27/25-25/21.

Equal temperaments with ragismic chords include 19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547.

Retrieved from "https://en.xen.wiki/index.php?title=Ragismic_chords&oldid=120308"