Wizardharry chords: Difference between revisions

Line 1:

'''Wizardharry chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the wizardharry comma, [[4000/3993]].

The wizardharry temperament has a [[1L 6s|seven-tone scale]] which consists of a chain of six submajor seconds, of size approximately [[11/10]], and a whole tone of size approximately [[9/8]], which closes at the octave since the wizardharry comma is [[Tempering out|tempered out]]. It contains two triads, four tetrads and two pentads as 33-odd-limit essentially tempered chords.

The wizardharry temperament has a [[1L 6s|seven-tone scale]] which consists of a chain of six submajor seconds, of size approximately [[11/10]], and a whole tone of size approximately [[9/8]], which closes at the octave since the wizardharry comma is [[Tempering out|tempered out]]. It contains two triads, four tetrads and two pentads as 2.3.11/5 [[subgroup]] 33-odd-limit essentially tempered chords.

The triads are

Line 16:

* 1-11/10-40/33-4/3-22/15 chord with steps of 11/10-11/10-11/10-11/10-15/11;

* 1-40/33-4/3-22/15-16/9 chord with steps of 40/33-11/10-11/10-40/33-9/8.

In the 2.3.5.11 subgroup, the wizardharry temperament contains many possibilities for essentially tempered chords, including 12 triads, and even nonads, as 33-odd-limit essentially tempered chords.

For triads, there are five additional pairs of chords in inverse relationship:

* 1-11/10-25/22 with steps of 11/10-33/32-44/25 and its inverse 1-33/32-25/22 with steps of 33/32-11/10-44/25;

* 1-40/33-11/8 with steps of 40/33-25/22-16/11 and its inverse 1-25/22-11/8 with steps of 25/22-40/33-16/11;

* 1-11/8-50/33 with steps of 11/8-11/10-33/25 and its inverse 1-11/10-50/33 with steps of 11/10-11/8-33/25;

* 1-22/15-50/33 with steps of 22/15-33/32-33/25 and its inverse 1-33/32-50/33 with steps of 33/32-22/15-33/25;

* 1-50/33-11/6 with steps of 50/33-40/33-12/11 and its inverse 1-40/33-11/6 with steps of 40/33-50/33-12/11.

Remarkable nonads include a pair of chords in inverse relationship:

* 1-11/10-40/33-4/3-11/8-22/15-50/33-5/3-11/6 with steps of 11/10-11/10-11/10-33/32-16/15-33/32-11/10-11/10-12/11, and its inverse

* 1-11/10-40/33-5/4-4/3-11/8-50/33-5/3-11/6 with steps of 11/10-11/10-33/32-16/15-33/32-11/10-11/10-11/10-12/11.

Equal temperaments with wizardharry chords include {{Optimal ET sequence| 7, 15, 22, 29, 43, 50, 58, 65, 72, 80, 87, 94, 137, 152, 159, 217, 224 and 289 }}.

Line 24:

Line 37:

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Nonads]]

[[Category:Wizardharry]]

@@ Line 1: / Line 1: @@
 '''Wizardharry chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the wizardharry comma, [[4000/3993]].
-The wizardharry temperament has a [[1L 6s|seven-tone scale]] which consists of a chain of six submajor seconds, of size approximately [[11/10]], and a whole tone of size approximately [[9/8]], which closes at the octave since the wizardharry comma is [[Tempering out|tempered out]]. It contains two triads, four tetrads and two pentads as 33-odd-limit essentially tempered chords.
+The wizardharry temperament has a [[1L 6s|seven-tone scale]] which consists of a chain of six submajor seconds, of size approximately [[11/10]], and a whole tone of size approximately [[9/8]], which closes at the octave since the wizardharry comma is [[Tempering out|tempered out]]. It contains two triads, four tetrads and two pentads as 2.3.11/5 [[subgroup]] 33-odd-limit essentially tempered chords.
 The triads are
@@ Line 16: / Line 16: @@
 * 1-11/10-40/33-4/3-22/15 chord with steps of 11/10-11/10-11/10-11/10-15/11;
 * 1-40/33-4/3-22/15-16/9 chord with steps of 40/33-11/10-11/10-40/33-9/8.
+In the 2.3.5.11 subgroup, the wizardharry temperament contains many possibilities for essentially tempered chords, including 12 triads, and even nonads, as 33-odd-limit essentially tempered chords.
+For triads, there are five additional pairs of chords in inverse relationship:
+* 1-11/10-25/22 with steps of 11/10-33/32-44/25 and its inverse 1-33/32-25/22 with steps of 33/32-11/10-44/25;
+* 1-40/33-11/8 with steps of 40/33-25/22-16/11 and its inverse 1-25/22-11/8 with steps of 25/22-40/33-16/11;
+* 1-11/8-50/33 with steps of 11/8-11/10-33/25 and its inverse 1-11/10-50/33 with steps of 11/10-11/8-33/25;
+* 1-22/15-50/33 with steps of 22/15-33/32-33/25 and its inverse 1-33/32-50/33 with steps of 33/32-22/15-33/25;
+* 1-50/33-11/6 with steps of 50/33-40/33-12/11 and its inverse 1-40/33-11/6 with steps of 40/33-50/33-12/11.
+Remarkable nonads include a pair of chords in inverse relationship:
+* 1-11/10-40/33-4/3-11/8-22/15-50/33-5/3-11/6 with steps of 11/10-11/10-11/10-33/32-16/15-33/32-11/10-11/10-12/11, and its inverse
+* 1-11/10-40/33-5/4-4/3-11/8-50/33-5/3-11/6 with steps of 11/10-11/10-33/32-16/15-33/32-11/10-11/10-11/10-12/11.
 Equal temperaments with wizardharry chords include {{Optimal ET sequence| 7, 15, 22, 29, 43, 50, 58, 65, 72, 80, 87, 94, 137, 152, 159, 217, 224 and 289 }}.
@@ Line 24: / Line 37: @@
 [[Category:Tetrads]]
 [[Category:Pentads]]
+[[Category:Nonads]]
 [[Category:Wizardharry]]