Wizardharry chords: Difference between revisions
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Created page with "'''Wizardharry chords''' are essentially tempered chords tempered by the wizardharry comma, 4000/3993. The wizardharry temperament has a 1L 6s|seven-to..." |
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'''Wizardharry chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the wizardharry comma, [[4000/3993]]. | '''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 | The triads are | ||
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* 1-11/10-40/33-4/3-22/15 chord with steps of 11/10-11/10-11/10-11/10-15/11; | * 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. | * 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. It includes 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: | |||
* 1-33/32-11/10-25/22-5/4-11/8-3/2-33/20-20/11 with steps of 33/32-16/15-33/32-11/10-11/10-12/11-11/10-11/10-11/10, and its inverse | |||
* 1-33/32-25/22-5/4-11/8-3/2-33/20-20/11-15/8 with steps of 33/32-11/10-11/10-11/10-12/11-11/10-11/10-33/32-16/15. | |||
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 }}. | 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 }}. | ||
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[[Category:Tetrads]] | [[Category:Tetrads]] | ||
[[Category:Pentads]] | [[Category:Pentads]] | ||
[[Category:Nonads]] | |||
[[Category:Wizardharry]] | [[Category:Wizardharry]] | ||
Latest revision as of 13:59, 17 July 2023
Wizardharry chords are essentially tempered chords tempered by the wizardharry comma, 4000/3993.
The wizardharry temperament has a 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 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
- 1-11/10-40/33 chord with steps of 11/10-11/10-33/20;
- 1-40/33-22/15 chord with steps of 40/33-40/33-15/11.
The tetrads are
- 1-11/10-40/33-4/3 chord with steps of 11/10-11/10-11/10-3/2;
- 1-11/10-40/33-22/15 chord with steps of 11/10-11/10-40/33-15/11, and its inverse
- 1-40/33-4/3-22/15 chord with steps of 40/33-11/10-11/10-15/11;
- 1-40/33-22/15-16/9 chord with steps of 40/33-40/33-40/33-9/8.
The pentads are
- 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. It includes 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:
- 1-33/32-11/10-25/22-5/4-11/8-3/2-33/20-20/11 with steps of 33/32-16/15-33/32-11/10-11/10-12/11-11/10-11/10-11/10, and its inverse
- 1-33/32-25/22-5/4-11/8-3/2-33/20-20/11-15/8 with steps of 33/32-11/10-11/10-11/10-12/11-11/10-11/10-33/32-16/15.
Equal temperaments with wizardharry chords include 7, 15, 22, 29, 43, 50, 58, 65, 72, 80, 87, 94, 137, 152, 159, 217, 224 and 289.