Fidesmic chords: Difference between revisions
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'''Fidesmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the fidesma, [[2025/2023]]. | '''Fidesmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the fidesma, [[2025/2023]]. | ||
Fidesmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.3.5.7.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. | |||
For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is | For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is | ||
* 1-17/15-9/7 | * 1-17/15-9/7 with steps of 17/15-17/15-14/9. | ||
The inversely related pair of chords is | The inversely related pair of chords is | ||
* 1-15/14-17/15 with steps of 15/14-18/17-30/17 and its inverse 1-18/17-17/15 with steps of 18/17-15/14-30/17. | * 1-15/14-17/15 with steps of 15/14-18/17-30/17, and its inverse | ||
* 1-18/17-17/15 with steps of 18/17-15/14-30/17. | |||
For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | ||
* 1-15/14-17/15-17/14 | * 1-15/14-17/15-17/14 with steps of 15/14-18/17-15/14-28/17; | ||
* 1-18/17-17/15-6/5 | * 1-18/17-17/15-6/5 with steps of 18/17-15/14-18/17-5/3. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-17/15-17/14-9/7 with steps of 17/15-15/14-18/17-14/9 and its inverse 1-18/17-17/15-9/7 with steps of 18/17-15/14-17/15-14/9; | * 1-17/15-17/14-9/7 with steps of 17/15-15/14-18/17-14/9, and its inverse | ||
* 1-17/15-6/5-9/7 with steps of 17/15-18/17-15/14-14/9 and its inverse 1-15/14-17/15-9/7 with steps of 15/14-18/17-17/15-14/9. | * 1-18/17-17/15-9/7 with steps of 18/17-15/14-17/15-14/9; | ||
* 1-17/15-6/5-9/7 with steps of 17/15-18/17-15/14-14/9, and its inverse | |||
* 1-15/14-17/15-9/7 with steps of 15/14-18/17-17/15-14/9. | |||
They can be extended to pentads: | They can be extended to pentads: | ||
* 1-15/14-17/15-17/14-9/7 with steps of 15/14-18/17-15/14-18/17-14/9 and its inverse 1-18/17-17/15-6/5-9/7 with steps of 18/17-15/14-18/17-15/14-14/9. | * 1-15/14-17/15-17/14-9/7 with steps of 15/14-18/17-15/14-18/17-14/9, and its inverse | ||
* 1-18/17-17/15-6/5-9/7 with steps of 18/17-15/14-18/17-15/14-14/9. | |||
Equal temperaments with fidesmic chords include {{Optimal ET sequence|10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354}}. | Equal temperaments with fidesmic chords include {{Optimal ET sequence|10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354}}. | ||
Latest revision as of 04:23, 26 November 2023
Fidesmic chords are essentially tempered chords tempered by the fidesma, 2025/2023.
Fidesmic chords are of pattern 1a in the 2.3.5.7.17 subgroup 17-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is
- 1-17/15-9/7 with steps of 17/15-17/15-14/9.
The inversely related pair of chords is
- 1-15/14-17/15 with steps of 15/14-18/17-30/17, and its inverse
- 1-18/17-17/15 with steps of 18/17-15/14-30/17.
For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
- 1-15/14-17/15-17/14 with steps of 15/14-18/17-15/14-28/17;
- 1-18/17-17/15-6/5 with steps of 18/17-15/14-18/17-5/3.
The inversely related pairs of chords are
- 1-17/15-17/14-9/7 with steps of 17/15-15/14-18/17-14/9, and its inverse
- 1-18/17-17/15-9/7 with steps of 18/17-15/14-17/15-14/9;
- 1-17/15-6/5-9/7 with steps of 17/15-18/17-15/14-14/9, and its inverse
- 1-15/14-17/15-9/7 with steps of 15/14-18/17-17/15-14/9.
They can be extended to pentads:
- 1-15/14-17/15-17/14-9/7 with steps of 15/14-18/17-15/14-18/17-14/9, and its inverse
- 1-18/17-17/15-6/5-9/7 with steps of 18/17-15/14-18/17-15/14-14/9.
Equal temperaments with fidesmic chords include 10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354.