Seminaiadmic chords: Difference between revisions
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'''Seminaiadmic chords''' are [[ | '''Seminaiadmic chords''' are [[dyadic chord|essentially tempered dyadic chords]] tempered by the seminaiadma, [[442/441]]. | ||
Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures. | Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-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: | For triads, there are three pairs of chords in inverse relationship: | ||
* | * 1–17/14–7/4 with steps of 17/14, 13/9, 8/7, and its inverse | ||
* | * 1–13/9–7/4 with steps of 13/9, 17/14, 8/7; | ||
* | * 1–9/8–17/14 with steps of 9/8, 14/13, 28/17, and its inverse | ||
* 1–14/13–17/14 with steps of 14/13, 9/8, 28/17; | |||
* 1–14/13–8/7 with steps of 14/13, 18/17, 7/4, and its inverse | |||
* 1–18/17–8/7 with steps of 18/17, 14/13, 7/4. | |||
For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are | ||
* | * 1–17/16–17/14–7/4 with steps of 17/16, 8/7, 13/9, 8/7; | ||
* | * 1–14/13–17/14–17/13 with steps of 14/13, 9/8, 14/13, 26/17; | ||
* | * 1–14/13–8/7–16/13 with steps of 14/13, 18/17, 14/13, 13/8. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–9/8–17/14–7/4 with steps of 9/8, 14/13, 13/9, 8/7, and its inverse | ||
* | * 1–13/9–14/9–7/4 with steps of 13/9, 14/13, 9/8, 8/7; | ||
* | * 1–9/8–17/14–18/13 with steps of 9/8, 14/13, 8/7, 13/9, and its inverse | ||
* | * 1–8/7–16/13–18/13 with steps of 8/7, 14/13, 9/8, 13/9; | ||
* | * 1–9/8–17/14–9/7 with steps of 9/8, 14/13, 18/17, 14/9, and its inverse | ||
* | * 1–18/17–8/7–9/7 with steps of 18/17, 14/13, 9/8, 14/9; | ||
* 1–17/16–9/8–17/14 with steps of 17/16, 18/17, 14/13, 28/17, and its inverse | |||
* 1–14/13–8/7–17/14 with steps of 14/13, 18/17, 17/16, 28/17; | |||
* 1–14/13–8/7–18/13 with steps of 14/13, 18/17, 17/14, 13/9, and its inverse | |||
* 1–17/14–9/7–18/13 with steps of 17/14, 18/17, 14/13, 13/9; | |||
* 1–14/13–8/7–28/17 with steps of 14/13, 18/17, 13/9, 17/14, and its inverse | |||
* 1–13/9–26/17–28/17 with steps of 13/9, 18/17, 14/13, 17/14. | |||
For pentads, there are three pairs of chords in inverse relationship: | For pentads, there are three pairs of chords in inverse relationship: | ||
* | * 1–17/16–9/8–17/14–7/4 with steps of 17/16, 18/17, 14/13, 13/9, 8/7, and its inverse | ||
* | * 1–17/16–17/14–7/4–17/9 with steps of 17/16, 8/7, 13/9, 14/13, 18/17; | ||
* | * 1–14/13–17/14–17/13–17/9 with steps of 14/13, 9/8, 14/13, 13/9, 18/17, and its inverse | ||
* 1–14/13–17/14–17/13–18/13 with steps of 14/13, 9/8, 14/13, 18/17, 13/9; | |||
* 1–9/8–17/14–9/7–18/13 with steps of 9/8, 14/13, 18/17, 14/13, 13/9, and its inverse | |||
* 1–14/13–8/7–16/13–18/13 with steps of 14/13, 18/17, 14/13, 9/8, 13/9. | |||
Equal temperaments with seminaiadmic chords include {{Optimal ET sequence|10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}. | Equal temperaments with seminaiadmic chords include {{Optimal ET sequence| 10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}. | ||
[[Category:17-odd-limit]] | [[Category:17-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||
Latest revision as of 07:59, 10 October 2025
Seminaiadmic chords are essentially tempered dyadic chords tempered by the seminaiadma, 442/441.
Seminaiadmic chords are of pattern 2 in the 2.3.7.13.17 subgroup 17-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:
- 1–17/14–7/4 with steps of 17/14, 13/9, 8/7, and its inverse
- 1–13/9–7/4 with steps of 13/9, 17/14, 8/7;
- 1–9/8–17/14 with steps of 9/8, 14/13, 28/17, and its inverse
- 1–14/13–17/14 with steps of 14/13, 9/8, 28/17;
- 1–14/13–8/7 with steps of 14/13, 18/17, 7/4, and its inverse
- 1–18/17–8/7 with steps of 18/17, 14/13, 7/4.
For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
- 1–17/16–17/14–7/4 with steps of 17/16, 8/7, 13/9, 8/7;
- 1–14/13–17/14–17/13 with steps of 14/13, 9/8, 14/13, 26/17;
- 1–14/13–8/7–16/13 with steps of 14/13, 18/17, 14/13, 13/8.
The inversely related pairs of chords are
- 1–9/8–17/14–7/4 with steps of 9/8, 14/13, 13/9, 8/7, and its inverse
- 1–13/9–14/9–7/4 with steps of 13/9, 14/13, 9/8, 8/7;
- 1–9/8–17/14–18/13 with steps of 9/8, 14/13, 8/7, 13/9, and its inverse
- 1–8/7–16/13–18/13 with steps of 8/7, 14/13, 9/8, 13/9;
- 1–9/8–17/14–9/7 with steps of 9/8, 14/13, 18/17, 14/9, and its inverse
- 1–18/17–8/7–9/7 with steps of 18/17, 14/13, 9/8, 14/9;
- 1–17/16–9/8–17/14 with steps of 17/16, 18/17, 14/13, 28/17, and its inverse
- 1–14/13–8/7–17/14 with steps of 14/13, 18/17, 17/16, 28/17;
- 1–14/13–8/7–18/13 with steps of 14/13, 18/17, 17/14, 13/9, and its inverse
- 1–17/14–9/7–18/13 with steps of 17/14, 18/17, 14/13, 13/9;
- 1–14/13–8/7–28/17 with steps of 14/13, 18/17, 13/9, 17/14, and its inverse
- 1–13/9–26/17–28/17 with steps of 13/9, 18/17, 14/13, 17/14.
For pentads, there are three pairs of chords in inverse relationship:
- 1–17/16–9/8–17/14–7/4 with steps of 17/16, 18/17, 14/13, 13/9, 8/7, and its inverse
- 1–17/16–17/14–7/4–17/9 with steps of 17/16, 8/7, 13/9, 14/13, 18/17;
- 1–14/13–17/14–17/13–17/9 with steps of 14/13, 9/8, 14/13, 13/9, 18/17, and its inverse
- 1–14/13–17/14–17/13–18/13 with steps of 14/13, 9/8, 14/13, 18/17, 13/9;
- 1–9/8–17/14–9/7–18/13 with steps of 9/8, 14/13, 18/17, 14/13, 13/9, and its inverse
- 1–14/13–8/7–16/13–18/13 with steps of 14/13, 18/17, 14/13, 9/8, 13/9.
Equal temperaments with seminaiadmic chords include 10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140.