Gassormic chords: Difference between revisions
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Gassormic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[13-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures. | Gassormic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[13-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: | ||
* | * 1–7/5–5/3 with steps of 7/5, 13/11, 6/5, and its inverse | ||
* | * 1–6/5–10/7 with steps of 6/5, 13/11, 7/5; | ||
* | * 1–14/11–5/3 with steps of 14/11, 13/10, 6/5, and its inverse | ||
* 1–6/5–11/7 with steps of 6/5, 13/10, 14/11; | |||
* 1–7/5–11/6 with steps of 7/5, 13/10, 12/11, and its inverse | |||
* 1–12/11–10/7 with steps of 12/11, 13/10, 7/5. | |||
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 | ||
* | * 1–6/5–10/7–12/7 with steps of 6/5, 13/11, 6/5, 7/6; | ||
* | * 1–6/5–13/10–11/7 with steps of 6/5, 13/12, 6/5, 14/11; | ||
* | * 1–13/10–10/7–13/7 with steps of 13/10, 12/11, 13/10, 14/13. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–13/10–11/7–11/6 with steps of 13/10, 6/5, 7/6, 12/11, and its inverse | ||
* | * 1–7/6–7/5–11/6 with steps of 7/6, 6/5, 13/10, 12/11; | ||
* | * 1–6/5–10/7–11/7 with steps of 6/5, 13/11, 11/10, 14/11, and its inverse | ||
* | * 1–14/11–7/5–5/3 with steps of 14/11, 11/10, 13/11, 6/5; | ||
* | * 1–13/10–11/7–13/7 with steps of 13/10, 6/5, 13/11, 14/13, and its inverse | ||
* | * 1–13/10–7/5–5/3 with steps of 13/10, 14/13, 13/11, 6/5; | ||
* 1–11/10–6/5–11/7 with steps of 11/10, 12/11, 13/10, 14/11, and its inverse | |||
* 1–11/10–7/5–11/6 with steps of 11/10, 14/11, 13/10, 12/11; | |||
* 1–7/5–20/13–5/3 with steps of 7/5, 12/11, 13/12, 6/5, and its inverse | |||
* 1–6/5–13/10–10/7 with steps of 6/5, 13/12, 12/11, 7/5; | |||
* 1–7/5–5/3–11/6 with steps of 7/5, 13/11, 11/10, 12/11, and its inverse | |||
* 1–12/11–6/5–10/7 with steps of 12/11, 11/10, 13/11, 7/5. | |||
For pentads, there are three pairs of chords in inverse relationship: | For pentads, there are three pairs of chords in inverse relationship: | ||
* | * 1–11/10–13/10–7/5–11/6 with steps of 11/10, 13/11, 14/13, 13/10, 12/11, and its inverse | ||
* | * 1–13/10–7/5–5/3–11/6 with steps of 13/10, 14/13, 13/11, 11/10, 12/11; | ||
* | * 1–6/5–13/10–10/7–11/7 with steps of 6/5, 13/12, 12/11, 11/10, 14/11, and its inverse | ||
* 1–13/12–13/10–5/3–11/6 with steps of 13/12, 6/5, 14/11, 11/10, 12/11; | |||
* 1–7/6–7/5–5/3–11/6 with steps of 7/6, 6/5, 13/11, 11/10, 12/11, and its inverse | |||
* 1–7/6–14/11–7/5–5/3 with steps of 7/6, 12/11, 11/10, 13/11, 6/5. | |||
Equal temperaments with gassormic chords include {{Optimal ET sequence| 10, 15, 22, 26, 29, 31, 41 and 53 }}. | Equal temperaments with gassormic chords include {{Optimal ET sequence| 10, 15, 22, 26, 29, 31, 41 and 53 }}. | ||
[[Category:13-odd-limit]] | [[Category:13-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||