Ratwolfsmic chords: Difference between revisions
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'''Ratwolfsmic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the ratwolfsma, [[351/350]]. | |||
Ratwolfsmic 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. The first two of these are called '''ratwolf triads'''. The name comes from the fact that one each of these triads appears in the 12-note meantone gamut [[ratwolf]]. | |||
* 1–9/7–20/13 with steps of 9/7, 6/5, 13/10, and its inverse | |||
* 1–6/5–20/13 with steps of 6/5, 9/7, 13/10; | |||
* 1–7/6–13/10 with steps of 7/6, 10/9, 20/13, and its inverse | |||
* 1–10/9–13/10 with steps of 10/9, 7/6, 20/13; | |||
* 1–10/9–6/5 with steps of 10/9, 14/13, 5/3, and its inverse | |||
* 1–14/13–6/5 with steps of 14/13, 10/9, 5/3. | |||
For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are | |||
* 1–6/5–13/10–14/7 with steps of 6/5, 13/12, 6/5, 9/7; | |||
* 1–7/6–13/10–9/5 with steps of 7/6, 10/9, 18/13, 10/9; | |||
* 1–3/2–5/3–9/5 with steps of 3/2, 10/9, 14/13, 10/9. | |||
The inversely related pairs of chords are | |||
* 1–7/6–13/10–5/3 with steps of 7/6, 10/9, 9/7, 6/5, and its inverse | |||
* 1–7/6–7/5–9/5 with steps of 7/6, 6/5, 9/7, 10/9; | |||
* 1–7/6–13/10–7/5 with steps of 7/6, 10/9, 14/13, 10/7, and its inverse | |||
* 1–7/6–5/3–9/5 with steps of 7/6, 10/7, 14/13, 10/9; | |||
* 1–13/10–5/3–13/7 with steps of 13/10, 9/7, 10/9, 14/13, and its inverse | |||
* 1–13/10–7/5–14/9 with steps of 13/10, 14/13, 10/9, 9/7; | |||
* 1–9/7–3/2–5/3 with steps of 9/7, 7/6, 10/9, 6/5, and its inverse | |||
* 1–7/6–3/2–9/5 with steps of 7/6, 9/7, 6/5, 10/9; | |||
* 1–9/7–5/3–13/7 with steps of 9/7, 13/10, 10/9, 14/13, and its inverse | |||
* 1–10/9–13/9–13/7 with steps of 10/9, 13/10, 9/7, 14/13; | |||
* 1–13/12–7/6–13/10 with steps of 13/12, 14/13, 10/9, 20/13, and its inverse | |||
* 1–10/9–6/5–13/10 with steps of 10/9, 14/13, 13/12, 20/13. | |||
For pentads, there are three pairs of chords in inverse relationship: | |||
* 1–10/9–13/10–13/9–13/7 with steps of 10/9, 7/6, 10/9, 9/7, 14/13, and its inverse | |||
* 1–9/7–10/7–5/3–13/7 with steps of 9/7, 10/9, 7/6, 10/9, 14/13; | |||
* 1–13/12–13/10–5/3–13/7 with steps of 13/12, 6/5, 9/7, 10/9, 14/13, and its inverse | |||
* 1–10/9–10/7–12/7–13/7 with steps of 10/9, 9/7, 6/5, 13/12, 14/13; | |||
* 1–9/7–3/2–5/3–9/5 with steps of 9/7, 7/6, 10/9, 14/13, 10/9, and its inverse | |||
* 1–7/6–3/2–5/3–9/5 with steps of 7/6, 9/7, 10/9, 14/13, 10/9. | |||
Equal temperaments with ratwolfsmic chords include {{Optimal ET sequence| 5, 7, 8d, 12f, 19, 22, 26, 27, 31, 34d, 46, 53, 58, 72, 77, 84, 111 and 130 }}. | |||
[[Category:13-odd-limit chords]] | |||
[[Category:Essentially tempered chords]] | |||
[[Category:Triads]] | |||
[[Category:Tetrads]] | |||
[[Category:Pentads]] | |||
[[Category:Ratwolf]] | |||
Latest revision as of 14:21, 19 March 2025
Ratwolfsmic chords are essentially tempered dyadic chords tempered by the ratwolfsma, 351/350.
Ratwolfsmic chords are of 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. The first two of these are called ratwolf triads. The name comes from the fact that one each of these triads appears in the 12-note meantone gamut ratwolf.
- 1–9/7–20/13 with steps of 9/7, 6/5, 13/10, and its inverse
- 1–6/5–20/13 with steps of 6/5, 9/7, 13/10;
- 1–7/6–13/10 with steps of 7/6, 10/9, 20/13, and its inverse
- 1–10/9–13/10 with steps of 10/9, 7/6, 20/13;
- 1–10/9–6/5 with steps of 10/9, 14/13, 5/3, and its inverse
- 1–14/13–6/5 with steps of 14/13, 10/9, 5/3.
For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
- 1–6/5–13/10–14/7 with steps of 6/5, 13/12, 6/5, 9/7;
- 1–7/6–13/10–9/5 with steps of 7/6, 10/9, 18/13, 10/9;
- 1–3/2–5/3–9/5 with steps of 3/2, 10/9, 14/13, 10/9.
The inversely related pairs of chords are
- 1–7/6–13/10–5/3 with steps of 7/6, 10/9, 9/7, 6/5, and its inverse
- 1–7/6–7/5–9/5 with steps of 7/6, 6/5, 9/7, 10/9;
- 1–7/6–13/10–7/5 with steps of 7/6, 10/9, 14/13, 10/7, and its inverse
- 1–7/6–5/3–9/5 with steps of 7/6, 10/7, 14/13, 10/9;
- 1–13/10–5/3–13/7 with steps of 13/10, 9/7, 10/9, 14/13, and its inverse
- 1–13/10–7/5–14/9 with steps of 13/10, 14/13, 10/9, 9/7;
- 1–9/7–3/2–5/3 with steps of 9/7, 7/6, 10/9, 6/5, and its inverse
- 1–7/6–3/2–9/5 with steps of 7/6, 9/7, 6/5, 10/9;
- 1–9/7–5/3–13/7 with steps of 9/7, 13/10, 10/9, 14/13, and its inverse
- 1–10/9–13/9–13/7 with steps of 10/9, 13/10, 9/7, 14/13;
- 1–13/12–7/6–13/10 with steps of 13/12, 14/13, 10/9, 20/13, and its inverse
- 1–10/9–6/5–13/10 with steps of 10/9, 14/13, 13/12, 20/13.
For pentads, there are three pairs of chords in inverse relationship:
- 1–10/9–13/10–13/9–13/7 with steps of 10/9, 7/6, 10/9, 9/7, 14/13, and its inverse
- 1–9/7–10/7–5/3–13/7 with steps of 9/7, 10/9, 7/6, 10/9, 14/13;
- 1–13/12–13/10–5/3–13/7 with steps of 13/12, 6/5, 9/7, 10/9, 14/13, and its inverse
- 1–10/9–10/7–12/7–13/7 with steps of 10/9, 9/7, 6/5, 13/12, 14/13;
- 1–9/7–3/2–5/3–9/5 with steps of 9/7, 7/6, 10/9, 14/13, 10/9, and its inverse
- 1–7/6–3/2–5/3–9/5 with steps of 7/6, 9/7, 10/9, 14/13, 10/9.
Equal temperaments with ratwolfsmic chords include 5, 7, 8d, 12f, 19, 22, 26, 27, 31, 34d, 46, 53, 58, 72, 77, 84, 111 and 130.