Minor minthmic chords: Difference between revisions
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The ''supermajor gentle triad'' (or ''gentle major triad'') is a tempering of | The ''supermajor gentle triad'' (or ''gentle major triad'') is a tempering of | ||
* | * 1–14/11–3/2 with steps of 14/11, 13/11, 4/3; | ||
and its inversion the ''subminor gentle triad'' (or ''gentle minor triad'') is a tempering of | and its inversion the ''subminor gentle triad'' (or ''gentle minor triad'') is a tempering of | ||
* | * 1–13/11–3/2 with steps of 13/11, 14/11, 4/3. | ||
The ''gothic gentle triads'' are temperings of | The ''gothic gentle triads'' are temperings of | ||
* | * 1–13/11–11/8 with steps of 13/11, 7/6, 16/11, | ||
and its inversion, | and its inversion, | ||
* | * 1–7/6–11/8 with steps of 7/6, 13/11, 16/11. | ||
The names refer to [[Margo Schulter]]'s [[Neo-gothic]] theory of harmony, which features a [[gentle region]] with a slightly sharpened fifth in which gentle triads and neogothic triads flourish. | The names refer to [[Margo Schulter]]'s [[Neo-gothic]] theory of harmony, which features a [[gentle region]] with a slightly sharpened fifth in which gentle triads and neogothic triads flourish. | ||
The rest three inversely related pairs of triads contain semitones, such as 12/11 or 13/12: | The rest three inversely related pairs of triads contain semitones, such as 12/11 or 13/12: | ||
* | * 1–14/11–18/13 with steps of 14/11, 12/11, 13/9, and its inverse | ||
* | * 1–12/11–18/13 with steps of 12/11, 14/11, 13/9; | ||
* | * 1–14/11–11/8 with steps of 14/11, 13/12, 16/11, and its inverse | ||
* | * 1–13/12–11/8 with steps of 13/12, 14/11, 16/11; | ||
* | * 1–13/11–9/7 with steps of 13/11, 12/11, 14/9, and its inverse | ||
* | * 1–12/11–9/7 with steps of 12/11, 13/11, 14/9. | ||
For tetrads, there are five palindromic chords and fourteen pairs of chords in inverse relationship. | For tetrads, there are five palindromic chords and fourteen pairs of chords in inverse relationship. | ||
The ''gentle major tetrad'' is a tempering of | The ''gentle major tetrad'' is a tempering of | ||
* | * 1–14/11–3/2–7/4 with steps of 14/11, 13/11, 7/6, 8/7; | ||
and its inversion the ''gentle minor tetrad'' is a tempering of | and its inversion the ''gentle minor tetrad'' is a tempering of | ||
* | * 1–13/11–3/2–12/7 with steps of 13/11, 14/11, 8/7, 7/6. | ||
The ''gothic gentle tetrad'' is palindromic, a tempering of | The ''gothic gentle tetrad'' is palindromic, a tempering of | ||
* | * 1–13/11–11/8–13/8 with steps of 13/11, 7/6, 13/11, 16/13. | ||
The rest four palindromic tetrads contain semitones, such as 12/11, 13/12 or 14/13: | The rest four palindromic tetrads contain semitones, such as 12/11, 13/12 or 14/13: | ||
* | * 1–13/11–14/11–3/2 with steps of 13/11, 14/13, 13/11, 4/3; | ||
* | * 1–14/11–11/8–7/4 with steps of 14/11, 13/12, 14/11, 8/7; | ||
* | * 1–12/11–14/11–18/13 with steps of 12/11, 7/6, 12/11, 13/9; | ||
* | * 1–12/11–13/11–9/7 with steps of 12/11, 13/12, 12/11, 14/9; | ||
as well as the rest thirteen inversely related pairs of tetrads: | as well as the rest thirteen inversely related pairs of tetrads: | ||
* | * 1–14/11–3/2–24/13 with steps of 14/11, 13/11, 16/13, 13/12, and its inverse | ||
* | * 1–13/11–3/2–13/8 with steps of 13/11, 14/11, 13/12, 16/13; | ||
* | * 1–14/11–3/2–11/6 with steps of 14/11, 13/11, 11/9, 12/11, and its inverse | ||
* | * 1–13/11–3/2–18/11 with steps of 13/11, 14/11, 12/11, 11/9; | ||
* | * 1–14/11–3/2–18/11 with steps of 14/11, 13/11, 12/11, 11/9, and its inverse | ||
* | * 1–13/11–3/2–11/6 with steps of 13/11, 14/11, 11/9, 12/11; | ||
* | * 1–7/6–14/11–3/2 with steps of 7/6, 12/11, 13/11, 4/3, and its inverse | ||
* | * 1–13/11–9/7–3/2 with steps of 13/11, 12/11, 7/6, 4/3; | ||
* | * 1–7/6–11/8–3/2 with steps of 7/6, 13/11, 12/11, 4/3, and its inverse | ||
* | * 1–12/11–9/7–3/2 with steps of 12/11, 13/11, 7/6, 4/3; | ||
* | * 1–14/11–11/8–3/2 with steps of 14/11, 13/12, 12/11, 4/3, and its inverse | ||
* | * 1–12/11–13/11–3/2 with steps of 12/11, 13/12, 14/11, 4/3; | ||
* | * 1–14/11–18/13–3/2 with steps of 14/11, 12/11, 13/12, 4/3, and its inverse | ||
* | * 1–13/12–13/11–3/2 with steps of 13/12, 12/11, 14/11, 4/3; | ||
* | * 1–13/11–11/8–3/2 with steps of 13/11, 7/6, 12/11, 4/3, and its inverse | ||
* | * 1–12/11–14/11–3/2 with steps of 12/11, 7/6, 13/11, 4/3; | ||
* | * 1–12/11–18/13–3/2 with steps of 12/11, 14/11, 13/12, 4/3, and its inverse | ||
* | * 1–13/12–11/8–3/2 with steps of 13/12, 14/11, 12/11, 4/3; | ||
* | * 1–11/9–13/9–11/7 with steps of 11/9, 13/11, 12/11, 14/11, and its inverse | ||
* | * 1–12/11–9/7–11/7 with steps of 12/11, 13/11, 11/9, 14/11; | ||
* | * 1–12/11–9/7–18/13 with steps of 12/11, 13/11, 14/13, 13/9, and its inverse | ||
* | * 1–14/13–14/11–18/13 with steps of 14/13, 13/11, 12/11, 13/9; | ||
* | * 1–13/11–14/11–11/8 with steps of 13/11, 14/13, 13/12, 16/11, and its inverse | ||
* | * 1–13/12–7/6–11/8 with steps of 13/12, 14/13, 13/11, 16/11; | ||
* | * 1–7/6–14/11–11/8 with steps of 7/6, 12/11, 13/12, 16/11, and its inverse | ||
* | * 1–13/12–13/11–11/8 with steps of 13/12, 12/11, 7/6, 16/11. | ||
For pentads, there are thirteen pairs of chords in inverse relationship, all of them involve semitones and the perfect fifth: | For pentads, there are thirteen pairs of chords in inverse relationship, all of them involve semitones and the perfect fifth: | ||
* | * 1–14/11–11/8–3/2–7/4 with steps of 14/11, 13/12, 12/11, 7/6, 8/7, and its inverse | ||
* | * 1–12/11–13/11–3/2–12/7 with steps of 12/11, 13/12, 14/11, 8/7, 7/6; | ||
* | * 1–13/11–9/7–3/2–12/7 with steps of 13/11, 12/11, 7/6, 8/7, 7/6, and its inverse | ||
* | * 1–7/6–14/11–3/2–7/4 with steps of 7/6, 12/11, 13/11, 7/6, 8/7; | ||
* | * 1–14/11–11/8–3/2–11/6 with steps of 14/11, 13/12, 12/11, 11/9, 12/11, and its inverse | ||
* | * 1–12/11–13/11–3/2–18/11 with steps of 12/11, 13/12, 14/11, 12/11, 11/9; | ||
* | * 1–14/11–18/13–3/2–18/11 with steps of 14/11, 12/11, 13/12, 12/11, 11/9, and its inverse | ||
* | * 1–13/12–13/11–3/2–11/6 with steps of 13/12, 12/11, 14/11, 11/9, 12/11; | ||
* | * 1–13/11–14/11–3/2–11/6 with steps of 13/11, 14/13, 13/11, 11/9, 12/11, and its inverse | ||
* | * 1–13/11–14/11–3/2–18/11 with steps of 13/11, 14/13, 13/11, 12/11, 11/9; | ||
* | * 1–13/11–9/7–3/2–18/11 with steps of 13/11, 12/11, 7/6, 12/11, 11/9, and its inverse | ||
* | * 1–7/6–14/11–3/2–11/6 with steps of 7/6, 12/11, 13/11, 11/9, 12/11; | ||
* | * 1–13/11–11/8–3/2–11/6 with steps of 13/11, 7/6, 12/11, 11/9, 12/11, and its inverse | ||
* | * 1–12/11–14/11–3/2–18/11 with steps of 12/11, 7/6, 13/11, 12/11, 11/9; | ||
* | * 1–14/11–18/13–3/2–24/13 with steps of 14/11, 12/11, 13/12, 16/13, 13/12, and its inverse | ||
* | * 1–13/12–13/11–3/2–13/8 with steps of 13/12, 12/11, 14/11, 13/12, 16/13; | ||
* | * 1–13/11–11/8–3/2–13/8 with steps of 13/11, 7/6, 12/11, 13/12, 16/13, and its inverse | ||
* | * 1–12/11–14/11–3/2–24/13 with steps of 12/11, 7/6, 13/11, 16/13, 13/12; | ||
* | * 1–13/11–14/11–11/8–3/2 with steps of 13/11, 14/13, 13/12, 12/11, 4/3, and its inverse | ||
* | * 1–12/11–13/11–14/11–3/2 with steps of 12/11, 13/12, 14/13, 13/11, 4/3; | ||
* | * 1–7/6–14/11–11/8–3/2 with steps of 7/6, 12/11, 13/12, 12/11, 4/3, and its inverse | ||
* | * 1–12/11–13/11–9/7–3/2 with steps of 12/11, 13/12, 12/11, 7/6, 4/3; | ||
* | * 1–12/11–9/7–18/13–3/2 with steps of 12/11, 13/11, 14/13, 13/12, 4/3, and its inverse | ||
* | * 1–13/12–7/6–11/8–3/2 with steps of 13/12, 14/13, 13/11, 12/11, 4/3; | ||
* | * 1–12/11–14/11–18/13–3/2 with steps of 12/11, 7/6, 12/11, 13/12, 4/3, and its inverse | ||
* | * 1–13/12–13/11–11/8–3/2 with steps of 13/12, 12/11, 7/6, 12/11, 4/3. | ||
For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | ||
* | * 1–7/6–14/11–11/8–3/2–7/4 with steps of 7/6, 12/11, 13/12, 12/11, 7/6, 8/7; | ||
* | * 1–12/11–14/11–18/13–3/2–24/13 with steps of 12/11, 7/6, 12/11, 13/12, 16/13, 13/12. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–7/6–14/11–11/8–3/2–11/6 with steps of 7/6, 12/11, 13/12, 12/11, 11/9, 12/11, and its inverse | ||
* | * 1–12/11–13/11–9/7–3/2–18/11 with steps of 12/11, 13/12, 12/11, 7/6, 12/11, 11/9; | ||
* | * 1–13/11–14/11–11/8–3/2–11/6 with steps of 13/11, 14/13, 13/12, 12/11, 11/9, 12/11, and its inverse | ||
* | * 1–12/11–13/11–14/11–3/2–18/11 with steps of 12/11, 13/12, 14/13, 13/11, 12/11, 11/9. | ||
Equal temperaments with minor minthmic chords include {{Optimal ET sequence| 17, 22, 29, 41, 46, 58, 72, 87, 104, 121, 130, 217, 232, 234, 289 and 456 }}. | Equal temperaments with minor minthmic chords include {{Optimal ET sequence| 17, 22, 29, 41, 46, 58, 72, 87, 104, 121, 130, 217, 232, 234, 289 and 456 }}. | ||
[[Category:13-odd-limit]] | [[Category:13-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||