Swetismic chords: Difference between revisions
Name two of the 15-odd-limit tetrads due to their significance in functional harmony |
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There are six swetismic triads, consisting of three pairs of chords in inverse relationship: | There are six swetismic triads, consisting of three pairs of chords in inverse relationship: | ||
* | * 1–7/5–12/7 with steps 7/5, 11/9, 7/6, and its inverse | ||
* | * 1–7/6–10/7 with steps 7/6, 11/9, 7/5; | ||
* | * 1–7/6–9/7 with steps 7/6, 11/10, 14/9, and its inverse | ||
* | * 1–14/9–12/7 with steps 14/9, 11/10, 7/6; | ||
* | * 1–9/7–7/5 with steps 9/7, 12/11, 10/7, and its inverse | ||
* | * 1–10/7–14/9 with steps 10/7, 12/11, 9/7. | ||
There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are: | There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are: | ||
* | * 1–7/6–9/7–3/2 with steps 7/6, 11/10, 7/6, 4/3; | ||
* | * 1–6/5–7/5–12/7 with steps 6/5, 7/6, 11/9, 7/6; | ||
* | * 1–9/7–7/5–9/5 with steps 9/7, 12/11, 9/7, 10/9. | ||
The six pairs are: | The six pairs are: | ||
* | * 1–9/7–3/2–11/6 with steps 9/7, 7/6, 11/9, 12/11, and its inverse | ||
* | * 1–7/6–3/2–18/11 with steps 7/6, 9/7, 12/11, 11/9; | ||
* | * 1–7/6–9/7–10/7 with steps 7/6, 11/10, 10/9, 7/5, and its inverse | ||
* | * 1–7/5–14/9–12/7 with steps 7/5, 10/9, 11/10, 7/6; | ||
* | * 1–7/6–9/7–18/11 with steps 7/6, 11/10, 14/11, 11/9, and its inverse | ||
* | * 1–14/11–7/5–18/11 with steps 14/11, 11/10, 7/6, 11/9; | ||
* | * 1–7/6–10/7–11/6 with steps 7/6, 11/9, 9/7, 12/11, and its inverse | ||
* | * 1–9/7–11/7–11/6 with steps 9/7, 11/9, 7/6, 12/11; | ||
* | * 1–7/6–9/7–11/6 with steps 7/6, 11/10, 10/7, 12/11, and its inverse | ||
* | * 1–10/7–11/7–11/6 with steps 10/7, 11/10, 7/6, 12/11; | ||
* | * 1–10/7–14/9–12/7 with steps 10/7, 12/11, 11/10, 7/6, and its inverse | ||
* | * 1–7/6–9/7–7/5 with steps 7/6, 11/10, 12/11, 10/7. | ||
Finally, there are six swetismic pentads coming in three pairs: | Finally, there are six swetismic pentads coming in three pairs: | ||
* | * 1–7/6–9/7–3/2–11/6 with steps 7/6, 11/10, 7/6, 11/9, 12/11, and its inverse | ||
* | * 1–7/6–9/7–3/2–18/11 with steps 7/6, 11/10, 7/6, 12/11, 11/9; | ||
* | * 1–7/6–10/7–5/3–11/6 with steps 7/6, 11/9, 7/6, 11/10, 12/11, and its inverse | ||
* | * 1–7/6–10/7–5/3–20/11 with steps 7/6, 11/9, 7/6, 12/11, 11/10; | ||
* | * 1–7/6–9/7–10/7–11/6 with steps 7/6, 11/10, 10/9, 9/7, 12/11, and its inverse | ||
* | * 1–9/7–10/7–11/7–11/6 with steps 9/7, 10/9, 11/10, 7/6, 12/11. | ||
If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads, including something important for functional harmony. The ''swetismic dominant seventh chord'' is a tempering of | If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads, including something important for functional harmony. The ''swetismic dominant seventh chord'' is a tempering of | ||
* | * 1–9/7–3/2–7/4 with steps 9/7, 7/6, 7/6, 8/7. | ||
Its inversion might be called the ''swetismic half-diminished chord'', a tempering of | Its inversion might be called the ''swetismic half-diminished chord'', a tempering of | ||
* | * 1–7/6–3/2–12/7 with steps 7/6, 9/7, 8/7, 7/6. | ||
We also have | We also have | ||
* | * 1–11/9–10/7–5/3 with steps 11/9, 7/6, 7/6, 6/5; and its inverse | ||
* | * 1–7/6–15/11–5/3 with steps 7/6, 7/6, 11/9, 6/5. | ||
[[Equal temperament]]s with swetismic chords include {{EDOs|19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de }}. | [[Equal temperament]]s with swetismic chords include {{EDOs| 19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de }}. | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||