Swetismic chords: Difference between revisions
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A '''swetismic chord''' is a swetismic (540/539) 11-odd-limit [[essentially tempered chord]]. | A '''swetismic chord''' is a swetismic ([[540/539]]) 11-odd-limit [[essentially tempered chord]]. | ||
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: | ||
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The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27. | The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27. | ||
If we are willing to consider the 15-limit, there are also 15-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5. | If we are willing to consider the 15-odd-limit, there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5. | ||
Equal temperaments 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 temperaments 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]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category: | [[Category:Triad]] | ||
[[Category:Tetrad]] | |||
[[Category:Pentad]] | |||
[[Category:Swetismic]] | [[Category:Swetismic]] | ||
{{Todo|add links}} | {{Todo| add links }} | ||
Revision as of 18:07, 8 February 2022
A swetismic chord is a swetismic (540/539) 11-odd-limit essentially tempered chord.
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 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 1-14/9-12/7 with steps 14/9-11/10-7/6;
- and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 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:
- 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;
- and 1-9/7-7/5-9/5 with steps 9/7-12/11-9/7-10/9.
The six pairs are:
- 1-9/7-3/2-11/6 with steps 9/7-7/6-11/9-12/11 and 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 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 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 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 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11;
- and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 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:
- 1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 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 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10;
- and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11 and 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.
The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.
If we are willing to consider the 15-odd-limit, there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.
Equal temperaments with swetismic chords include 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.