Undecimal sensamagic chords: Difference between revisions

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'''Undecimal sensamagic chords''' are [[essentially tempered chord]]s of undecimal (11-limit) [[sensamagic]], with intervals in the [[11-odd-limit]] [[tonality diamond]]. Since [[245/243]] is tempered out in undecimal sensamagic, 9-odd-limit [[sensamagic chords]] are undecimal sensamagic chords. Since [[385/384]] is tempered out, [[keenanismic chords]] are also undecimal sensamagic chords. Finally, since [[896/891]] is tempered out, [[pentacircle chords]] are undecimal sensamagic chords. There are also undecimal sensamagic chords which are none of these, the essentially undecimal sensamagic chords.

'''Undecimal sensamagic chords''' are [[essentially tempered chord]]s of undecimal ([[11-limit]]) [[sensamagic]], with intervals in the [[11-odd-limit]] [[tonality diamond]]. Since [[245/243]] is tempered out in undecimal sensamagic, 9-odd-limit [[sensamagic chords]] are undecimal sensamagic chords. Since [[385/384]] is tempered out, [[keenanismic chords]] are also undecimal sensamagic chords. Finally, since [[896/891]] is tempered out, [[pentacircle chords]] are undecimal sensamagic chords. There are also undecimal sensamagic chords which are none of these, the essentially undecimal sensamagic chords.

There are two pairs of inversely related tetrads:

* ~~1-9~~/~~8-16~~/~~11-7~~/4 with steps 9/8-9/7-6/5-8/7 and its inversion,

* 1–9/8–16/11–7/4 with steps 9/8, 9/7, 6/5, 8/7 and its inversion,

* ~~1-9~~/~~7-16~~/~~11-5~~/3 with steps 9/7-9/8-8/7-6/5;

* 1–9/7–16/11–5/3 with steps 9/7, 9/8, 8/7, 6/5;

* ~~1-9~~/~~8-5~~/~~4-16~~/11 with steps 9/8-10/9-7/6-11/8 and its inversion,

* 1–9/8–5/4–16/11 with steps 9/8, 10/9, 7/6, 11/8 and its inversion,

* ~~1-9~~/~~8-14~~/~~9-9~~/5 with steps 9/8-11/8-7/6-10/9.

* 1–9/8–14/9–9/5 with steps 9/8, 11/8, 7/6, 10/9.

There is one pair of inversely related pentads:

* ~~1-9~~/~~8-5~~/~~4-16~~/~~11-7~~/4 with steps 9/8-10/9-7/6-6/5-8/7 and its inversion

* 1–9/8–5/4–16/11–7/4 with steps 9/8, 10/9, 7/6, 6/5, 8/7 and its inversion

* ~~1-7~~/~~6-9~~/~~7-16~~/~~11-5~~/3 with steps 7/6-10/9-9/8-8/7-6/5.

* 1–7/6–9/7–16/11–5/3 with steps 7/6, 10/9, 9/8, 8/7, 6/5.

And one in palindromic form:

* ~~1-9~~/~~8-9~~/~~7-14~~/~~9-16~~/9 with steps 9/8-8/7-6/5-8/7-9/8.

* 1–9/8–9/7–14/9–16/9 with steps 9/8, 8/7, 6/5, 8/7, 9/8.

The number of chords is tetrad: 4 and pentad: 3, for a total of 7.

[[Category:11-odd-limit]]

[[Category:11-odd-limit chords]]

[[Category:Essentially tempered chords]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Sensamagic]]

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-'''Undecimal sensamagic chords''' are [[essentially tempered chord]]s of undecimal (11-limit) [[sensamagic]], with intervals in the [[11-odd-limit]] [[tonality diamond]]. Since [[245/243]] is tempered out in undecimal sensamagic, 9-odd-limit [[sensamagic chords]] are undecimal sensamagic chords. Since [[385/384]] is tempered out, [[keenanismic chords]] are also undecimal sensamagic chords. Finally, since [[896/891]] is tempered out, [[pentacircle chords]] are undecimal sensamagic chords. There are also undecimal sensamagic chords which are none of these, the essentially undecimal sensamagic chords.
+'''Undecimal sensamagic chords''' are [[essentially tempered chord]]s of undecimal ([[11-limit]]) [[sensamagic]], with intervals in the [[11-odd-limit]] [[tonality diamond]]. Since [[245/243]] is tempered out in undecimal sensamagic, 9-odd-limit [[sensamagic chords]] are undecimal sensamagic chords. Since [[385/384]] is tempered out, [[keenanismic chords]] are also undecimal sensamagic chords. Finally, since [[896/891]] is tempered out, [[pentacircle chords]] are undecimal sensamagic chords. There are also undecimal sensamagic chords which are none of these, the essentially undecimal sensamagic chords.
 There are two pairs of inversely related tetrads:
-* 1-9/8-16/11-7/4 with steps 9/8-9/7-6/5-8/7 and its inversion,
+* 1–9/8–16/11–7/4 with steps 9/8, 9/7, 6/5, 8/7 and its inversion,
-* 1-9/7-16/11-5/3 with steps 9/7-9/8-8/7-6/5;
+* 1–9/7–16/11–5/3 with steps 9/7, 9/8, 8/7, 6/5;
-* 1-9/8-5/4-16/11 with steps 9/8-10/9-7/6-11/8 and its inversion,
+* 1–9/8–5/4–16/11 with steps 9/8, 10/9, 7/6, 11/8 and its inversion,
-* 1-9/8-14/9-9/5 with steps 9/8-11/8-7/6-10/9.
+* 1–9/8–14/9–9/5 with steps 9/8, 11/8, 7/6, 10/9.
 There is one pair of inversely related pentads:
-* 1-9/8-5/4-16/11-7/4 with steps 9/8-10/9-7/6-6/5-8/7 and its inversion
+* 1–9/8–5/4–16/11–7/4 with steps 9/8, 10/9, 7/6, 6/5, 8/7 and its inversion
-* 1-7/6-9/7-16/11-5/3 with steps 7/6-10/9-9/8-8/7-6/5.
+* 1–7/6–9/7–16/11–5/3 with steps 7/6, 10/9, 9/8, 8/7, 6/5.
 And one in palindromic form:
-* 1-9/8-9/7-14/9-16/9 with steps 9/8-8/7-6/5-8/7-9/8.
+* 1–9/8–9/7–14/9–16/9 with steps 9/8, 8/7, 6/5, 8/7, 9/8.
 The number of chords is tetrad: 4 and pentad: 3, for a total of 7.
-[[Category:11-odd-limit]]
+[[Category:11-odd-limit chords]]
 [[Category:Essentially tempered chords]]
 [[Category:Tetrads]]
 [[Category:Pentads]]
 [[Category:Sensamagic]]