Ratwolfsmic chords: Difference between revisions

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~~The~~ '''~~ratwolf triad~~''' is the [[13-limit]] 1-6/5-20/13 [[~~Dyadic~~ chord|essentially tempered ~~dyadic~~ chord~~]] or~~ its inversion 1-9/7-20/13, tempered by the ratwolfsma, [[351/350]]. The name comes from the fact that one each of these triads appears in the 12-note meantone gamut [[ratwolf]]~~. Equal temperaments with ratwolf triads include {{EDOs|19, 22, 26, 31, 46, 53, 58, 72, 103, 111, 130, 183, 313, 416 and 546}}~~.

'''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:

* 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; (→[[#Ratwolf triad|ratwolf triad]])

* 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 chord with steps of 6/5-13/12-6/5-9/7;

* 1-7/6-13/10-9/5 chord with steps of 7/6-10/9-18/13-10/9;

* 1-3/2-5/3-9/5 chord 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 }}.

== Ratwolf triad ==

The '''ratwolf triad''' is the 13-limit essentially tempered chord of 1-6/5-20/13 of its inversion 1-9/7-20/13, tempered by the ratwolfsma, [[351/350]]. The name comes from the fact that one each of these triads appears in the 12-note meantone gamut [[ratwolf]].

[[Category:13-odd-limit]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Ratwolf]]

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-The '''ratwolf triad''' is the [[13-limit]] 1-6/5-20/13 [[Dyadic chord|essentially tempered dyadic chord]] or its inversion 1-9/7-20/13, tempered by the ratwolfsma, [[351/350]]. The name comes from the fact that one each of these triads appears in the 12-note meantone gamut [[ratwolf]]. Equal temperaments with ratwolf triads include {{EDOs|19, 22, 26, 31, 46, 53, 58, 72, 103, 111, 130, 183, 313, 416 and 546}}.
+'''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:
+* 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; (→[[#Ratwolf triad|ratwolf triad]])
+* 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 chord with steps of 6/5-13/12-6/5-9/7;
+* 1-7/6-13/10-9/5 chord with steps of 7/6-10/9-18/13-10/9;
+* 1-3/2-5/3-9/5 chord 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 }}.
+== Ratwolf triad ==
+The '''ratwolf triad''' is the 13-limit essentially tempered chord of 1-6/5-20/13 of its inversion 1-9/7-20/13, tempered by the ratwolfsma, [[351/350]]. The name comes from the fact that one each of these triads appears in the 12-note meantone gamut [[ratwolf]].
 [[Category:13-odd-limit]]
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
 [[Category:Ratwolf]]