Buzurgismic chords: Difference between revisions

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'''Buzurgismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].

The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has 2 triads and ~~6 tetrads~~ in ~~the [[13-odd-limit]] of~~ the 2.3.7.13 subgroup~~, but these all become essentially just in the~~ [[21-odd-limit]].

The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]].

The two buzurgismic triads are in inverse relationship:

* ~~1-16~~/~~13-12~~/7 with steps ~~of 16~~/~~13-~~18/13-7/6;

* 1–7/6–13/8 with steps 7/6, 18/13, 16/13;

* ~~1-7~~/~~6-13~~/8 with steps of 7/6~~-18/13-~~16/13.

* 1–18/13–13/8 with steps 18/13, 7/6, 16/13.

For tetrads, there are ~~two~~ palindromic chords and ~~two~~ pairs of chords in inverse relationship. The palindromic chords are

For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are

* ~~1-16~~/~~13-18~~/~~13-12~~/7 with steps ~~of 16/13-~~9/8-16/13-7/6;

* 1–9/8–18/13–13/8 with steps 9/8, 16/13, 7/6, 16/13;

* 1-3/2-13/8-13/7 with steps ~~of 3/2-~~13/12-8/7-13/12.

* 1–3/2–13/8–13/7 with steps 3/2, 13/12, 8/7, 13/12;

* 1–13/12–18/13–3/2 with steps 13/12, 9/7, 13/12, 4/3.

The inversely related pairs of chords are

* ~~1-18~~/~~13-3~~/~~2-13~~/8 with steps of 18/13-13/12-13/12-16/13 and ~~1-13~~/~~12-3~~/~~2-13~~/7 with steps of 13/12-18/13-16/13-13/12;

* 1–18/13–3/2–13/8 with steps 18/13, 13/12, 13/12, 16/13, and its inverse

* 1-7/6-3/2-13/8 with steps of 7/6-9/7-13/12-16/13 and ~~1-9~~/~~7-3~~/~~2-13~~/7 with steps of 9/7-7/6-16/13-13/12.

* 1–13/12–3/2–13/7 with steps 13/12, 18/13, 16/13, 13/12;

* 1–13/12–3/2–7/4 with steps 13/12, 18/13, 7/6, 8/7, and its inverse

* 1–18/13–3/2–12/7 with steps 18/13, 13/12, 8/7, 7/6;

* 1–7/6–3/2–13/8 with steps 7/6, 9/7, 13/12, 16/13, and its inverse

* 1–9/7–3/2–13/7 with steps 9/7, 7/6, 16/13, 13/12.

[[Category:13-odd-limit]]

For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is

* 1–9/8–18/13–3/2–13/8 with steps 9/8, 16/13, 13/12, 13/12, 16/13.

The inversely related pairs of chords are

* 1–13/12–7/6–3/2–13/8 with steps 13/12, 13/12, 9/7, 13/12, 16/13, and its inverse

* 1–9/7–18/13–3/2–13/7 with steps 9/7, 13/12, 13/12, 16/13, 13/12;

* 1–13/12–7/6–3/2–7/4 with steps 13/12, 13/12, 9/7, 7/6, 8/7, and its inverse

* 1–9/7–18/13–3/2–12/7 with steps 9/7, 13/12, 13/12, 8/7, 7/6;

* 1–13/12–3/2–13/8–7/4 with steps 13/12, 18/13, 13/12, 13/12, 8/7, and its inverse

* 1–18/13–3/2–12/7–13/7 with steps 18/13, 13/12, 8/7, 13/12, 13/12;

Finally, there is a palindromic hexad,

* 1–13/12–7/6–3/2–13/8–7/4 with steps 13/12, 13/12, 9/7, 13/12, 13/12, 8/7.

Equal temperaments with buzurgismic chords include {{Optimal ET sequence|7, 9, 10, 17, 19, 26, 27, 36, 46, 53, 63 and 72}}.

[[Category:13-odd-limit chords]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Hexads]]

[[Category:Buzurgismic]]

@@ Line 1: / Line 1: @@
 '''Buzurgismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]].
-The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has 2 triads and 6 tetrads in the [[13-odd-limit]] of the 2.3.7.13 subgroup, but these all become essentially just in the [[21-odd-limit]].
+The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]].
 The two buzurgismic triads are in inverse relationship:
-* 1-16/13-12/7 with steps of 16/13-18/13-7/6;
+* 1–7/6–13/8 with steps 7/6, 18/13, 16/13;
-* 1-7/6-13/8 with steps of 7/6-18/13-16/13.
+* 1–18/13–13/8 with steps 18/13, 7/6, 16/13.
-For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
+For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are
-* 1-16/13-18/13-12/7 with steps of 16/13-9/8-16/13-7/6;
+* 1–9/8–18/13–13/8 with steps 9/8, 16/13, 7/6, 16/13;
-* 1-3/2-13/8-13/7 with steps of 3/2-13/12-8/7-13/12.
+* 1–3/2–13/8–13/7 with steps 3/2, 13/12, 8/7, 13/12;
+* 1–13/12–18/13–3/2 with steps 13/12, 9/7, 13/12, 4/3.
 The inversely related pairs of chords are
-* 1-18/13-3/2-13/8 with steps of 18/13-13/12-13/12-16/13 and 1-13/12-3/2-13/7 with steps of 13/12-18/13-16/13-13/12;
+* 1–18/13–3/2–13/8 with steps 18/13, 13/12, 13/12, 16/13, and its inverse
-* 1-7/6-3/2-13/8 with steps of 7/6-9/7-13/12-16/13 and 1-9/7-3/2-13/7 with steps of 9/7-7/6-16/13-13/12.
+* 1–13/12–3/2–13/7 with steps 13/12, 18/13, 16/13, 13/12;
+* 1–13/12–3/2–7/4 with steps 13/12, 18/13, 7/6, 8/7, and its inverse
+* 1–18/13–3/2–12/7 with steps 18/13, 13/12, 8/7, 7/6;
+* 1–7/6–3/2–13/8 with steps 7/6, 9/7, 13/12, 16/13, and its inverse
+* 1–9/7–3/2–13/7 with steps 9/7, 7/6, 16/13, 13/12.
-[[Category:13-odd-limit]]
+For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
+* 1–9/8–18/13–3/2–13/8 with steps 9/8, 16/13, 13/12, 13/12, 16/13.
+The inversely related pairs of chords are
+* 1–13/12–7/6–3/2–13/8 with steps 13/12, 13/12, 9/7, 13/12, 16/13, and its inverse
+* 1–9/7–18/13–3/2–13/7 with steps 9/7, 13/12, 13/12, 16/13, 13/12;
+* 1–13/12–7/6–3/2–7/4 with steps 13/12, 13/12, 9/7, 7/6, 8/7, and its inverse
+* 1–9/7–18/13–3/2–12/7 with steps 9/7, 13/12, 13/12, 8/7, 7/6;
+* 1–13/12–3/2–13/8–7/4 with steps 13/12, 18/13, 13/12, 13/12, 8/7, and its inverse
+* 1–18/13–3/2–12/7–13/7 with steps 18/13, 13/12, 8/7, 13/12, 13/12;
+Finally, there is a palindromic hexad,
+* 1–13/12–7/6–3/2–13/8–7/4 with steps 13/12, 13/12, 9/7, 13/12, 13/12, 8/7.
+Equal temperaments with buzurgismic chords include {{Optimal ET sequence|7, 9, 10, 17, 19, 26, 27, 36, 46, 53, 63 and 72}}.
+[[Category:13-odd-limit chords]]
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]
 [[Category:Tetrads]]
+[[Category:Pentads]]
+[[Category:Hexads]]
 [[Category:Buzurgismic]]