Major minthmic chords: Difference between revisions

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A ''minthmic chord'' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the 13-limit rank five temperament, and in addition the rank three 2.3.11.13 temperament, tempering out the minthma, 352/351. We have the four minthmic tetrads, with steps the minthmic tempering of 11/9-16/13-7/6-8/7, 11/9-16/13-8/7-7/6, 16/13-11/9-7/6-8/7, and 16/13-11/9-8/7-7/6, leading to temperings of 1-11/9-3/2-7/4, 1-11/9-3/2-12/7, 1-16/13-3/2-7/4 and 1-16/13-3/2-12/7. These in turn have subchords such as the minthmic temperings of 1-11/9-3/2 and 1-16/13-3/2. Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in [[jove tetrads|jove]] is also possible, leading to a similar but not identical chord.

A '''minthmic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the [[13-limit]] rank five temperament, and in addition the rank three 2.3.11.13 temperament, tempering out the minthma, [[352/351]].

We have the four minthmic tetrads, with steps the minthmic tempering of [[11/9]]-[[16/13]]-[[7/6]]-[[8/7]], 11/9-16/13-8/7-7/6, 16/13-11/9-7/6-8/7, and 16/13-11/9-8/7-7/6, leading to temperings of 1-11/9-[[3/2]]-[[7/4]], 1-11/9-3/2-[[12/7]], 1-16/13-3/2-7/4 and 1-16/13-3/2-12/7. These in turn have subchords such as the minthmic temperings of 1-11/9-3/2 and 1-16/13-3/2. Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in [[jove tetrads|jove]] is also possible, leading to a similar but not identical chord.

Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of, and minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example.) Equal temperaments with minthmic chords include {{EDOs|22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205}}.

Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of, and minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example.) Equal temperaments with minthmic chords include 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205.

[[Category:13-limit]]

[[Category:Chords]]

[[Category:Minthmic]]

~~[[Category:Todo:add links]]~~

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-A ''minthmic chord'' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the 13-limit rank five temperament, and in addition the rank three 2.3.11.13 temperament, tempering out the minthma, 352/351. We have the four minthmic tetrads, with steps the minthmic tempering of 11/9-16/13-7/6-8/7, 11/9-16/13-8/7-7/6, 16/13-11/9-7/6-8/7, and 16/13-11/9-8/7-7/6, leading to temperings of 1-11/9-3/2-7/4, 1-11/9-3/2-12/7, 1-16/13-3/2-7/4 and 1-16/13-3/2-12/7. These in turn have subchords such as the minthmic temperings of 1-11/9-3/2 and 1-16/13-3/2. Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in [[jove tetrads|jove]] is also possible, leading to a similar but not identical chord.
+A '''minthmic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the [[13-limit]] rank five temperament, and in addition the rank three 2.3.11.13 temperament, tempering out the minthma, [[352/351]].
+We have the four minthmic tetrads, with steps the minthmic tempering of [[11/9]]-[[16/13]]-[[7/6]]-[[8/7]], 11/9-16/13-8/7-7/6, 16/13-11/9-7/6-8/7, and 16/13-11/9-8/7-7/6, leading to temperings of 1-11/9-[[3/2]]-[[7/4]], 1-11/9-3/2-[[12/7]], 1-16/13-3/2-7/4 and 1-16/13-3/2-12/7. These in turn have subchords such as the minthmic temperings of 1-11/9-3/2 and 1-16/13-3/2. Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in [[jove tetrads|jove]] is also possible, leading to a similar but not identical chord.
+Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of, and minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example.) Equal temperaments with minthmic chords include {{EDOs|22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205}}.
-Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of, and minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate ([[Margo Schulter]] has expressed great fondness for this comma, for example.) Equal temperaments with minthmic chords include 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205.
 [[Category:13-limit]]
 [[Category:Chords]]
 [[Category:Minthmic]]
-[[Category:Todo:add links]]