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]].  
A '''minthmic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] which is defined in the [[13-limit]] rank-5 temperament, and in addition the rank-3 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.
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,  


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}}.
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.  


[[Category:13-limit]]
These in turn have subchords such as the minthmic temperings of
[[Category:Chords]]
* 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 }}.
 
[[Category:Essentially tempered chords]]
[[Category:Minthmic]]
[[Category:Minthmic]]

Revision as of 12:56, 18 February 2023

A minthmic chord is an essentially tempered dyadic chord which is defined in the 13-limit rank-5 temperament, and in addition the rank-3 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 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 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205.