Counterpyth: Difference between revisions

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'''Counterpyth''' was the older name of [[countercomp]]. It was renamed following the consolidation of the [[compton]] temperament's name for fear of confusion with [[Pythagorean tuning]]. This term is now potentially of use as a region of fifths around 24\41, with the major seventh targeting [[19/10]] in such a tuning.
{{About|a rank-3 temperament|the 41st-octave rank-2 temperament that used to go by this name|Countercomp}}


[[Category:Smart redirect]]
'''Counterpyth''' is the [[rank-3 temperament|rank-3]] [[temperament]] tempering out [[400/399]] and [[1216/1215]] in the 2.3.5.7.19 [[subgroup]].
 
Inspired by [[Margo Schulter]]'s [[parapyth]], counterpyth was named and first explored by [[Flora Canou]] in 2024.
 
In counterpyth, the fifth is tuned a little sharp such that
* the major seventh (+5 fifths) hits [[19/10]], tempering out 1216/1215;
* the augmented fourth (+6 fifths) hits [[10/7]], tempering out [[5120/5103]];
* the augmented third (+11 fifths) hits [[19/14]], tempering out [[1245184/1240029]].
 
It also features a commas step representing [[64/63]]~[[81/80]]. Prime harmonics 5, 7 and 19 are all made available simply using two chains of fifths.
 
See [[Hemifamity family #Counterpyth]] for technical data.
 
== Interval lattice ==
<gallery>
File:Lattice Counterpyth RTT.png
</gallery>
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.19-subgroup norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~3/2 = 702.6411{{c}}, ~5/4 = 385.4452{{c}}
| CWE: ~3/2 = 702.6771{{c}}, ~5/4 = 386.0544{{c}}
| POTE: ~3/2 = 702.6953{{c}}, ~5/4 = 386.3629{{c}}
|}
 
[[Category:Counterpyth| ]] <!-- main article -->
[[Category:Rank-3 temperaments]]
[[Category:Hemifamity family]]

Revision as of 07:11, 22 October 2025

This page is about a rank-3 temperament. For the 41st-octave rank-2 temperament that used to go by this name, see Countercomp.

Counterpyth is the rank-3 temperament tempering out 400/399 and 1216/1215 in the 2.3.5.7.19 subgroup.

Inspired by Margo Schulter's parapyth, counterpyth was named and first explored by Flora Canou in 2024.

In counterpyth, the fifth is tuned a little sharp such that

  • the major seventh (+5 fifths) hits 19/10, tempering out 1216/1215;
  • the augmented fourth (+6 fifths) hits 10/7, tempering out 5120/5103;
  • the augmented third (+11 fifths) hits 19/14, tempering out 1245184/1240029.

It also features a commas step representing 64/63~81/80. Prime harmonics 5, 7 and 19 are all made available simply using two chains of fifths.

See Hemifamity family #Counterpyth for technical data.

Interval lattice

Tunings

2.3.5.7.19-subgroup norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~3/2 = 702.6411 ¢, ~5/4 = 385.4452 ¢ CWE: ~3/2 = 702.6771 ¢, ~5/4 = 386.0544 ¢ POTE: ~3/2 = 702.6953 ¢, ~5/4 = 386.3629 ¢