Counterpyth: Difference between revisions
Jump to navigation
Jump to search
Removed redirect to Counterpyth family#Counterpyth Tag: Removed redirect |
+ basic tunings |
||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{About|a rank-3 temperament|the 41st-octave rank-2 temperament that used to go by this name|Countercomp}} | |||
[[Category: | '''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
| 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 ¢ |