Gamelismic and portent: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Expansion
Tag: Removed redirect
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,636 edits
 
(10 intermediate revisions by 3 users not shown)
Line 1: Line 1:
The '''portent''' temperament is the rank-3 [[regular temperament]] tempering out [[385/384]] and [[441/440]]. It is the most efficient 11-limit extension to '''gamelan''', the 7-limit version tempering out [[1029/1024]].  
{{Infobox regtemp
| Title = Gamelismic; portent
| Subgroups = 2.3.5.7, 2.3.5.7.11
| Comma basis = [[1029/1024]] (7-limit); <br>[[385/384]], [[441/440]] (11-limit)
| Edo join 1 = 15 | Edo join 2 = 26 | Edo join 3 = 31
| Mapping = 1; 3 0 -1 4; 0 1 0 -1
| Generators = 8/7, 5/4
| Generators tuning = 233.8, 385.3
| Optimization method = CWE
| Odd limit 1 = 9 | Mistuning 1 = 2.41 | Complexity 1 = ?
| Odd limit 2 = 11-limit 21 | Mistuning 2 = 2.81 | Complexity 2 = ?
}}
'''Gamelismic''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] [[generator|generated]] by a supermajor second of [[~]][[8/7]], three of them stacking to ~[[3/2]], and an independent dimension for [[prime interval|prime]] [[5/1|5]]. Thus it [[tempering out|tempers out]] [[1029/1024]], the gamelisma, in the [[7-limit]], which means it is an [[expansion]] of [[slendric]], the [[rank-2 temperament|rank-2]] [[2.3.7 subgroup|2.3.7-subgroup]] temperament that tempers out the same comma. It has an obvious [[extension]] to the [[11-limit]] tempering out [[385/384]] and [[441/440]], called '''portent''', as {{nowrap| 1029/1024 {{=}} (385/384)(441/440) }}.  


See [[Gamelismic family #Portent]] for more technical data.  
See [[Gamelismic family #Gamelismic]] and [[Gamelismic family #Portent]] for technical data.  


== Interval lattice ==
== Interval lattice ==
[[File:Lattice Portent.png]]
<gallery>
File:Lattice Portent.png|11-limit portent
</gallery>
 
== Chords ==
Portent enables [[essentially tempered chord]]s of [[Slendric pentad|gamelismic]], [[keenanismic chords|keenanismic]], and [[werckismic chords|werckismic]].


== Scales ==
== Scales ==
* [[Portent11tri]] – 11-tone trivalence scale in 190edo tuning
* [[Portent11tri]] – 11-tone [[trivalent scale]] in 190edo tuning
* [[Portent26]] – 26-tone hobbit scale in 11-odd-limit minimax tuning
* [[Portent26]] – 26-tone [[hobbit scale]] in 11-odd-limit minimax tuning
* [[Penslen]]
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~8/7 = 233.8889{{c}}, ~5/4 = 385.3137{{c}}
| CWE: ~8/7 = 233.7474{{c}}, ~5/4 = 385.5205{{c}}
| POTE: ~8/7 = 233.6875{{c}}, ~5/4 = 385.1853{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~8/7 = 233.9922{{c}}, ~5/4 = 385.7972{{c}}
| CWE: ~8/7 = 233.7616{{c}}, ~5/4 = 385.3149{{c}}
| POTE: ~8/7 = 233.6884{{c}}, ~5/4 = 385.1618{{c}}
|}


[[Category:Temperaments]]
[[Category:Portent| ]] <!-- main article -->
[[Category:Rank-3 temperaments]]
[[Category:Gamelismic family]]
[[Category:Gamelismic family]]
[[Category:Keenanismic temperaments]]
[[Category:Keenanismic temperaments]]
[[Category:Werckismic temperaments]]
[[Category:Werckismic temperaments]]

Latest revision as of 18:35, 19 March 2026

Gamelismic; portent
Subgroups 2.3.5.7, 2.3.5.7.11
Comma basis 1029/1024 (7-limit);
385/384, 441/440 (11-limit)
Reduced mapping ⟨1; 3 0 -1 4; 0 1 0 -1]
ET join 15 & 26 & 31
Generators (CWE) ~8/7 = 233.8 ¢, ~5/4 = 385.3 ¢
MOS scales n/a
Ploidacot n/a
Minimax error 9-odd-limit: 2.41 ¢;
11-limit 21-odd-limit: 2.81 ¢
Target scale size 9-odd-limit: ? notes;
11-limit 21-odd-limit: ? notes

Gamelismic is a rank-3 temperament generated by a supermajor second of ~8/7, three of them stacking to ~3/2, and an independent dimension for prime 5. Thus it tempers out 1029/1024, the gamelisma, in the 7-limit, which means it is an expansion of slendric, the rank-2 2.3.7-subgroup temperament that tempers out the same comma. It has an obvious extension to the 11-limit tempering out 385/384 and 441/440, called portent, as 1029/1024 = (385/384)(441/440).

See Gamelismic family #Gamelismic and Gamelismic family #Portent for technical data.

Interval lattice

  • 11-limit portent
    11-limit portent

Chords

Portent enables essentially tempered chords of gamelismic, keenanismic, and werckismic.

Scales

Tunings

7-limit norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~8/7 = 233.8889 ¢, ~5/4 = 385.3137 ¢ CWE: ~8/7 = 233.7474 ¢, ~5/4 = 385.5205 ¢ POTE: ~8/7 = 233.6875 ¢, ~5/4 = 385.1853 ¢
11-limit norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~8/7 = 233.9922 ¢, ~5/4 = 385.7972 ¢ CWE: ~8/7 = 233.7616 ¢, ~5/4 = 385.3149 ¢ POTE: ~8/7 = 233.6884 ¢, ~5/4 = 385.1618 ¢
Retrieved from "https://en.xen.wiki/index.php?title=Gamelismic_and_portent&oldid=226422"