Wizard: Difference between revisions

Lériendil (talk | contribs)
m Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)"
Tags: Mobile edit Mobile web edit
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
{{Infobox regtemp
| Title = Wizard
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.17
| Comma basis = [[225/224]], [[118098/117649]] (7-limit); <br>[[225/224]], [[385/384]], [[4000/3993]] (11-limit); <br>[[225/224]], [[289/288]], [[385/384]], [[561/560]]<br>(2.3.5.7.11.17)
| Edo join 1 = 22 | Edo join 2 = 72
| Mapping = 2; 6 -1 10 -3 6
| Generators = 17/15 | Generators tuning = 216.8 | Optimization method = CWE
| MOS scales = [[6L 4s]], [[6L 10s]], [[6L 16s]], [[22L 6s]]
| Odd limit 1 = 9 | Mistuning 1 = 3.05 | Complexity 1 = 28
| Odd limit 2 = 11-limit 21 | Mistuning 2 = 3.05 | Complexity 2 = 50
}}
'''Wizard''' is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a wide whole tone of about 217 cents which is the semi-octave complement of [[~]][[5/4]]. Six generators minus a semi-octave represents [[3/2]], and ten generators minus a full octave represents [[7/4]], [[tempering out]] the commas [[225/224]] and [[stearnsma|118098/117649]].  
'''Wizard''' is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a wide whole tone of about 217 cents which is the semi-octave complement of [[~]][[5/4]]. Six generators minus a semi-octave represents [[3/2]], and ten generators minus a full octave represents [[7/4]], [[tempering out]] the commas [[225/224]] and [[stearnsma|118098/117649]].  


Line 97: Line 108:
<nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning, octave reduced
<nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning, octave reduced


== Chords ==
== Chords and harmony ==
{{Main| Chords of wizard }}
{{See also| Chords of wizard }}


== Scales ==
== Scales ==
Line 104: Line 115:


== Tunings ==
== 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: ~245/216 = 216.9187{{c}}
| CWE: ~245/216 = 216.7977{{c}}
| POTE: ~245/216 = 216.7438{{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: ~25/22 = 216.9001{{c}}
| CWE: ~25/22 = 216.7961{{c}}
| POTE: ~25/22 = 216.7679{{c}}
|}
=== Tuning spectrum ===
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
Line 269: Line 311:
<nowiki/>* Besides the octave
<nowiki/>* Besides the octave


== Notes ==
== References ==


[[Category:Wizard| ]] <!-- main article -->
[[Category:Wizard| ]] <!-- main article -->