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== Temperaments ==
== Temperaments ==
Tempering out this comma in the 17-limit leads to the rank-6 '''ursulismic temperament'''. Tempering it out in the 2.3.5.11.17 subgroup leads to the rank-4 '''ursulic temperament'''. Both enables [[ursulismic chords]].  
Tempering out this comma in the 17-limit leads to the rank-6 '''ursulismic temperament'''. Tempering it out in the 2.3.5.11.17 subgroup leads to the rank-4 '''ursulic temperament'''. Both enables [[ursulismic chords]].
 
=== Ursulismic ===
[[Subgroup]]: 2.3.5.7.11.13.17
 
[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 3 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
|}
 
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.8093, ~5/4 = 385.3757, ~7/4, ~11/8 = 552.0120, ~13/8
 
{{Optimal ET sequence|legend=1| 12f, 15g, 16, 19g, 22, 27eg, 29g, 31, 38df, 41g, 43, 49fg, 50, 53, 60e, 65d, 72, 103, 121, 152fg, 159, 171, 193, 224, 296, 395e, 467, 554g, 691eg }}
 
=== Ursulic ===
[[Subgroup]]: 2.3.5.11.17
 
{{Mapping|legend=2| 1 0 0 0 -1 | 0 1 0 0 1 | 0 0 1 0 3 | 0 0 0 1 -1 }}
 
: sval mapping generators: ~2, ~3, ~5, ~11
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.8093, ~5/4 = 385.3757, ~11/8 = 552.0120
 
{{Optimal ET sequence|legend=1| 12, 15g, 19g, 22, 31, 34, 50, 53, 56, 60e, 65, 72, 137, 159, 296, 455, 489 }}


== Etymology ==
== Etymology ==