Subgroup temperaments: Difference between revisions

Line 1,236:

Marveltri, the 3 &~~amp;~~ 13 temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed 22 &~~amp;~~ 47 temperament.

Marveltri, the {{nowrap| 3 & 13 }} temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed {{nowrap| 22 & 47 }} temperament. The tonic and the first two generator steps make a [[marvel triad]], hence the name.

[[Subgroup]]: 2.5.9/7

[[Comma list]]: 225/224

[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})

~~{{Mapping|legend=3| 1~~ 2/5 ~~2 -1/5 | 0 -4/5 1 2/5 }}~~

: mapping generators: ~2, ~5

~~: [[gencom]]: [~~2 5/~~4; 225/224]~~

[[~~Optimal tuning~~]] ([[~~Tp tuning|subgroup POTE]]): ~~~5/~~4 = 383.638~~

: [[gencom]]: [2 5; 225/224]

{{Optimal ~~ET sequence~~|~~legend~~=~~1| 12~~, ~~13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}~~

[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1200.000, ~5/4 = 383.638

~~<nowiki />* Wart for 9/7~~

{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122 }}

[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents

==== Sulis ====

Related temperament: [[~~Marvel~~ family|minerva]], [[~~Würschmidt~~ family|würschmidt]]

Related temperament: [[marvel family|minerva]], [[würschmidt family|würschmidt]]

[[Subgroup]]: 2.5.9/7.11/7

[[Subgroup]]: 2.5.9/7.11/9

[[Comma list]]: 99/98, 176/175

[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})

{{Mapping|legend=2| ~~1 2~~ 1 0 | 0 1 -2 2 }}]

{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]

[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558

[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1200.000, ~5/4 = 386.558

[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents

@@ Line 1,236: / Line 1,236: @@
 {{See also| Chromatic pairs #Marveltri }}
-Marveltri, the 3 &amp; 13 temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed 22 &amp; 47 temperament.
+Marveltri, the {{nowrap| 3 & 13 }} temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed {{nowrap| 22 & 47 }} temperament. The tonic and the first two generator steps make a [[marvel triad]], hence the name.
 [[Subgroup]]: 2.5.9/7
-[[Comma list]]: 225/224
+[[Comma list]]: 225/224 ({{monzo| -5 2 1 }})
-{{Mapping|legend=2| 1 2 1 | 0 1 -2 }}
+{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
-{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}
+: mapping generators: ~2, ~5
-: [[gencom]]: [2 5/4; 225/224]
+{{Mapping|legend=3| 1 2 0 -1 | 0 -4/5 1 2/5 }}
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 383.638
+: [[gencom]]: [2 5; 225/224]
-{{Optimal ET sequence|legend=1| 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269c*, 660c* }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1200.000, ~5/4 = 383.638
-<nowiki />* Wart for 9/7
+{{Optimal ET sequence|legend=1| 3, 13, 16, 19, 22, 25, 72, 97, 122 }}
 [[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents
 ==== Sulis ====
-Related temperament: [[Marvel family|minerva]], [[Würschmidt family|würschmidt]]
+Related temperament: [[marvel family|minerva]], [[würschmidt family|würschmidt]]
-[[Subgroup]]: 2.5.9/7.11/7
+[[Subgroup]]: 2.5.9/7.11/9
-[[Comma list]]: 99/98, 176/175
+[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }})
-{{Mapping|legend=2| 1 2 1 0 | 0 1 -2 2 }}]
+{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}]
-[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~5/4 = 386.558
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1200.000, ~5/4 = 386.558
-{{Optimal ET sequence|legend=1| 3, …, 22, 25, 28, 31, 59 }}
+{{Optimal ET sequence|legend=1| 3, 22, 25, 28, 31, 59 }}
 [[Tp tuning #T2 tuning|RMS error]]: 1.074 cents