21st-octave temperaments: Difference between revisions

Line 101:

== Scandium ==

Described as the 525 & 1911 temperament, and named after the 21st element for splitting the octave into 21 parts. Coincidentally, ''Encyclopaedia Britannica'' entry for scandium was written in the year 1911 which was used as the reason for the naming. Remarkably, unlike akjayland, it is ''not'' a landscape system.

Described as the 525 & 1911 temperament, and named after the 21st element for splitting the octave into 21 parts. Coincidentally, ''Encyclopaedia Britannica'' entry for scandium was written in the year 1911 which was used as the reason for the naming. Remarkably, unlike akjayland or many temperaments in the thousands which contain 3edo as a subset, it is ''not'' a landscape system. [[39/32]] is mapped into 6\21 and [[23/16]] is, as usual, mapped into 11\21.

Subgroup: 2.3.5.7

Comma list: 47 -7 -7 -7, -29 0 27 -12

Comma list: {{monzo|47 -7 -7 -7}}, {{monzo|-29 0 27 -12}}

: mapping generators: ~403368/390625 = 1\21, ~160/147 = 146.305

[[Optimal tuning]] ([[CTE]]): ~160/147 = 146.305

[[Support]]ing [[ET]]s: {{EDOs|189b, 525, 861, 1050, 1386, 1911, 2436}}

=== 23-limit ===

Subgroup: 2.3.5.7.11.13.17.19.21.23

Comma list: 2500/2499, 3025/3024, 3060/3059, 3520/3519, 4096/4095, 6175/6174, 79135/79092

{{Mapping|legend=1| 21 0 59 82 24 111 114 38 95 | 0 13 -4 -9 19 -13 -11 20 0}}

: mapping generators: ~216/209 = 1\21, ~160/147 = 146.308

[[Optimal tuning]] ([[CTE]]): ~160/147 = 146.305

[[Support]]ing [[ET]]s: {{EDOs|525, 861h, 1050f, 1911}}

@@ Line 101: / Line 101: @@
 == Scandium ==
-Described as the 525 & 1911 temperament, and named after the 21st element for splitting the octave into 21 parts. Coincidentally, ''Encyclopaedia Britannica'' entry for scandium was written in the year 1911 which was used as the reason for the naming. Remarkably, unlike akjayland, it is ''not'' a landscape system.
+Described as the 525 & 1911 temperament, and named after the 21st element for splitting the octave into 21 parts. Coincidentally, ''Encyclopaedia Britannica'' entry for scandium was written in the year 1911 which was used as the reason for the naming. Remarkably, unlike akjayland or many temperaments in the thousands which contain 3edo as a subset, it is ''not'' a landscape system. [[39/32]] is mapped into 6\21 and [[23/16]] is, as usual, mapped into 11\21.
 Subgroup: 2.3.5.7
-Comma list: 47 -7 -7 -7, -29 0 27 -12
+Comma list: {{monzo|47 -7 -7 -7}}, {{monzo|-29 0 27 -12}}
+{{Mapping|legend=1| 21 0 59 82 | 0 13 -4 -9 }}
+: mapping generators: ~403368/390625 = 1\21, ~160/147 = 146.305
+[[Optimal tuning]] ([[CTE]]): ~160/147 = 146.305
+[[Support]]ing [[ET]]s: {{EDOs|189b, 525, 861, 1050, 1386, 1911, 2436}}
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.21.23
+Comma list: 2500/2499, 3025/3024, 3060/3059, 3520/3519, 4096/4095, 6175/6174, 79135/79092
+{{Mapping|legend=1| 21 0 59 82 24 111 114 38 95 | 0 13 -4 -9 19 -13 -11 20 0}}
+: mapping generators: ~216/209 = 1\21, ~160/147 = 146.308
+[[Optimal tuning]] ([[CTE]]): ~160/147 = 146.305
+[[Support]]ing [[ET]]s: {{EDOs|525, 861h, 1050f, 1911}}