Cotoneum: Difference between revisions

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{{Todo|inline=1|improve synopsis|improve readability|comment= ~~Add infobox.~~ Review if tables of these sizes are necessary.}}

{{Todo|inline=1|improve synopsis|improve readability|comment=Review if tables of these sizes are necessary.}}

{{Infobox regtemp

| Title = Cotoneum

| Subgroups = 2.3.5.7, 2.3.5.7.11.13, 2.3.5.7.11.13.17.19

| Comma basis = [[10976/10935]], [[823543/819200]] (7-limit);<br>[[364/363]], [[441/440]], [[3584/3575]], [[10976/10935]] (13-limit);<br>[[343/342]], [[364/363]], [[441/440]], [[595/594]], [[1216/1215]],<br> [[1729/1728]] (19-limit)

| Edo join 1 = 41 | Edo join 2 = 217

| Mapping = 1; 1 -49 -14 23 61 89 -44

| Generators = 3/2

| Generators tuning = 702.308

| Optimization method = CWE

| MOS scales = [[12L 17s]], [[12L 29s]], [[41L 12s]], [[41L 53s]]

| Pergen = (P8, P5)

| Odd limit 1 = 15 | Mistuning 1 = 2.48 | Complexity 1 = 135

| Odd limit 2 = 21 | Mistuning 2 = 2.48 | Complexity 2 = 176

}}

'''Cotoneum''' is a [[rank]]-2 [[regular temperament|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.4-0.5 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.

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-{{Todo|inline=1|improve synopsis|improve readability|comment= Add infobox. Review if tables of these sizes are necessary.}}
+{{Todo|inline=1|improve synopsis|improve readability|comment=Review if tables of these sizes are necessary.}}
+{{Infobox regtemp
+| Title = Cotoneum
+| Subgroups = 2.3.5.7, 2.3.5.7.11.13, 2.3.5.7.11.13.17.19
+| Comma basis = [[10976/10935]], [[823543/819200]] (7-limit);<br>[[364/363]], [[441/440]], [[3584/3575]], [[10976/10935]] (13-limit);<br>[[343/342]], [[364/363]], [[441/440]], [[595/594]], [[1216/1215]],<br> [[1729/1728]] (19-limit)
+| Edo join 1 = 41 | Edo join 2 = 217
+| Mapping = 1; 1 -49 -14 23 61 89 -44
+| Generators = 3/2
+| Generators tuning = 702.308
+| Optimization method = CWE
+| MOS scales = [[12L 17s]], [[12L 29s]], [[41L 12s]], [[41L 53s]]
+| Pergen = (P8, P5)
+| Odd limit 1 = 15 | Mistuning 1 = 2.48 | Complexity 1 = 135
+| Odd limit 2 = 21 | Mistuning 2 = 2.48 | Complexity 2 = 176
+}}
 '''Cotoneum''' is a [[rank]]-2 [[regular temperament|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.4-0.5 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.