Zeus: Difference between revisions

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{{Infobox regtemp

| Title = Zeus

| Subgroups = 2.3.5.7.11; 2.3.5.7.11.13

| Comma basis = [[121/120]], [[176/175]] (11-limit); <br>[[121/120]], [[176/175]], [[351/350]] (13-limit)

| Edo join 1 = 31 | Edo join 2 = 46 | Edo join 3 = 53

| Mapping = 1; 1 1 -1 1 -2; 0 -2 3 -1 -1

| Generators = 3/2, 12/11

| Generators tuning = 701.9, 157.0

| Optimization method = CWE

| Odd limit 1 = 11 | Mistuning 1 = 7.48 | Complexity 1 = ?

| Odd limit 2 = 13-limit 21 | Mistuning 2 = 7.72 | Complexity 2 = ?

}}

'''Zeus''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] generated by an [[2/1|octave]], a [[3/2|fifth]], and a neutral second which stands in for both undecimal neutral seconds of [[11/10]] and [[12/11]] as well as the septimal neutral second of [[35/32]], [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap| 121/120 {{=}} (176/175)⋅(385/384)}}. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.

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+{{Infobox regtemp
+| Title = Zeus
+| Subgroups = 2.3.5.7.11; 2.3.5.7.11.13
+| Comma basis = [[121/120]], [[176/175]] (11-limit); <br>[[121/120]], [[176/175]], [[351/350]] (13-limit)
+| Edo join 1 = 31 | Edo join 2 = 46 | Edo join 3 = 53
+| Mapping = 1; 1 1 -1 1 -2; 0 -2 3 -1 -1
+| Generators = 3/2, 12/11
+| Generators tuning = 701.9, 157.0
+| Optimization method = CWE
+| Odd limit 1 = 11 | Mistuning 1 = 7.48 | Complexity 1 = ?
+| Odd limit 2 = 13-limit 21 | Mistuning 2 = 7.72 | Complexity 2 = ?
+}}
 '''Zeus''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] generated by an [[2/1|octave]], a [[3/2|fifth]], and a neutral second which stands in for both undecimal neutral seconds of [[11/10]] and [[12/11]] as well as the septimal neutral second of [[35/32]], [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap| 121/120 {{=}} (176/175)⋅(385/384)}}. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.