Zeus: Difference between revisions

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'''Zeus''' is ~~the~~ [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap| 121/120 {{=}} (176/175)⋅(385/384)}}~~. It thus equates the septimal neutral second of [[35/32]] with both [[11/10]] and [[12/11]]~~. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. ~~The~~ 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.

'''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.

It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].

Revision as of 08:03, 4 April 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 18,317 edits Cleanup ← Older edit		Revision as of 08:10, 4 April 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 18,317 edits Improve the intro Newer edit →
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	'''Zeus''' is ~~the~~ [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap\| 121/120 {{=}} (176/175)⋅(385/384)}}~~. It thus equates the septimal neutral second of [[35/32]] with both [[11/10]] and [[12/11]]~~. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. ~~The~~ 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.		'''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.

	It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].		It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].