32edo: Difference between revisions

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'''32 equal divisions of the octave''' ('''32edo'''), or '''32(-tone) equal temperament''' ('''32tet''', '''32et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived from dividing the octave in 32 [[equal]] steps of 37.5{{~~cent~~}}.

While even advocates of less-common [[EDO]]s can struggle to find something about it worth noting, it does provide an excellent tuning for [[Petr Pařízek]]'s [[sixix]] temperament, which tempers out the [[5-limit|5-limit]] sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Pařízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents and which gives equal error to fifths and major thirds, so 32edo does sixix about as well as sixix can be done. It also can be used (with the 9\32 generator) to tune mohavila, an 11-limit temperament which does not temper out sixix.

Revision as of 20:56, 5 June 2022 view source Fredg999 (talk \| contribs) autopatrolled, Interface administrators, Sysops 6,129 edits m Improve intro (cannot use EDO intro template yet because it says "about x cents"), categories ← Older edit		Revision as of 04:16, 7 June 2022 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits No edit summary Newer edit →
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	'''32 equal divisions of the octave''' ('''32edo'''), or '''32(-tone) equal temperament''' ('''32tet''', '''32et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived from dividing the octave in 32 [[equal]] steps of 37.5{{~~cent~~}}.		{{EDO prologue\|32}}

	While even advocates of less-common [[EDO]]s can struggle to find something about it worth noting, it does provide an excellent tuning for [[Petr Pařízek]]'s [[sixix]] temperament, which tempers out the [[5-limit\|5-limit]] sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Pařízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents and which gives equal error to fifths and major thirds, so 32edo does sixix about as well as sixix can be done. It also can be used (with the 9\32 generator) to tune mohavila, an 11-limit temperament which does not temper out sixix.		While even advocates of less-common [[EDO]]s can struggle to find something about it worth noting, it does provide an excellent tuning for [[Petr Pařízek]]'s [[sixix]] temperament, which tempers out the [[5-limit\|5-limit]] sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Pařízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents and which gives equal error to fifths and major thirds, so 32edo does sixix about as well as sixix can be done. It also can be used (with the 9\32 generator) to tune mohavila, an 11-limit temperament which does not temper out sixix.