Hemipyth: Difference between revisions

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A '''hemipyth''' (or '''"hemipythagorean"''') interval is an [[interval]] in the <math>\sqrt{2}\,.\sqrt{3}</math> [[subgroup]] i.e. intervals that can be constructed by multiplying half-integer powers of 2 and 3. Hemipythagorean is the pure tuning of [[Ploidacot/Diploid dicot|diploid dicot]].

A '''hemipyth''' (or '''"hemipythagorean"''') interval is an [[interval]] in the <math>\sqrt{2}\,.\sqrt{3}-</math>[[subgroup]]; i.e. intervals that can be constructed by multiplying half-integer powers of primes [[2/1|2]] and [[3/1|3]]. Hemipythagorean is the pure tuning of [[Ploidacot/Diploid dicot|diploid dicot]].

Notable hemipyth intervals include the neutral third <math>\sqrt{\frac{3}{2}} = \frac{\sqrt{3}}{\sqrt{2}}</math>, semioctave <math>\sqrt{2}</math>, and the semifourth <math>\sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}</math>.

Notable hemipyth intervals include the [[neutral third]] <math>\sqrt{\frac{3}{2}} = \frac{\sqrt{3}}{\sqrt{2}}</math>, [[semioctave]] <math>\sqrt{2}</math>, and the [[semifourth]] <math>\sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}</math>.

Many temperaments naturally produce intervals that split ~{{sfrac|3|2}}, ~2, or ~{{sfrac|4|3}} exactly in half and can thus be interpreted as neutral thirds, semioctaves, or semifourths within the temperament.

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-A '''hemipyth''' (or '''"hemipythagorean"''') interval is an [[interval]] in the <math>\sqrt{2}\,.\sqrt{3}</math> [[subgroup]] i.e. intervals that can be constructed by multiplying half-integer powers of 2 and 3. Hemipythagorean is the pure tuning of [[Ploidacot/Diploid dicot|diploid dicot]].
+A '''hemipyth''' (or '''"hemipythagorean"''') interval is an [[interval]] in the <math>\sqrt{2}\,.\sqrt{3}-</math>[[subgroup]]; i.e. intervals that can be constructed by multiplying half-integer powers of primes [[2/1|2]] and [[3/1|3]]. Hemipythagorean is the pure tuning of [[Ploidacot/Diploid dicot|diploid dicot]].
-Notable hemipyth intervals include the neutral third <math>\sqrt{\frac{3}{2}} = \frac{\sqrt{3}}{\sqrt{2}}</math>, semioctave <math>\sqrt{2}</math>, and the semifourth <math>\sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}</math>.
+Notable hemipyth intervals include the [[neutral third]] <math>\sqrt{\frac{3}{2}} = \frac{\sqrt{3}}{\sqrt{2}}</math>, [[semioctave]] <math>\sqrt{2}</math>, and the [[semifourth]] <math>\sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}</math>.
 Many temperaments naturally produce intervals that split ~{{sfrac|3|2}}, ~2, or ~{{sfrac|4|3}} exactly in half and can thus be interpreted as neutral thirds, semioctaves, or semifourths within the temperament.