Hemipyth: Difference between revisions

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=== Signposts ===

Due to their low damage in supporting temperaments, the octave ({{~~sfrac~~|2|1}}), semioctave <math>\left(\sqrt{2}\right)</math>, perfect fifth ({{~~sfrac~~|3|2}}), perfect fourth ({{~~sfrac~~|4|3}}), neutral third <math>\left(\sqrt{\frac{3}{2}}\right)</math>, neutral sixth <math>\left(\sqrt{\frac{8}{3}}\right)</math>, semifourth <math>\left(\sqrt{\frac{4}{3}}\right)</math>, semitwelfth <math>\left(\sqrt{3}\right)</math>, "hemitone" <math>\left(\sqrt{\frac{9}{8}}\right)</math>, and "contrahemitone" <math>\left(\sqrt{\frac{32}{9}}\right)</math> all provide good signposts for navigating around otherwise unfamiliar scales.

Due to their low damage in supporting temperaments, the octave ({{frac|2|1}}), semioctave <math>\left(\sqrt{2}\right)</math>, perfect fifth ({{frac|3|2}}), perfect fourth ({{frac|4|3}}), neutral third <math>\left(\sqrt{\frac{3}{2}}\right)</math>, neutral sixth <math>\left(\sqrt{\frac{8}{3}}\right)</math>, semifourth <math>\left(\sqrt{\frac{4}{3}}\right)</math>, semitwelfth <math>\left(\sqrt{3}\right)</math>, "hemitone" <math>\left(\sqrt{\frac{9}{8}}\right)</math>, and "contrahemitone" <math>\left(\sqrt{\frac{32}{9}}\right)</math> all provide good signposts for navigating around otherwise unfamiliar scales.

While untempered semitones usually come as unequal pairs consisting of an augmented unison and a minor second, the "hemitone" is always exactly the geometric half of a {{sfrac|9|8}} whole tone. The "contrahemitone" is its octave-complement.

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 === Signposts ===
-Due to their low damage in supporting temperaments, the octave&nbsp;({{sfrac|2|1}}), semioctave&nbsp;<math>\left(\sqrt{2}\right)</math>, perfect&nbsp;fifth&nbsp;({{sfrac|3|2}}), perfect&nbsp;fourth&nbsp;({{sfrac|4|3}}), neutral&nbsp;third&nbsp;<math>\left(\sqrt{\frac{3}{2}}\right)</math>, neutral&nbsp;sixth&nbsp;<math>\left(\sqrt{\frac{8}{3}}\right)</math>, semifourth&nbsp;<math>\left(\sqrt{\frac{4}{3}}\right)</math>, semitwelfth&nbsp;<math>\left(\sqrt{3}\right)</math>, "hemitone"&nbsp;<math>\left(\sqrt{\frac{9}{8}}\right)</math>, and "contrahemitone"&nbsp;<math>\left(\sqrt{\frac{32}{9}}\right)</math> all provide good signposts for navigating around otherwise unfamiliar scales.
+Due to their low damage in supporting temperaments, the octave&nbsp;({{frac|2|1}}), semioctave&nbsp;<math>\left(\sqrt{2}\right)</math>, perfect&nbsp;fifth&nbsp;({{frac|3|2}}), perfect&nbsp;fourth&nbsp;({{frac|4|3}}), neutral&nbsp;third&nbsp;<math>\left(\sqrt{\frac{3}{2}}\right)</math>, neutral&nbsp;sixth&nbsp;<math>\left(\sqrt{\frac{8}{3}}\right)</math>, semifourth&nbsp;<math>\left(\sqrt{\frac{4}{3}}\right)</math>, semitwelfth&nbsp;<math>\left(\sqrt{3}\right)</math>, "hemitone"&nbsp;<math>\left(\sqrt{\frac{9}{8}}\right)</math>, and "contrahemitone"&nbsp;<math>\left(\sqrt{\frac{32}{9}}\right)</math> all provide good signposts for navigating around otherwise unfamiliar scales.
 While untempered semitones usually come as unequal pairs consisting of an augmented unison and a minor second, the "hemitone" is always exactly the geometric half of a {{sfrac|9|8}} whole tone. The "contrahemitone" is its octave-complement.