Leapday: Difference between revisions

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: ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]] or [[Irvic scale|Irvian mode]].''

'''Leapday''' is a [[regular temperament]] for the 7-, 11-, 13-, 17-, and 19-limit JI. It is based on the [[chain of fifths]], but here, the fifth is tuned slightly sharp of just so that 8 fifths give a 13/8, 11 fifths make an 11/8, 15 fifths give 7/4, twenty-one fifths give [[5/4]], and twenty-four of them makes ~17/16. Equivalently, the fifth in leapday is ~2.3 cents sharp of 3/2 (approximately 704{{cent}}), so that 13/8 is represented by an augmented fifth (e.g. C–G♯), 11/8 is represented by an augmented third (e.g. C–E♯), the harmonic seventh is represented by a doubly augmented fifth (e.g. C–G𝄪), the classical major third is represented by a triply augmented unison (e.g. C–C𝄪♯), and 17/16 is represented by an octave-reduced triply-augmented sixth (e.g. C–G𝄪♯).

'''Leapday''' is a [[regular temperament]] for the 7-, 11-, 13-, 17-, and 19-limit JI. It is based on the [[chain of fifths]], but here, the fifth is tuned slightly sharp of just so that 8 fifths give a 13/8, 11 fifths make an 11/8, 15 fifths give 7/4, twenty-one fifths give [[5/4]], and twenty-four of them makes ~17/16. Equivalently, the fifth in leapday is ~2.3 cents sharp of 3/2 (approximately 704{{cent}}), so that 13/8 is represented by an augmented fifth (e.g. C–G♯), 11/8 is represented by an augmented third (e.g. C–E♯), the harmonic seventh is represented by a doubly augmented fifth (e.g. C–G𝄪), the classical major third is represented by a triply augmented unison (e.g. C–C𝄪♯), and 17/16 is represented by an octave-reduced triply-augmented sixth (e.g. C–A𝄪♯).

The temperament was named by [[Herman Miller]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10589.html Yahoo! Tuning Group (Archive) | ''Some 13-limit temperaments'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10604.html Yahoo! Tuning Group (Archive) | ''24 13-limit temperaments supported by 46'']</ref>.

@@ Line 1: / Line 1: @@
 : ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]] or [[Irvic scale|Irvian mode]].''
-'''Leapday''' is a [[regular temperament]] for the 7-, 11-, 13-, 17-, and 19-limit JI. It is based on the [[chain of fifths]], but here, the fifth is tuned slightly sharp of just so that 8 fifths give a 13/8, 11 fifths make an 11/8, 15 fifths give 7/4, twenty-one fifths give [[5/4]], and twenty-four of them makes ~17/16. Equivalently, the fifth in leapday is ~2.3 cents sharp of 3/2 (approximately 704{{cent}}), so that 13/8 is represented by an augmented fifth (e.g.&nbsp;C&ndash;G&#x266F;), 11/8 is represented by an augmented third (e.g.&nbsp;C&ndash;E&#x266F;), the harmonic seventh is represented by a doubly augmented fifth (e.g.&nbsp;C&ndash;G&#x1D12A;), the classical major third is represented by a triply augmented unison (e.g.&nbsp;C&ndash;C&#x1D12A;&#x266F;), and 17/16 is represented by an octave-reduced triply-augmented sixth (e.g.&nbsp;C&ndash;G&#x1D12A;&#x266F;).
+'''Leapday''' is a [[regular temperament]] for the 7-, 11-, 13-, 17-, and 19-limit JI. It is based on the [[chain of fifths]], but here, the fifth is tuned slightly sharp of just so that 8 fifths give a 13/8, 11 fifths make an 11/8, 15 fifths give 7/4, twenty-one fifths give [[5/4]], and twenty-four of them makes ~17/16. Equivalently, the fifth in leapday is ~2.3 cents sharp of 3/2 (approximately 704{{cent}}), so that 13/8 is represented by an augmented fifth (e.g.&nbsp;C&ndash;G&#x266F;), 11/8 is represented by an augmented third (e.g.&nbsp;C&ndash;E&#x266F;), the harmonic seventh is represented by a doubly augmented fifth (e.g.&nbsp;C&ndash;G&#x1D12A;), the classical major third is represented by a triply augmented unison (e.g.&nbsp;C&ndash;C&#x1D12A;&#x266F;), and 17/16 is represented by an octave-reduced triply-augmented sixth (e.g.&nbsp;C&ndash;A&#x1D12A;&#x266F;).
 The temperament was named by [[Herman Miller]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10589.html Yahoo! Tuning Group (Archive) | ''Some 13-limit temperaments'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10604.html Yahoo! Tuning Group (Archive) | ''24 13-limit temperaments supported by 46'']</ref>.