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. 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 major third is represented by a ~~triple-~~augmented unison (e.g. C–C𝄪♯), and 17/16 is represented by an inverted triply-diminished third (e.g. E𝄫𝄫–C).

'''Leapday''' is a [[regular temperament]] for the 7-, 11-, 13-, 17-, and 19-limit JI. 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 inverted triply diminished third (e.g. E𝄫𝄫–C).

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>.

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Gencom: [2 3/2; 91/90 121/120 133/132 136/135 154/153 169/168]

Gencom mapping: [{{~~val~~| 1 1 -10 -6 -3 -1 -10 6 ~~}}, {{val~~| 0 1 21 15 11 8 24 -3 }}]

Gencom mapping: {{mapping| 1 1 -10 -6 -3 -1 -10 6 | 0 1 21 15 11 8 24 -3 }}

{| class="wikitable center-all"

|-

! ~~EDO~~ ~~generator~~

! Edo Generator

! [[~~eigenmonzo~~|~~eigenmonzo~~ (unchanged-interval)]]

! [[Eigenmonzo|Eigenmonzo (unchanged-interval)]]*

! ~~generator ~~(¢)

! Generator (¢)

! ~~comments~~

! Comments

|-

|

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|

|}

<nowiki>*</nowiki> besides the octave

== Notes ==

[[Category:Leapday| ]]

[[Category:Temperaments]]

[[Category:Sengic temperaments]]

[[Category:Hemifamity temperaments]]

@@ 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. 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 major third is represented by a triple-augmented unison (e.g.&nbsp;C&ndash;C&#x1D12A;&#x266F;), and 17/16 is represented by an inverted triply-diminished third (e.g.&nbsp;E&#x1D12B;&#x1D12B;&ndash;C).
+'''Leapday''' is a [[regular temperament]] for the 7-, 11-, 13-, 17-, and 19-limit JI. 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 inverted triply diminished third (e.g.&nbsp;E&#x1D12B;&#x1D12B;&ndash;C).
 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 116: / Line 116: @@
 Gencom: [2 3/2; 91/90 121/120 133/132 136/135 154/153 169/168]
-Gencom mapping: [{{val| 1 1 -10 -6 -3 -1 -10 6 }}, {{val| 0 1 21 15 11 8 24 -3 }}]
+Gencom mapping: {{mapping| 1 1 -10 -6 -3 -1 -10 6 | 0 1 21 15 11 8 24 -3 }}
 {| class="wikitable center-all"
 |-
-! EDO<br>generator
+! Edo<br>Generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
+! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
-! generator<br>(¢)
+! Generator (¢)
-! comments
+! Comments
 |-
 |
@@ Line 390: / Line 390: @@
 |
 |}
+<nowiki>*</nowiki> besides the octave
 == Notes ==
+[[Category:Leapday| ]] <!-- main article -->
 [[Category:Temperaments]]
+[[Category:Sengic temperaments]]
 [[Category:Hemifamity temperaments]]