Leapday: Difference between revisions

Cmloegcmluin (talk | contribs)
map → mapping
Xenllium (talk | contribs)
No edit summary
Line 1: Line 1:
See [[Hemifamity_temperaments#Leapday|Hemifamity temperaments]].
'''Leapday''' is a temperament for the 7, 11, 13, 17, and 19 [[Harmonic limit|prime limit]]s. It is a member of [[High badness temperaments #Leapday|trisayo family]], sengic temperaments and [[hemifamity temperaments]]. It has a fifth generator of ~3/2 = 704.2¢, eight of them makes ~13/8, eleven of them makes ~11/8, fifteen of them makes ~7/4, twenty-one of them makes ~5/4 and twenty-four of them makes ~17/16. Equivalently, 13/8 is represented by an augmented fifth, 11/8 is represented by an augmented third, 7/4 is represented by a double-augmented fifth, 5/4 is represented by a triple-augmented unison, and 17/16 is represented by a negative triple-diminished third.


See [[Hemifamity temperaments #Leapday|Hemifamity temperaments]] for more technical data.
== Tuning spectrum ==
Gencom: [2 3/2; 91/90 121/120 133/132 136/135 154/153 169/168]
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: [{{val|1 1 -10 -6 -3 -1 -10 6}}, {{val|0 1 21 15 11 8 24 -3}}]
== Tuning spectrum ==


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 127: Line 128:
| | 19/17
| | 19/17
| | 703.979
| | 703.979
| | 19 and 21 limit minimax
| | 19 and 21-odd-limit minimax
|-
|-
| | 44\75
| | 44\75
Line 157: Line 158:
| | 5/4
| | 5/4
| | 704.110
| | 704.110
| | 5 limit minimax
| | 5-odd-limit minimax
|-
|-
| |  
| |  
Line 172: Line 173:
| | 6/5
| | 6/5
| | 704.218
| | 704.218
| | 7, 15 and 17 limit minimax
| | 7, 15 and 17-odd-limit minimax
|-
|-
| |  
| |  
Line 182: Line 183:
| | 10/9
| | 10/9
| | 704.337
| | 704.337
| | 9, 11 and 13 limit minimax
| | 9, 11 and 13-odd-limit minimax
|-
|-
| | 27\46
| | 27\46
Line 280: Line 281:
|}
|}


[[Category:Smart redirect]]
[[Category:Hemifamity temperaments]]
[[Category:todo:add definition]]
{{IoT}}
[[Category:todo:intro]]