Leapday: Difference between revisions

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{{Infobox regtemp

| Title = Leapday

| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13

| Comma basis = [[686/675]], [[5120/5103]] (7-limit); [[121/120]], [[441/440]], [[686/675]] (11-limit); [[91/90]], [[121/120]], [[169/168]], [[352/351]] (13-limit)

| Edo join 1 = 29 | Edo join 2 = 46

| Mapping = 1; 1 21 15 11 8

| Generators = 3/2 | Generators tuning = 704.2 | Optimization method = CWE

| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]]

| Odd limit 1 = 9 | Mistuning 1 = 8.53 | Complexity 1 = 29

| Odd limit 2 = 13-limit 21 | Mistuning 2 = 10.6 | Complexity 2 = 29

}}

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

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Further extensions for [[prime]]s [[17/1|17]] and [[23/1|23]] are available, where 17/16 is represented by an octave-reduced triple-augmented sixth (C–A𝄪♯), and 23/16 is represented by an augmented fourth (C–F♯).

If ratios of 5 are omitted, the 2.3.7.11.13 [[subgroup]] version of leapday is known as ~~'''~~leapfrog~~'''~~, notable as tempering [[parapyth]] (a rank-3 temperament of the 2.3.7.11.13 subgroup) to rank 2 by finding [[~]][[13/8]] at ([[~]][[9/8]])4, that is, by tempering out the [[tetris comma]], and is a good combination of simplicity and accuracy~~, as 5/4 is complex and the canonical mapping for prime 19 is fairly inaccurate~~.

Since ratios of 5 are complex, they can be omitted, and the [[2.3.7.11.13 subgroup|2.3.7.11.13-subgroup]] version of leapday is known as [[leapfrog]], notable as tempering [[parapyth]] (a rank-3 temperament of the 2.3.7.11.13 subgroup) to rank 2 by finding [[~]][[13/8]] at ([[~]][[9/8]])4, that is, by tempering out the [[tetris comma]], and is a good combination of simplicity and accuracy.

Leapday 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>.

See [[Hemifamity temperaments #Leapday~~]] or [[No-fives subgroup temperaments #Leapfrog~~]] for ~~more~~ technical data.

See [[Hemifamity temperaments #Leapday]] for technical data.

== Interval chain ==

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|-

! 13-limit

! Additional ratios of 17 and 23

! Additional ratios of 17 and 23

|-

| 0

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[[Category:Rank-2 temperaments]]

[[Category:Sengic temperaments]]

[[Category:~~Hemifamity~~ temperaments]]

[[Category:Aberschismic temperaments]]

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+{{Infobox regtemp
+| Title = Leapday
+| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
+| Comma basis = [[686/675]], [[5120/5103]] (7-limit); <br>[[121/120]], [[441/440]], [[686/675]] (11-limit); <br>[[91/90]], [[121/120]], [[169/168]], [[352/351]]<br>(13-limit)
+| Edo join 1 = 29 | Edo join 2 = 46
+| Mapping = 1; 1 21 15 11 8
+| Generators = 3/2 | Generators tuning = 704.2 | Optimization method = CWE
+| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]]
+| Odd limit 1 = 9 | Mistuning 1 = 8.53 | Complexity 1 = 29
+| Odd limit 2 = 13-limit 21 | Mistuning 2 = 10.6 | Complexity 2 = 29
+}}
 : ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]], or [[Irvic scale|Irvian mode]].''
@@ Line 9: / Line 20: @@
 Further extensions for [[prime]]s [[17/1|17]] and [[23/1|23]] are available, where 17/16 is represented by an octave-reduced triple-augmented sixth (C–A𝄪♯), and 23/16 is represented by an augmented fourth (C–F♯).
-If ratios of 5 are omitted, the 2.3.7.11.13 [[subgroup]] version of leapday is known as '''leapfrog''', notable as tempering [[parapyth]] (a rank-3 temperament of the 2.3.7.11.13 subgroup) to rank 2 by finding [[~]][[13/8]] at ([[~]][[9/8]])<sup>4</sup>, that is, by tempering out the [[tetris comma]], and is a good combination of simplicity and accuracy, as 5/4 is complex and the canonical mapping for prime 19 is fairly inaccurate.
+Since ratios of 5 are complex, they can be omitted, and the [[2.3.7.11.13 subgroup|2.3.7.11.13-subgroup]] version of leapday is known as [[leapfrog]], notable as tempering [[parapyth]] (a rank-3 temperament of the 2.3.7.11.13 subgroup) to rank 2 by finding [[~]][[13/8]] at ([[~]][[9/8]])<sup>4</sup>, that is, by tempering out the [[tetris comma]], and is a good combination of simplicity and accuracy.
 Leapday 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>.
-See [[Hemifamity temperaments #Leapday]] or [[No-fives subgroup temperaments #Leapfrog]] for more technical data.
+See [[Hemifamity temperaments #Leapday]] for technical data.
 == Interval chain ==
@@ Line 25: / Line 36: @@
 |-
 ! 13-limit
-! Additional ratios<br />of 17 and 23
+! Additional ratios<br>of 17 and 23
 |-
 | 0
@@ Line 483: / Line 494: @@
 [[Category:Rank-2 temperaments]]
 [[Category:Sengic temperaments]]
-[[Category:Hemifamity temperaments]]
+[[Category:Aberschismic temperaments]]