Landscape microtemperaments: Difference between revisions
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'''Landscape microtemperaments''' are rank two temperaments tempering out the [[landscape comma]] ({{Monzo| -4 6 -6 3 }} = 250047/250000). | '''Landscape microtemperaments''' are rank two temperaments tempering out the [[landscape comma]] ({{Monzo| -4 6 -6 3 }} = 250047/250000). | ||
Landscape rank-two temperaments include sextile, septichrome, pnict, and domain. Considered elsewhere are [[ennealimmal]], [[Hemimean clan#Misty|misty]], [[nessafof]], and [[chromat]]. | Landscape rank-two temperaments include sextile, septichrome, pnict, and domain. Considered elsewhere are [[Ragismic microtemperaments|ennealimmal]], [[Hemimean clan#Misty|misty]], [[Horwell temperaments|mutt]], [[Porwell temperaments|nessafof]], and [[Hemimage temperaments|chromat]]. | ||
=Sextile= | = Sextile = | ||
[[Comma list]]: 250047/250000, 33554432/33480783 | |||
POTE generator: ~3/2 = 702.212 | [[POTE tuning|POTE generator]]: ~3/2 = 702.212 | ||
[[Mapping]]: [<6 0 71 150|, <0 1 -6 -14|] | |||
Wedgie: <<6 -36 -84 -71 -150 -94|| | [[Wedgie]]: <<6 -36 -84 -71 -150 -94|| | ||
{{ | {{Val list|legend=1| 12, 258, 270, 1362c, 1632c, 1902c, 2172c }} | ||
Badness: 0. | [[Badness]]: 0.070097 | ||
==11-limit== | == 11-limit == | ||
Comma list: 5632/5625, 9801/9800, 151263/151250 | |||
POTE generator: ~3/2 = 702.202 | POTE generator: ~3/2 = 702.202 | ||
Mapping: [<6 0 71 150 230|, <0 1 -6 -14 -22|] | |||
{{ | Vals: {{Val list| 12, 270, 822, 1092 }} | ||
Badness: 0. | Badness: 0.029677 | ||
=Septichrome= | = Septichrome = | ||
[[Comma list]]: 250047/250000, 2460375/2458624 | |||
POTE generator: ~243/224 = 140.367 | [[POTE tuning|POTE generator]]: ~243/224 = 140.367 | ||
[[Mapping]]: [<3 3 1 0|, <0 5 17 24|] | |||
Wedgie: <<15 51 72 46 72 24|| | [[Wedgie]]: <<15 51 72 46 72 24|| | ||
{{ | {{Val list|legend=1| 60, 111, 171, 795, 966, 1137, 1308, 5403b, 6711b }} | ||
Badness: 0. | [[Badness]]: 0.016814 | ||
=Pnict= | = Pnict = | ||
[[Comma list]]: 250047/250000, 2100875/2097152 | |||
POTE generator: ~192/175 = 161.399 | [[POTE tuning|POTE generator]]: ~192/175 = 161.399 | ||
[[Mapping]]: [<3 10 11 6|, <0 -13 -10 6|] | |||
Wedgie: <<39 30 -18 -43 -138 -126|| | [[Wedgie]]: <<39 30 -18 -43 -138 -126|| | ||
{{ | {{Val list|legend=1| 15, 141, 156, 171 }} | ||
Badness: 0. | [[Badness]]: 0.045660 | ||
=Domain= | = Domain = | ||
{{see also|Minortonic family}} | |||
[[Comma list]]: 250047/250000, 645700815/645657712 | |||
[[POTE tuning|POTE generator]]: ~10/9 = 182.467 | |||
[[Mapping]]: [<3 -3 -9 -8|, <0 17 35 36|] | |||
{{ | [[Wedgie]]: <<-51 -105 -108 -48 -28 44|| | ||
{{Val list|legend=1| 171, 1335, 1506, 1677, 1848, 2019, 2190 }} | |||
[[Badness]]: 0.013979 | |||
[[Category:Microtemperament]] | [[Category:Microtemperament]] | ||
[[Category:Landscape]] | [[Category:Landscape]] | ||
Revision as of 12:18, 8 April 2021
Landscape microtemperaments are rank two temperaments tempering out the landscape comma ([-4 6 -6 3⟩ = 250047/250000).
Landscape rank-two temperaments include sextile, septichrome, pnict, and domain. Considered elsewhere are ennealimmal, misty, mutt, nessafof, and chromat.
Sextile
Comma list: 250047/250000, 33554432/33480783
POTE generator: ~3/2 = 702.212
Mapping: [<6 0 71 150|, <0 1 -6 -14|]
Wedgie: <<6 -36 -84 -71 -150 -94||
Badness: 0.070097
11-limit
Comma list: 5632/5625, 9801/9800, 151263/151250
POTE generator: ~3/2 = 702.202
Mapping: [<6 0 71 150 230|, <0 1 -6 -14 -22|]
Vals: Template:Val list
Badness: 0.029677
Septichrome
Comma list: 250047/250000, 2460375/2458624
POTE generator: ~243/224 = 140.367
Mapping: [<3 3 1 0|, <0 5 17 24|]
Wedgie: <<15 51 72 46 72 24||
Badness: 0.016814
Pnict
Comma list: 250047/250000, 2100875/2097152
POTE generator: ~192/175 = 161.399
Mapping: [<3 10 11 6|, <0 -13 -10 6|]
Wedgie: <<39 30 -18 -43 -138 -126||
Badness: 0.045660
Domain
Comma list: 250047/250000, 645700815/645657712
POTE generator: ~10/9 = 182.467
Mapping: [<3 -3 -9 -8|, <0 17 35 36|]
Wedgie: <<-51 -105 -108 -48 -28 44||
Badness: 0.013979