Quintile family: Difference between revisions

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The pental family tempers out the pental comma, 847288609443/838860800000 = |-28 25 -5>.
The pental family tempers out the pental comma, 847288609443/838860800000 = {{Monzo|-28 25 -5}}.


=Pental=
= Pental =
Comma: 847288609443/838860800000
[[Comma]]: 847288609443/838860800000


[[POTE tuning|POTE generator]]: ~3/2 = 701.210
[[Mapping]]: [{{val|5 0 -28}}, {{val|0 1 5}}]


[[Map]]: [<5 0 -28|, <0 1 5|]
[[POTE generator]]: ~3/2 = 701.210


{{Vals|legend=1| 5, 60, 65, 190, 255, 575, 830b, 1405b }}
{{Vals|legend=1| 5, 60, 65, 190, 255, 575, 830b, 1405b }}
Line 12: Line 12:
[[Badness]]: 0.240050
[[Badness]]: 0.240050


==7-limit==
== 7-limit ==
The pental temperament can be described as 5&60 temperament (''pentacloud'', named by [[User:Xenllium|Xenllium]]), tempering out the [[cloudy comma]], 16807/16384 and the [[245/243|sensamagic comma]], 245/243 in the 7-limit.
The pental temperament can be described as 5&60 temperament (''pentacloud'', named by [[User:Xenllium|Xenllium]]), tempering out the [[cloudy comma]], 16807/16384 and the [[245/243|sensamagic comma]], 245/243 in the 7-limit.


[[Comma list]]: 245/243, 16807/16384
[[Comma list]]: 245/243, 16807/16384


[[POTE tuning|POTE generator]]: ~3/2 = 700.548
[[Mapping]]: [{{val|5 0 -28 14}}, {{val|0 1 5 0}}]


[[Map]]: [<5 0 -28 14|, <0 1 5 0|]
[[POTE generator]]: ~3/2 = 700.548


{{Vals|legend=1| 5, 60, 65, 125d, 185cdd }}
{{Val list|legend=1| 5, 60, 65, 125d, 185cdd }}


[[Badness]]: 0.120942
[[Badness]]: 0.120942


==11-limit==
== 11-limit ==
Comma list: 245/243, 385/384, 3087/3025
Comma list: 245/243, 385/384, 3087/3025
Mapping: [{{val|5 0 -28 14 49}}, {{val|0 1 5 0 -4}}]


POTE generator: ~3/2 = 701.377
POTE generator: ~3/2 = 701.377


Map: [<5 0 -28 14 49|, <0 1 5 0 -4|]
Vals: {{Val list| 5, 60, 65 }}
 
Vals: {{Vals| 5, 60, 65 }}


Badness: 0.093248
Badness: 0.093248


==13-limit==
== 13-limit ==
Comma list: 105/104, 144/143, 245/243, 3087/3025
Comma list: 105/104, 144/143, 245/243, 3087/3025
Mapping: [{{val|5 0 -28 14 49 -29}}, {{val|0 1 5 0 -4 6}}]


POTE generator: ~3/2 = 700.996
POTE generator: ~3/2 = 700.996


Map: [<5 0 -28 14 49 -29|, <0 1 5 0 -4 6|]
Vals: {{Val list| 5, 60, 65, 125de, 190ddef }}
 
Vals: {{Vals| 5, 60, 65, 125de, 190ddef }}


Badness: 0.067549
Badness: 0.067549


=Hemipental=
= Hemipental =
The ''hemipental'' temperament (125&130, named by [[User:Xenllium|Xenllium]]) tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 (hewuermera, satribiru-agu) and 5250987/5242880 (laquadzo-agu).
The ''hemipental'' temperament (125&130, named by [[User:Xenllium|Xenllium]]) tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 ([[Hewuermera temperaments|hewuermera]], satribiru-agu) and 5250987/5242880 (laquadzo-agu).


[[Comma list]]: 19683/19600, 589824/588245
[[Comma list]]: 19683/19600, 589824/588245


[[POTE tuning|POTE generator]]: ~8/7 = 230.654
[[Mapping]]: [{{val|5 8 12 14}}, {{val|0 -2 -10 1}}]


[[Map]]: [<5 8 12 14|, <0 -2 -10 1|]
[[POTE generator]]: ~8/7 = 230.654


{{Vals|legend=1| 5, 125, 130, 255, 385 }}
{{Val list|legend=1| 5, 125, 130, 255, 385 }}


[[Badness]]: 0.104163
[[Badness]]: 0.104163


==11-limit==
== 11-limit ==
Comma list: 540/539, 8019/8000, 180224/180075
Comma list: 540/539, 8019/8000, 180224/180075
Mapping: [{{val|5 8 12 14 18}}, {{val|0 -2 -10 1 -18}}]


POTE generator: ~8/7 = 230.634
POTE generator: ~8/7 = 230.634


Map: [<5 8 12 14 18|, <0 -2 -10 1 -18|]
Vals: {{Val list| 5e, 125, 130, 255, 385, 640, 1025b }}
 
Vals: {{Vals| 5e, 125, 130, 255, 385, 640, 1025b }}


Badness: 0.047624
Badness: 0.047624


==13-limit==
== 13-limit ==
Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000
Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000
Mapping: [{{val|5 8 12 14 18 18}}, {{val|0 -2 -10 1 -18 13}}]


POTE generator: ~8/7 = 230.668
POTE generator: ~8/7 = 230.668


Map: [<5 8 12 14 18 18|, <0 -2 -10 1 -18 13|]
Vals: {{Val list| 5ef, 125, 130, 255, 385, 515, 900ef }}
 
Vals: {{Vals| 5ef, 125, 130, 255, 385, 515, 900ef }}


Badness: 0.041043
Badness: 0.041043


=Decal=
= Decal =
The decal temperament (130&190) tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellsma, tribizo-asepgu), 2460375/2458624 (laquadru-atriyo), and the [[15/14ths equal temperament|linus comma]], |11 -10 -10 10>.
The decal temperament (130&190) tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellisma, tribizo-asepgu), 2460375/2458624 (sesquiquartisma, laquadru-atriyo), and the [[15/14ths equal temperament|linus comma]], {{Monzo|11 -10 -10 10}}.


[[Comma list]]: 235298/234375, 321489/320000
[[Comma list]]: 235298/234375, 321489/320000


[[POTE tuning|POTE generator]]: ~3/2 = 701.303
[[Mapping]]: [{{val|10 0 -56 -67}}, {{val|0 1 5 6}}]


[[Map]]: [<10 0 -56 -67|, <0 1 5 6|]
[[POTE generator]]: ~3/2 = 701.303


{{Vals|legend=1| 60, 130, 320, 450, 770d }}
{{Val list|legend=1| 60, 130, 320, 450, 770d }}


[[Badness]]: 0.104859
[[Badness]]: 0.104859


==11-limit==
== 11-limit ==
Comma list: 441/440, 8019/8000, 234375/234256
Comma list: 441/440, 8019/8000, 234375/234256
Mapping: [{{val|10 0 -56 -67 -108}}, {{val|0 1 5 6 9}}]


POTE generator: ~3/2 = 701.240
POTE generator: ~3/2 = 701.240


Map: [<10 0 -56 -67 -108|, <0 1 5 6 9|]
Vals: {{Val list| 60e, 130, 190, 320 }}
 
Vals: {{Vals| 60e, 130, 190, 320 }}


Badness: 0.040633
Badness: 0.040633


==13-limit==
== 13-limit ==
Comma list: 441/440, 729/728, 1001/1000, 4225/4224
Comma list: 441/440, 729/728, 1001/1000, 4225/4224
Mapping: [{{val|10 0 -56 -67 -108 37}}, {{val|0 1 5 6 9 0}}]


POTE generator: ~3/2 = 701.252
POTE generator: ~3/2 = 701.252


Map: [<10 0 -56 -67 -108 37|, <0 1 5 6 9 0|]
Vals: {{Val list| 60e, 130, 190, 320 }}
 
Vals: {{Vals| 60e, 130, 190, 320 }}


Badness: 0.023948
Badness: 0.023948

Revision as of 08:23, 28 May 2021

The pental family tempers out the pental comma, 847288609443/838860800000 = [-28 25 -5⟩.

Pental

Comma: 847288609443/838860800000

Mapping: [⟨5 0 -28], ⟨0 1 5]]

POTE generator: ~3/2 = 701.210

Optimal ET sequence: 5, 60, 65, 190, 255, 575, 830b, 1405b

Badness: 0.240050

7-limit

The pental temperament can be described as 5&60 temperament (pentacloud, named by Xenllium), tempering out the cloudy comma, 16807/16384 and the sensamagic comma, 245/243 in the 7-limit.

Comma list: 245/243, 16807/16384

Mapping: [⟨5 0 -28 14], ⟨0 1 5 0]]

POTE generator: ~3/2 = 700.548

Template:Val list

Badness: 0.120942

11-limit

Comma list: 245/243, 385/384, 3087/3025

Mapping: [⟨5 0 -28 14 49], ⟨0 1 5 0 -4]]

POTE generator: ~3/2 = 701.377

Vals: Template:Val list

Badness: 0.093248

13-limit

Comma list: 105/104, 144/143, 245/243, 3087/3025

Mapping: [⟨5 0 -28 14 49 -29], ⟨0 1 5 0 -4 6]]

POTE generator: ~3/2 = 700.996

Vals: Template:Val list

Badness: 0.067549

Hemipental

The hemipental temperament (125&130, named by Xenllium) tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 (hewuermera, satribiru-agu) and 5250987/5242880 (laquadzo-agu).

Comma list: 19683/19600, 589824/588245

Mapping: [⟨5 8 12 14], ⟨0 -2 -10 1]]

POTE generator: ~8/7 = 230.654

Template:Val list

Badness: 0.104163

11-limit

Comma list: 540/539, 8019/8000, 180224/180075

Mapping: [⟨5 8 12 14 18], ⟨0 -2 -10 1 -18]]

POTE generator: ~8/7 = 230.634

Vals: Template:Val list

Badness: 0.047624

13-limit

Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000

Mapping: [⟨5 8 12 14 18 18], ⟨0 -2 -10 1 -18 13]]

POTE generator: ~8/7 = 230.668

Vals: Template:Val list

Badness: 0.041043

Decal

The decal temperament (130&190) tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (triwellisma, tribizo-asepgu), 2460375/2458624 (sesquiquartisma, laquadru-atriyo), and the linus comma, [11 -10 -10 10⟩.

Comma list: 235298/234375, 321489/320000

Mapping: [⟨10 0 -56 -67], ⟨0 1 5 6]]

POTE generator: ~3/2 = 701.303

Template:Val list

Badness: 0.104859

11-limit

Comma list: 441/440, 8019/8000, 234375/234256

Mapping: [⟨10 0 -56 -67 -108], ⟨0 1 5 6 9]]

POTE generator: ~3/2 = 701.240

Vals: Template:Val list

Badness: 0.040633

13-limit

Comma list: 441/440, 729/728, 1001/1000, 4225/4224

Mapping: [⟨10 0 -56 -67 -108 37], ⟨0 1 5 6 9 0]]

POTE generator: ~3/2 = 701.252

Vals: Template:Val list

Badness: 0.023948

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