Father family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,170 edits
unchanged interval → unchanged-interval
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,170 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 17: Line 17:
: [[Eigenmonzo]]s (unchanged-intervals): 2, 6/5
: [[Eigenmonzo]]s (unchanged-intervals): 2, 6/5


{{Val list|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }}
{{Optimal ET sequence|legend=1| 1, 2, 3, 5, 8, 13c, 21bcc }}


[[Badness]]: 0.014884
[[Badness]]: 0.014884
Line 40: Line 40:
: Eigenmonzos (unchanged-intervals): 2, 9/7
: Eigenmonzos (unchanged-intervals): 2, 9/7


{{Val list|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }}
{{Optimal ET sequence|legend=1| 2d, 3d, 5, 8d, 13cd, 21bccdd }}


[[Badness]]: 0.021312
[[Badness]]: 0.021312
Line 53: Line 53:
POTE generator: ~3/2 = 747.156
POTE generator: ~3/2 = 747.156


Optimal GPV sequence: {{Val list| 2de, 3de, 5, 8d }}
{{Optimal ET sequence|legend=1| 2de, 3de, 5, 8d }}


Badness: 0.020589
Badness: 0.020589
Line 68: Line 68:
[[POTE generator]]: ~3/2 = 721.569
[[POTE generator]]: ~3/2 = 721.569


{{Val list|legend=1| 2, 3, 5 }}
{{Optimal ET sequence|legend=1| 2, 3, 5 }}


[[Badness]]: 0.024152
[[Badness]]: 0.024152
Line 81: Line 81:
POTE generator: ~3/2 = 717.364
POTE generator: ~3/2 = 717.364


Optimal GPV sequence: {{Val list| 2, 3, 5 }}
{{Optimal ET sequence|legend=1| 2, 3, 5 }}


Badness: 0.021957
Badness: 0.021957
Line 96: Line 96:
[[POTE generator]]: ~3/2 = 753.113
[[POTE generator]]: ~3/2 = 753.113


{{Val list|legend=1| 3, 5d, 8d }}
{{Optimal ET sequence|legend=1| 3, 5d, 8d }}


[[Badness]]: 0.053001
[[Badness]]: 0.053001
Line 109: Line 109:
POTE generator: ~3/2 = 751.396
POTE generator: ~3/2 = 751.396


Optimal GPV sequence: {{Val list| 3, 5de, 8d }}
{{Optimal ET sequence|legend=1| 3, 5de, 8d }}


Badness: 0.035487
Badness: 0.035487
Line 126: Line 126:
{{Multival|legend=1| 2 -2 1 -8 -4 8 }}
{{Multival|legend=1| 2 -2 1 -8 -4 8 }}


{{Val list|legend=1| 5, 11b, 16bc }}
{{Optimal ET sequence|legend=1| 5, 11b, 16bc }}


[[Badness]]: 0.044321
[[Badness]]: 0.044321
Line 139: Line 139:
POTE generator: ~7/4 = 978.164
POTE generator: ~7/4 = 978.164


Optimal GPV sequence: {{Val list| 5, 11b, 16bc, 27bbcc }}
{{Optimal ET sequence|legend=1| 5, 11b, 16bc, 27bbcc }}


Badness: 0.036538
Badness: 0.036538
Line 156: Line 156:
[[POTE generator]]: ~3/2 = 749.415
[[POTE generator]]: ~3/2 = 749.415


{{Val list|legend=1| 2, 6, 8d }}
{{Optimal ET sequence|legend=1| 2, 6, 8d }}


[[Badness]]: 0.048978
[[Badness]]: 0.048978
Line 169: Line 169:
POTE generator: ~3/2 = 749.756
POTE generator: ~3/2 = 749.756


Optimal GPV sequence: {{Val list| 2, 6, 8d }}
{{Optimal ET sequence|legend=1| 2, 6, 8d }}


Badness: 0.029193
Badness: 0.029193
Line 186: Line 186:
[[POTE generator]]: ~7/4 = 1034.013
[[POTE generator]]: ~7/4 = 1034.013


{{Val list|legend=1| 3d, 6, 9bd, 15bbd }}
{{Optimal ET sequence|legend=1| 3d, 6, 9bd, 15bbd }}


[[Badness]]: 0.028673
[[Badness]]: 0.028673
Line 199: Line 199:
POTE generator: ~7/4 = 1033.153
POTE generator: ~7/4 = 1033.153


Optimal GPV sequence: {{Val list| 3de, 6, 15bbdee }}
{{Optimal ET sequence|legend=1| 3de, 6, 15bbdee }}


Badness: 0.025592
Badness: 0.025592
Line 216: Line 216:
[[POTE generator]]: ~7/4 = 1017.903
[[POTE generator]]: ~7/4 = 1017.903


{{Val list|legend=1| 5, 15ccd }}
{{Optimal ET sequence|legend=1| 5, 15ccd }}


[[Badness]]: 0.048312
[[Badness]]: 0.048312

Revision as of 16:17, 7 May 2023

The father family of temperaments tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments. In a sense, what father is all about is using semisixths or subfourths and pretending that's 5-limit, and like any temperament which seems to involve pretending, father is at the edge of what can sensibly be called a temperament at all. In other words, it is an exotemperament.

Father

Subgroup: 2.3.5

Comma list: 16/15

Mapping: [⟨1 0 4], ⟨0 1 -1]]

Mapping generators: ~2, ~3

POTE generator: ~3/2 = 743.986

Minimax tuning:

Eigenmonzos (unchanged-intervals): 2, 6/5

Optimal ET sequence: 1, 2, 3, 5, 8, 13c, 21bcc

Badness: 0.014884

Septimal father

See also: Trienstonic clan § Father

Subgroup: 2.3.5.7

Comma list: 16/15, 28/27

Mapping: [⟨1 0 4 -2], ⟨0 1 -1 3]]

Wedgie: ⟨⟨ 1 -1 3 -4 2 10 ]]

POTE generator: ~3/2 = 742.002

Minimax tuning:

Eigenmonzos (unchanged-intervals): 2, 7/5
Eigenmonzos (unchanged-intervals): 2, 9/7

Optimal ET sequence: 2d, 3d, 5, 8d, 13cd, 21bccdd

Badness: 0.021312

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 28/27

Mapping: [⟨1 0 4 -2 -3], ⟨0 1 -1 3 4]]

POTE generator: ~3/2 = 747.156

Optimal ET sequence: 2de, 3de, 5, 8d

Badness: 0.020589

Mother

Subgroup: 2.3.5.7

Comma list: 16/15, 21/20

Mapping: [⟨1 0 4 6], ⟨0 1 -1 -2]]

Wedgie: ⟨⟨ 1 -1 -2 -4 -6 -2 ]]

POTE generator: ~3/2 = 721.569

Optimal ET sequence: 2, 3, 5

Badness: 0.024152

11-limit

Subgroup: 2.3.5.7.11

Comma list: 11/10, 16/15, 21/20

Mapping: [⟨1 0 4 6 5], ⟨0 1 -1 -2 -1]]

POTE generator: ~3/2 = 717.364

Optimal ET sequence: 2, 3, 5

Badness: 0.021957

Pater

Subgroup: 2.3.5.7

Comma list: 16/15, 126/125

Mapping: [⟨1 0 4 11], ⟨0 1 -1 -5]]

Wedgie: ⟨⟨ 1 -1 -5 -4 -11 -9 ]]

POTE generator: ~3/2 = 753.113

Optimal ET sequence: 3, 5d, 8d

Badness: 0.053001

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 100/99

Mapping: [⟨1 0 4 11 10], ⟨0 1 -1 -5 -4]]

POTE generator: ~3/2 = 751.396

Optimal ET sequence: 3, 5de, 8d

Badness: 0.035487

Baba

Subgroup: 2.3.5.7

Comma list: 16/15, 49/45

Mapping: [⟨1 0 4 2], ⟨0 2 -2 1]]

Mapping generators: ~2, ~7/4

POTE generator: ~7/4 = 973.296

Wedgie: ⟨⟨ 2 -2 1 -8 -4 8 ]]

Optimal ET sequence: 5, 11b, 16bc

Badness: 0.044321

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 49/45

Mapping: [⟨1 0 4 2 1], ⟨0 2 -2 1 3]]

POTE generator: ~7/4 = 978.164

Optimal ET sequence: 5, 11b, 16bc, 27bbcc

Badness: 0.036538

Walid

Subgroup: 2.3.5.7

Comma list: 16/15, 50/49

Mapping: [⟨2 0 8 9], ⟨0 1 -1 -1]]

Mapping generators: ~7/5, ~3

Wedgie: ⟨⟨ 2 -2 -2 -8 -9 1 ]]

POTE generator: ~3/2 = 749.415

Optimal ET sequence: 2, 6, 8d

Badness: 0.048978

11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 50/49

Mapping: [⟨2 0 8 9 7], ⟨0 1 -1 -1 0]]

POTE generator: ~3/2 = 749.756

Optimal ET sequence: 2, 6, 8d

Badness: 0.029193

Ternary

Subgroup: 2.3.5.7

Comma list: 10/9, 16/15

Mapping: [⟨3 5 7 0], ⟨0 0 0 1]]

Mapping generators: ~5/4, ~7

Wedgie: ⟨⟨ 0 0 3 0 5 7 ]]

POTE generator: ~7/4 = 1034.013

Optimal ET sequence: 3d, 6, 9bd, 15bbd

Badness: 0.028673

11-limit

Subgroup: 2.3.5.7.11

Comma list: 10/9, 16/15, 22/21

Mapping: [⟨3 5 7 0 2], ⟨0 0 0 1 1]]

POTE generator: ~7/4 = 1033.153

Optimal ET sequence: 3de, 6, 15bbdee

Badness: 0.025592

Quint

Subgroup: 2.3.5.7

Comma list: 16/15, 27/25

Mapping: [⟨5 8 12 0], ⟨0 0 0 1]]

Mapping generators: ~9/8, ~7

Wedgie: ⟨⟨ 0 0 5 0 8 12 ]]

POTE generator: ~7/4 = 1017.903

Optimal ET sequence: 5, 15ccd

Badness: 0.048312

Retrieved from "https://en.xen.wiki/index.php?title=Father_family&oldid=112492"