Misty family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
mNo edit summary
Line 1: Line 1:
The '''misty family''' tempers out the [[misty comma]], 67108864/66430125 = {{monzo| 26 -12 -3 }}.
The '''misty family''' tempers out the [[misty comma]], 67108864/66430125 = {{monzo| 26 -12 -3 }}.


== Misty ==
== Misty ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 14: Line 14:
[[Badness]]: 0.106540
[[Badness]]: 0.106540


=== 7-limit ===
=== Extensions ===
The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which 7-limit family member we are looking at.
* Adding 3136/3125 (hemimean) leads septimal misty.
* Adding 225/224 (marvel) leads fog.
 
== Septimal misty ==
{{see also|Hemimean clan #Misty}}
{{see also|Hemimean clan #Misty}}


Line 31: Line 36:
[[Badness]]: 0.036802
[[Badness]]: 0.036802


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 44: Line 49:
Badness: 0.035932
Badness: 0.035932


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 57: Line 62:
Badness: 0.027820
Badness: 0.027820


===== 17-limit =====
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 70: Line 75:
Badness: 0.023908
Badness: 0.023908


===== 19-limit =====
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 83: Line 88:
Badness: 0.019878
Badness: 0.019878


==== Mystic ====
==== Mystic ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 96: Line 101:
Badness: 0.036872
Badness: 0.036872


=== Hemimist ===
=== Hemimist ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 109: Line 114:
Badness: 0.047439
Badness: 0.047439


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 122: Line 127:
Badness: 0.022923
Badness: 0.022923


== Fog ==
== Fog ==
The ''fog'' temperament (12&63, named by [[User:Xenllium|Xenllium]]) tempers out the [[225/224|marvel comma]] 225/224.
The ''fog'' temperament (12&63) tempers out the [[225/224|marvel comma]] 225/224.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 139: Line 144:
[[Badness]]: 0.086866
[[Badness]]: 0.086866


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Revision as of 01:43, 6 June 2021

The misty family tempers out the misty comma, 67108864/66430125 = [26 -12 -3⟩.

Misty

Subgroup: 2.3.5

Comma list: 67108864/66430125

Mapping: [⟨3 0 26], ⟨0 1 -4]]

POTE generator: ~3/2 = 703.111

Template:Val list

Badness: 0.106540

Extensions

The second comma of the normal comma list defines which 7-limit family member we are looking at.

  • Adding 3136/3125 (hemimean) leads septimal misty.
  • Adding 225/224 (marvel) leads fog.

Septimal misty

See also: Hemimean clan § Misty

Subgroup: 2.3.5.7

Comma list: 3136/3125, 5120/5103

Mapping: [⟨3 0 26 56], ⟨0 1 -4 -10]]

Wedgie: ⟨⟨ 3 -12 -30 -26 -56 -36 ]]

POTE generator: ~3/2 = 703.021

Template:Val list

Badness: 0.036802

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3136/3125, 4375/4356

Mapping: [⟨3 0 26 56 77], ⟨0 1 -4 -10 -14]]

POTE generator: ~3/2 = 703.210

Vals: Template:Val list

Badness: 0.035932

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 364/363, 625/624

Mapping: [⟨3 0 26 56 77 92], ⟨0 1 -4 -10 -14 -17]]

POTE generator: ~3/2 = 703.303

Vals: Template:Val list

Badness: 0.027820

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 196/195, 352/351, 364/363, 375/374, 595/594

Mapping: [⟨3 0 26 56 77 92 -2], ⟨0 1 -4 -10 -14 -17 3]]

POTE generator: ~3/2 = 703.233

Vals: Template:Val list

Badness: 0.023908

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594

Mapping: [⟨3 0 26 56 77 92 -2 8], ⟨0 1 -4 -10 -14 -17 3 1]]

POTE generator: ~3/2 = 703.253

Vals: Template:Val list

Badness: 0.019878

Mystic

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 441/440, 896/891, 1001/1000

Mapping: [⟨3 0 26 56 77 -46], ⟨0 1 -4 -10 -14 12]]

POTE generator: ~3/2 = 703.311

Vals: Template:Val list

Badness: 0.036872

Hemimist

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 3136/3125, 5120/5103

Mapping: [⟨3 0 26 56 8], ⟨0 2 -8 -20 1]]

POTE generator: ~11/8 = 551.527

Vals: Template:Val list

Badness: 0.047439

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 676/675, 847/845, 3025/3024

Mapping: [⟨3 0 26 56 8 23], ⟨0 2 -8 -20 1 -5]]

POTE generator: ~11/8 = 551.525

Vals: Template:Val list

Badness: 0.022923

Fog

The fog temperament (12&63) tempers out the marvel comma 225/224.

Subgroup: 2.3.5.7

Comma list: 225/224, 156250/151263

Mapping: [⟨3 5 6 7], ⟨0 -1 4 6]]

Wedgie: ⟨⟨ 3 -12 -18 -26 -37 -8 ]]

POTE generator: ~3/2 = 704.118

Template:Val list

Badness: 0.086866

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 225/224, 2420/2401

Mapping: [⟨3 5 6 7 8], ⟨0 -1 4 6 10]]

POTE generator: ~3/2 = 704.411

Vals: Template:Val list

Badness: 0.051348

Retrieved from "https://en.xen.wiki/index.php?title=Misty_family&oldid=71977"