Immunity family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Update keys
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,030 edits
No edit summary
Tags: Mobile edit Mobile web edit
 
(11 intermediate revisions by 8 users not shown)
Line 1: Line 1:
Temperaments of '''immunity family''' temper out the [[immunity comma]], 1638400/1594323 = {{monzo| 16-13 2 }} (sasayoyo).
{{Technical data page}}
The '''immunity family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[immunity comma]], 1638400/1594323 ({{monzo| 16 -13 2 }}).


== Immunity ==
== Immunity ==
Immunity is naturally a 2.3.5.13 [[subgroup temperament]] as the generator serves as ~[[26/15]] (or its [[octave complement]] ~[[15/13]]), tempering out [[676/675]].
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


Line 10: Line 13:
: mapping generators: ~2, ~1280/729
: mapping generators: ~2, ~1280/729


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1280/729 = 952.930
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000¢, ~1280/729 = 952.7056¢
: [[error map]]: {{val| 0.000 +3.456 -1.141 }}
* [[CWE]]: ~2 = 1200.0000¢, ~1280/729 = 952.8424¢
: error map: {{val| 0.000 +3.730 +0.638 }}
 
{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}
 
[[Badness]] (Sintel): 4.334


{{Optimal ET sequence|legend=1| 5, 29, 34 }}
=== 2.3.5.13 subgroup ===
Subgroup: 2.3.5.13


[[Badness]]: 0.184738
Comma list: 676/675, 3200/3159
 
Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
 
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.6431¢
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.7890¢
 
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
 
Badness (Sintel): 0.858
 
=== Overview to extensions ===
The second comma of the comma list defines which 7-limit family member we are looking at:
* Septimal immunity adds [[49/48]];
* Immunized adds [[64/63]];
* Immune adds [[225/224]].


== Septimal immunity ==
== Septimal immunity ==
{{See also| Slendro clan }}
{{See also| Semaphoresmic clan }}


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 25: Line 53:
{{Mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}
{{Mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}


{{Multival|legend=1| 2 13 1 16 -4 -34 }}
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000¢, ~7/4 = 952.7674¢
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
* [[CWE]]: ~2 = 1200.0000¢, ~7/4 = 952.5376¢
: error map: {{val| 0.000 +3.120 -3.325 -16.288 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 952.445
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}


{{Optimal ET sequence|legend=1| 5, 29, 34, 63d }}
[[Badness]] (Sintel): 1.965
 
[[Badness]]: 0.077631


=== 11-limit ===
=== 11-limit ===
Line 40: Line 70:
Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}
Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.074
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4418¢
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1429¢


{{Optimal ET sequence|legend=1| 5, 24c, 29, 63de, 92cddee }}
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}


Badness: 0.052661
Badness (Sintel): 1.741


==== 13-limit ====
==== 13-limit ====
Line 53: Line 85:
Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}
Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.031
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4723¢
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1117¢


{{Optimal ET sequence|legend=1| 5, 24cf, 29, 92cddee }}
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}


Badness: 0.037078
Badness (Sintel): 1.532


=== Impunity ===
=== Impunity ===
Line 66: Line 100:
Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}
Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.227
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5282¢
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3120¢


{{Optimal ET sequence|legend=1| 29, 63d, 92cdd }}
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}


Badness: 0.055243
Badness (Sintel): 1.826


==== 13-limit ====
==== 13-limit ====
Line 79: Line 115:
Mapping: {{mapping| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}
Mapping: {{mapping| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/4 = 952.217
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5292¢
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3038¢


{{Optimal ET sequence|legend=1| 29, 63d, 92cdd }}
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}


Badness: 0.033196
Badness (Sintel): 1.372


== Immunized ==
== Immunized ==
Line 92: Line 130:
{{Mapping|legend=1| 1 0 -8 6 | 0 2 13 -4 }}
{{Mapping|legend=1| 1 0 -8 6 | 0 2 13 -4 }}


{{Multival|legend=1| 2 13 -4 16 -12 -46 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1200.0000¢, ~140/81 = 953.0010¢
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~140/81 = 953.521
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
* [[CWE]]: ~2 = 1200.0000¢, ~140/81 = 953.3954¢
: error map: {{val| 0.000 +4.836 +7.827 +17.592 }}


{{Optimal ET sequence|legend=1| 5, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}


[[Badness]]: 0.082592
[[Badness]] (Sintel): 2.090


=== 11-limit ===
=== 11-limit ===
Line 107: Line 147:
Mapping: {{mapping| 1 0 -8 6 13 | 0 2 13 -4 -12 }}
Mapping: {{mapping| 1 0 -8 6 13 | 0 2 13 -4 -12 }}


Optimal tuning (POTE): ~2 = 1\1, ~55/32 = 953.397
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~55/32 = 953.2713¢
* CWE: ~2 = 1200.0000¢, ~55/32 = 953.3755¢


{{Optimal ET sequence|legend=1| 5, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}


Badness: 0.051515
Badness (Sintel): 1.703


== Immune ==
== Immune ==
Line 120: Line 162:
{{Mapping|legend=1| 1 2 5 9 | 0 -2 -13 -30 }}
{{Mapping|legend=1| 1 2 5 9 | 0 -2 -13 -30 }}


{{Multival|legend=1| 2 13 30 16 42 33 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1200.0000¢, ~1000/567 = 952.3863¢
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1000/567 = 952.417
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
* [[CWE]]: ~2 = 1200.0000¢, ~1000/567 = 952.4061¢
: error map: {{val| 0.000 +2.857 -5.034 +3.357 }}


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}


[[Badness]]: 0.144835
[[Badness]] (Sintel): 3.665


=== 11-limit ===
=== 11-limit ===
Line 135: Line 179:
Mapping: {{mapping| 1 2 5 9 8 | 0 -2 -13 -30 -22 }}
Mapping: {{mapping| 1 2 5 9 8 | 0 -2 -13 -30 -22 }}


Optimal tuning (POTE): ~2 = 1\1, ~121/70 = 952.411
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~121/70 = 952.3747¢
* CWE: ~2 = 1200.0000¢, ~121/70 = 952.3983¢


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}


Badness: 0.050990
Badness (Sintel): 1.686


=== 13-limit ===
=== 13-limit ===
Line 148: Line 194:
Mapping: {{mapping| 1 2 5 9 8 7 | 0 -2 -13 -30 -22 -16 }}
Mapping: {{mapping| 1 2 5 9 8 7 | 0 -2 -13 -30 -22 -16 }}


Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 952.407
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.3891¢
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.4008¢


{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}


Badness: 0.028521
Badness (Sintel): 1.179


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Immunity family| ]] <!-- main article -->
[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity| ]] <!-- key article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 07:50, 27 February 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The immunity family of temperaments tempers out the immunity comma, 1638400/1594323 ([16 -13 2⟩).

Immunity

Immunity is naturally a 2.3.5.13 subgroup temperament as the generator serves as ~26/15 (or its octave complement ~15/13), tempering out 676/675.

Subgroup: 2.3.5

Comma list: 1638400/1594323

Mapping: [⟨1 0 -8], ⟨0 2 13]]

mapping generators: ~2, ~1280/729

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~1280/729 = 952.7056¢
error map: ⟨0.000 +3.456 -1.141]
  • CWE: ~2 = 1200.0000¢, ~1280/729 = 952.8424¢
error map: ⟨0.000 +3.730 +0.638]

Optimal ET sequence: 5, …, 29, 34

Badness (Sintel): 4.334

2.3.5.13 subgroup

Subgroup: 2.3.5.13

Comma list: 676/675, 3200/3159

Sval mapping: [⟨1 0 -8 -9], ⟨0 2 13 16]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~26/15 = 952.6431¢
  • CWE: ~2 = 1200.0000¢, ~26/15 = 952.7890¢

Optimal ET sequence: 5, …, 29, 34

Badness (Sintel): 0.858

Overview to extensions

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

Septimal immunity

See also: Semaphoresmic clan

Subgroup: 2.3.5.7

Comma list: 49/48, 2240/2187

Mapping: [⟨1 0 -8 2], ⟨0 2 13 1]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~7/4 = 952.7674¢
error map: ⟨0.000 +3.580 -0.337 -16.058]
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.5376¢
error map: ⟨0.000 +3.120 -3.325 -16.288]

Optimal ET sequence: 5, …, 29, 34, 63d

Badness (Sintel): 1.965

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 896/891

Mapping: [⟨1 0 -8 2 9], ⟨0 2 13 1 -7]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~7/4 = 952.4418¢
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.1429¢

Optimal ET sequence: 5, 24c, 29, 63de

Badness (Sintel): 1.741

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 91/90, 896/891

Mapping: [⟨1 0 -8 2 9 -9], ⟨0 2 13 1 -7 16]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~7/4 = 952.4723¢
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.1117¢

Optimal ET sequence: 5, 24cf, 29

Badness (Sintel): 1.532

Impunity

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 1232/1215

Mapping: [⟨1 0 -8 2 -14], ⟨0 2 13 1 22]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~7/4 = 952.5282¢
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.3120¢

Optimal ET sequence: 5e, 24cee, 29

Badness (Sintel): 1.826

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 91/90, 100/99, 352/351

Mapping: [⟨1 0 -8 2 -14 -9], ⟨0 2 13 1 22 16]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~7/4 = 952.5292¢
  • CWE: ~2 = 1200.0000¢, ~7/4 = 952.3038¢

Optimal ET sequence: 5e, 24ceef, 29

Badness (Sintel): 1.372

Immunized

Subgroup: 2.3.5.7

Comma list: 64/63, 8748/8575

Mapping: [⟨1 0 -8 6], ⟨0 2 13 -4]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~140/81 = 953.0010¢
error map: ⟨0.000 +4.047 +2.669 +19.170]
  • CWE: ~2 = 1200.0000¢, ~140/81 = 953.3954¢
error map: ⟨0.000 +4.836 +7.827 +17.592]

Optimal ET sequence: 5, 29d, 34d, 39d, 73dd, 112cddd

Badness (Sintel): 2.090

11-limit

Subgroup: 2.3.5.7.11

Comma list: 64/63, 99/98, 1944/1925

Mapping: [⟨1 0 -8 6 13], ⟨0 2 13 -4 -12]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~55/32 = 953.2713¢
  • CWE: ~2 = 1200.0000¢, ~55/32 = 953.3755¢

Optimal ET sequence: 5, 29de, 34d, 39d, 73dd

Badness (Sintel): 1.703

Immune

Subgroup: 2.3.5.7

Comma list: 225/224, 781250/750141

Mapping: [⟨1 2 5 9], ⟨0 -2 -13 -30]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~1000/567 = 952.3863¢
error map: ⟨0.000 +2.818 -5.292 +2.763]
  • CWE: ~2 = 1200.0000¢, ~1000/567 = 952.4061¢
error map: ⟨0.000 +2.857 -5.034 +3.357]

Optimal ET sequence: 29, 34d, 63

Badness (Sintel): 3.665

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 225/224, 1331/1323

Mapping: [⟨1 2 5 9 8], ⟨0 -2 -13 -30 -22]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~121/70 = 952.3747¢
  • CWE: ~2 = 1200.0000¢, ~121/70 = 952.3983¢

Optimal ET sequence: 29, 34d, 63

Badness (Sintel): 1.686

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 169/168, 225/224, 275/273

Mapping: [⟨1 2 5 9 8 7], ⟨0 -2 -13 -30 -22 -16]]

Optimal tunings:

  • CTE: ~2 = 1200.0000¢, ~26/15 = 952.3891¢
  • CWE: ~2 = 1200.0000¢, ~26/15 = 952.4008¢

Optimal ET sequence: 29, 34d, 63

Badness (Sintel): 1.179

Retrieved from "https://en.xen.wiki/index.php?title=Immunity_family&oldid=224852"