Immunity family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
m Recategorize
m Formatting & misc. cleanup
Line 3: Line 3:


== 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]].  
Immunity is naturally a [[2.3.5.13 subgroup|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 10:


{{Mapping|legend=1| 1 0 -8 | 0 2 13 }}
{{Mapping|legend=1| 1 0 -8 | 0 2 13 }}
: mapping generators: ~2, ~1280/729
: mapping generators: ~2, ~1280/729


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000¢, ~1280/729 = 952.7056¢
* [[CTE]]: ~2 = 1200.0000{{c}}, ~1280/729 = 952.7056{{c}}
: [[error map]]: {{val| 0.000 +3.456 -1.141 }}
: [[error map]]: {{val| 0.000 +3.456 -1.141 }}
* [[CWE]]: ~2 = 1200.0000¢, ~1280/729 = 952.8424¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1280/729 = 952.8424{{c}}
: error map: {{val| 0.000 +3.730 +0.638 }}
: error map: {{val| 0.000 +3.730 +0.638 }}


{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}
{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}


[[Badness]] (Sintel): 4.334
[[Badness]] (Sintel): 4.33


=== 2.3.5.13 subgroup ===
=== 2.3.5.13 subgroup ===
Line 28: Line 27:
Comma list: 676/675, 3200/3159
Comma list: 676/675, 3200/3159


Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
Subgroup-val mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.6431¢
* CTE: ~2 = 1200.0000{{c}}, ~26/15 = 952.6431{{c}}
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.7890¢
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 952.7890{{c}}


{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
Line 54: Line 53:


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


{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}


[[Badness]] (Sintel): 1.965
[[Badness]] (Sintel): 1.96


=== 11-limit ===
=== 11-limit ===
Line 71: Line 70:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4418¢
* CTE: ~2 = 1200.0000{{c}}, ~7/4 = 952.4418{{c}}
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1429¢
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.1429{{c}}


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


Badness (Sintel): 1.741
Badness (Sintel): 1.74


==== 13-limit ====
==== 13-limit ====
Line 86: Line 85:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4723¢
* CTE: ~2 = 1200.0000{{c}}, ~7/4 = 952.4723{{c}}
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1117¢
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.1117{{c}}


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


Badness (Sintel): 1.532
Badness (Sintel): 1.53


=== Impunity ===
=== Impunity ===
Line 101: Line 100:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5282¢
* CTE: ~2 = 1200.0000{{c}}, ~7/4 = 952.5282{{c}}
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3120¢
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.3120{{c}}


{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}


Badness (Sintel): 1.826
Badness (Sintel): 1.83


==== 13-limit ====
==== 13-limit ====
Line 116: Line 115:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5292¢
* CTE: ~2 = 1200.0000{{c}}, ~7/4 = 952.5292{{c}}
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3038¢
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.3038{{c}}


{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}


Badness (Sintel): 1.372
Badness (Sintel): 1.37


== Immunized ==
== Immunized ==
Line 131: Line 130:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000¢, ~140/81 = 953.0010¢
* [[CTE]]: ~2 = 1200.0000{{c}}, ~140/81 = 953.0010{{c}}
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
* [[CWE]]: ~2 = 1200.0000¢, ~140/81 = 953.3954¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 953.3954{{c}}
: error map: {{val| 0.000 +4.836 +7.827 +17.592 }}
: error map: {{val| 0.000 +4.836 +7.827 +17.592 }}


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


[[Badness]] (Sintel): 2.090
[[Badness]] (Sintel): 2.09


=== 11-limit ===
=== 11-limit ===
Line 148: Line 147:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~55/32 = 953.2713¢
* CTE: ~2 = 1200.0000{{c}}, ~55/32 = 953.2713{{c}}
* CWE: ~2 = 1200.0000¢, ~55/32 = 953.3755¢
* CWE: ~2 = 1200.0000{{c}}, ~55/32 = 953.3755{{c}}


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


Badness (Sintel): 1.703
Badness (Sintel): 1.70


== Immune ==
== Immune ==
Line 163: Line 162:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000¢, ~1000/567 = 952.3863¢
* [[CTE]]: ~2 = 1200.0000{{c}}, ~1000/567 = 952.3863{{c}}
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
* [[CWE]]: ~2 = 1200.0000¢, ~1000/567 = 952.4061¢
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1000/567 = 952.4061{{c}}
: error map: {{val| 0.000 +2.857 -5.034 +3.357 }}
: 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]] (Sintel): 3.665
[[Badness]] (Sintel): 3.67


=== 11-limit ===
=== 11-limit ===
Line 180: Line 179:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~121/70 = 952.3747¢
* CTE: ~2 = 1200.0000{{c}}, ~121/70 = 952.3747{{c}}
* CWE: ~2 = 1200.0000¢, ~121/70 = 952.3983¢
* CWE: ~2 = 1200.0000{{c}}, ~121/70 = 952.3983{{c}}


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


Badness (Sintel): 1.686
Badness (Sintel): 1.69


=== 13-limit ===
=== 13-limit ===
Line 195: Line 194:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.3891¢
* CTE: ~2 = 1200.0000{{c}}, ~26/15 = 952.3891{{c}}
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.4008¢
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 952.4008{{c}}


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


Badness (Sintel): 1.179
Badness (Sintel): 1.18


[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity family| ]] <!-- Main article -->

Revision as of 02:35, 27 August 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): 4.33

2.3.5.13 subgroup

Subgroup: 2.3.5.13

Comma list: 676/675, 3200/3159

Subgroup-val 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): 1.96

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): 1.74

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): 1.53

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): 1.83

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): 1.37

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): 2.09

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): 1.70

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): 3.67

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): 1.69

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): 1.18

Retrieved from "https://en.xen.wiki/index.php?title=Immunity_family&oldid=236301"