Immunity family: Difference between revisions

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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~1280/729 = 952.706
* [[CTE]]: ~2 = 1200.0000¢, ~1280/729 = 952.7056¢
: [[error map]]: {{val| 0.000 +3.456 -1.141 }}
: [[error map]]: {{val| 0.000 +3.456 -1.141 }}
* [[POTE]]: ~2 = 1200.000, ~1280/729 = 952.930
* [[CWE]]: ~2 = 1200.0000¢, ~1280/729 = 952.8424¢
: error map: {{val| 0.000 +3.905 +1.775 }}
: 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]] (Smith): 0.184738
[[Badness]] (Sintel): 4.334


=== 2.3.5.13 subgroup ===
=== 2.3.5.13 subgroup ===
Line 31: Line 31:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~26/15 = 952.643
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.6431¢
* CWE: ~2 = 1200.000, ~26/15 = 952.789
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.7890¢


{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}


Badness (Smith): 0.257
Badness (Sintel): 0.858


== Septimal immunity ==
== Septimal immunity ==
Line 48: Line 48:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/4 = 952.767
* [[CTE]]: ~2 = 1200.0000¢, ~7/4 = 952.7674¢
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
* [[POTE]]: ~2 = 1200.000, ~7/4 = 952.445
* [[CWE]]: ~2 = 1200.0000¢, ~7/4 = 952.5376¢
: error map: {{val| 0.000 +2.936 -4.525 -16.381 }}
: 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]] (Smith): 0.077631
[[Badness]] (Sintel): 1.965


=== 11-limit ===
=== 11-limit ===
Line 65: Line 65:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 952.442
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4418¢
* POTE: ~2 = 1200.000, ~7/4 = 952.074
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1429¢


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


Badness (Smith): 0.052661
Badness (Sintel): 1.741


==== 13-limit ====
==== 13-limit ====
Line 80: Line 80:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 952.472
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.4723¢
* POTE: ~2 = 1200.000, ~7/4 = 952.031
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.1117¢


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


Badness (Smith): 0.037078
Badness (Sintel): 1.532


=== Impunity ===
=== Impunity ===
Line 95: Line 95:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 952.528
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5282¢
* POTE: ~2 = 1200.000, ~7/4 = 952.227
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3120¢


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


Badness (Smith): 0.055243
Badness (Sintel): 1.826


==== 13-limit ====
==== 13-limit ====
Line 110: Line 110:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 952.529
* CTE: ~2 = 1200.0000¢, ~7/4 = 952.5292¢
* POTE: ~2 = 1200.000, ~7/4 = 952.217
* CWE: ~2 = 1200.0000¢, ~7/4 = 952.3038¢


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


Badness (Smith): 0.033196
Badness (Sintel): 1.372


== Immunized ==
== Immunized ==
Line 125: Line 125:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~140/81 = 953.001
* [[CTE]]: ~2 = 1200.0000¢, ~140/81 = 953.0010¢
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
* [[POTE]]: ~2 = 1200.000, ~140/81 = 953.521
* [[CWE]]: ~2 = 1200.0000¢, ~140/81 = 953.3954¢
: error map: {{val| 0.000 +5.088 +9.463 +17.089 }}
: 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]] (Smith): 0.082592
[[Badness]] (Sintel): 2.090


=== 11-limit ===
=== 11-limit ===
Line 142: Line 142:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~55/32 = 953.271
* CTE: ~2 = 1200.0000¢, ~55/32 = 953.2713¢
* POTE: ~2 = 1200.000, ~55/32 = 953.397
* CWE: ~2 = 1200.0000¢, ~55/32 = 953.3755¢


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


Badness (Smith): 0.051515
Badness (Sintel): 1.703


== Immune ==
== Immune ==
Line 157: Line 157:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~1000/567 = 952.386
* [[CTE]]: ~2 = 1200.0000¢, ~1000/567 = 952.3863¢
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
* [[POTE]]: ~2 = 1200.000, ~1000/567 = 952.417
* [[CWE]]: ~2 = 1200.0000¢, ~1000/567 = 952.4061¢
: error map: {{val| 0.000 +2.879 -4.893 +3.683 }}
: 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]] (Smith): 0.144835
[[Badness]] (Sintel): 3.665


=== 11-limit ===
=== 11-limit ===
Line 174: Line 174:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~121/70 = 952.375
* CTE: ~2 = 1200.0000¢, ~121/70 = 952.3747¢
* POTE: ~2 = 1200.000, ~121/70 = 952.411
* CWE: ~2 = 1200.0000¢, ~121/70 = 952.3983¢


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


Badness (Smith): 0.050990
Badness (Sintel): 1.686


=== 13-limit ===
=== 13-limit ===
Line 189: Line 189:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~26/15 = 952.389
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.3891¢
* POTE: ~2 = 1200.000, ~26/15 = 952.407
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.4008¢


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


Badness (Smith): 0.028521
Badness (Sintel): 1.179


[[Category:Temperament families]]
[[Category:Temperament families]]

Revision as of 22:56, 26 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

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=224835"