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Immunity family: Difference between revisions

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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]].  
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 12: 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 }}
{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}


[[Badness]]: 0.184738
[[Badness]] (Sintel): 4.334


=== 2.3.5.13 subgroup ===
=== 2.3.5.13 subgroup ===
Line 25: Line 30:
Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}


Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 952.6431
Optimal tunings:
* CTE: ~2 = 1200.0000¢, ~26/15 = 952.6431¢
* CWE: ~2 = 1200.0000¢, ~26/15 = 952.7890¢


{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
 
Badness (Sintel): 0.858


Badness: 0.257
=== 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 40: 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¢
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/4 = 952.445
: [[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 ET sequence|legend=1| 5, …, 29, 34, 63d }}
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}


[[Badness]]: 0.077631
[[Badness]] (Sintel): 1.965


=== 11-limit ===
=== 11-limit ===
Line 55: 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 }}
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}


Badness: 0.052661
Badness (Sintel): 1.741


==== 13-limit ====
==== 13-limit ====
Line 68: 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 }}
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}


Badness: 0.037078
Badness (Sintel): 1.532


=== Impunity ===
=== Impunity ===
Line 81: 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| 5e, 24cee, 29 }}
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}


Badness: 0.055243
Badness (Sintel): 1.826


==== 13-limit ====
==== 13-limit ====
Line 94: 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| 5e, 24ceef, 29 }}
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}


Badness: 0.033196
Badness (Sintel): 1.372


== Immunized ==
== Immunized ==
Line 107: 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, 29d, 34d, 39d, 73dd, 112cddd }}
{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}


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


=== 11-limit ===
=== 11-limit ===
Line 122: 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, 29de, 34d, 39d, 73dd }}
{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}


Badness: 0.051515
Badness (Sintel): 1.703


== Immune ==
== Immune ==
Line 135: 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 150: 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 163: 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]]
Retrieved from "https://en.xen.wiki/w/Immunity_family"