Septisemi temperaments: Difference between revisions

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{{Technical data page}}
These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]], and hence equating 5/3 with 7/4, and 10/7 with 3/2.
This is a collection of very low [[complexity]] temperaments [[tempering out]] the septimal minor semitone, [[21/20]], and hence equating 5/3 with 7/4, and 10/7 with 3/2.


Discussed elsewhere are [[Father family #Mother|mother]], [[Dicot family #Flat|flat]], [[Bug family #Beep|beep]], [[Meantone family #Sharptone|sharptone]] and [[Pelogic family #Pelogic|pelogic]].
Temperaments discussed elsewhere are:
* ''[[Mother]]'' (+16/15) → [[Father family #Mother|Father family]]
* ''[[Sharptone]]'' (+28/27) → [[Meantone family #Sharptone|Meantone family]]
* ''[[Pelogic]]'' (+135/128) → [[Mavila family #Pelogic|Mavila family]]
* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]]
* [[Beep]] (+27/25) → [[Bug family #Beep|Bug family]]
* ''[[Deflated]]'' (+128/125) → [[Augmented family #Deflated|Augmented family]]
* ''[[Gidorah]]'' (+144/125) → [[Gamelismic clan #Gidorah|Gamelismic clan]]
* ''[[Oxygen]]'' (+175/162) → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]]


= Fluorine =
Considered below are fluorine and sodium.


Period: 1\1
== Fluorine ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Avila]].''


Optimal ([[POTE]]) generator: ~3/2 = 663.059
[[Subgroup]]: 2.3.5.7


EDO generators: [[9edo|5\9]]
[[Comma list]]: 21/20, 243/224


Scales (Scala files):  
{{Mapping|legend=1| 1 0 -7 -5 | 0 1 6 5 }}
: mapping generators: ~2, ~3


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Optimal tuning]]s:
<div style="line-height:1.6;">Technical data</div>
* [[WE]]: ~2 = 1211.420{{c}}, ~3/2 = 669.369{{c}}
<div class="mw-collapsible-content">
: [[error map]]: {{val| +11.420 -21.165 +18.481 -21.980 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 665.210{{c}}
: error map: {{val| 0.000 -36.745 +4.945 -42.777 }}


Comma list: 21/20, 243/224
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20bdd, 29bdd }}


Mapping: [{{val| 1 0 -7 -5 }}, {{val| 0 1 6 5 }}]
[[Badness]] (Sintel): 1.41


Wedgie: {{wedgie| 1 6 5 7 5 -5 }}
== Sodium ==
[[Subgroup]]: 2.3.5.7


{{Val list|legend=1| 9, 20bd, 29bd }}
[[Comma list]]: 21/20, 54/49


Badness: 0.0556
{{Mapping|legend=1| 1 1 1 2 | 0 2 5 3 }}
: mapping generators: ~2, ~7/6


</div></div>
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1207.624{{c}}, ~7/6 = 322.216{{c}}
: [[error map]]: {{val| +7.624 -49.898 +32.393 +13.072 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~7/6 = 322.210{{c}}
: error map: {{val| 0.000 -57.535 +24.737 -2.196 }}


= Sodium =
{{Optimal ET sequence|legend=1| 4, 11 }}


Period: 1\1
[[Badness]] (Sintel): 1.41


Optimal ([[POTE]]) generator: ~7/6 = 320.182
[[Category:Temperament collections]]
 
[[Category:Septisemi temperaments| ]] <!-- main article -->
EDO generators: [[11edo|3\11]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Comma list: 21/20, 54/49
 
Mapping: [{{val| 1 1 1 2 }}, {{val| 0 2 5 3 }}]
 
Wedgie: {{wedgie| 2 5 3 3 -1 -7 }}
 
{{Val list|legend=1| 4, 11, 15b }}
 
Badness: 0.0558
 
</div></div>
 
= Oxygen =
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~7/6 = 169.112
 
EDO generators: [[8edo|1\7]], [[8edo|1\8]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Comma list: 21/20, 175/162
 
Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -3 -5 -2 }}]
 
Wedgie: {{wedgie| 3 5 2 1 -5 -9 }}
 
{{Val list|legend=1| 7d, 8 }}
 
Badness: 0.0599
 
</div></div>
 
[[Category:Theory]]
[[Category:Temperament]]
[[Category:Septisemi]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 12:31, 27 November 2025

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.

This is a collection of very low complexity temperaments tempering out the septimal minor semitone, 21/20, and hence equating 5/3 with 7/4, and 10/7 with 3/2.

Temperaments discussed elsewhere are:

Considered below are fluorine and sodium.

Fluorine

For the 5-limit version, see Miscellaneous 5-limit temperaments #Avila.

Subgroup: 2.3.5.7

Comma list: 21/20, 243/224

Mapping: [⟨1 0 -7 -5], ⟨0 1 6 5]]

mapping generators: ~2, ~3

Optimal tunings:

  • WE: ~2 = 1211.420 ¢, ~3/2 = 669.369 ¢
error map: ⟨+11.420 -21.165 +18.481 -21.980]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 665.210 ¢
error map: ⟨0.000 -36.745 +4.945 -42.777]

Optimal ET sequence: 2c, 7c, 9, 20bdd, 29bdd

Badness (Sintel): 1.41

Sodium

Subgroup: 2.3.5.7

Comma list: 21/20, 54/49

Mapping: [⟨1 1 1 2], ⟨0 2 5 3]]

mapping generators: ~2, ~7/6

Optimal tunings:

  • WE: ~2 = 1207.624 ¢, ~7/6 = 322.216 ¢
error map: ⟨+7.624 -49.898 +32.393 +13.072]
  • CWE: ~2 = 1200.000 ¢, ~7/6 = 322.210 ¢
error map: ⟨0.000 -57.535 +24.737 -2.196]

Optimal ET sequence: 4, 11

Badness (Sintel): 1.41

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