Septisemi temperaments: Difference between revisions

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These are 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.
{{Technical data page}}
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:  
Temperaments discussed elsewhere are:  
* [[Mother]], {16/15, 21/20} → [[Father family #Mother]]
* ''[[Mother]]'' (+16/15) → [[Father family #Mother|Father family]]
* [[Flat]], {21/20, 25/24} → [[Dicot family #Flat]]
* ''[[Sharptone]]'' (+28/27) → [[Meantone family #Sharptone|Meantone family]]
* [[Beep]], {21/20, 27/25} → [[Bug family #Beep]]
* ''[[Pelogic]]'' (+135/128) → [[Mavila family #Pelogic|Mavila family]]
* [[Sharptone]], {21/20, 28/27} → [[Meantone family #Sharptone]]
* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]]
* [[Pelogic]], {21/20, 135/128} → [[Pelogic family #Pelogic]]
* [[Beep]] (+27/25) → [[Bug family #Beep|Bug family]]
* [[Gidorah]], {21/20, 144/125} → [[Gamelismic clan #Gidorah]]
* ''[[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]]


Considered below are fluorine, sodium and oxygen.  
Considered below are fluorine and sodium.  


== Fluorine ==
== Fluorine ==
=== 5-limit (avila) ===
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Avila]].''
Subgroup: 2.3.5


[[Comma list]]: 729/640
[[Subgroup]]: 2.3.5.7
 
[[Mapping]]: [{{val| 1 0 -7 }}, {{val| 0 1 6 }}]
 
[[POTE generator]]: ~3/2 = 661.593
 
{{Val list|legend=1| 2c, 7c, 9, 20b, 29b }}
 
[[Badness]]: 0.181941
 
=== 7-limit ===
Subgroup: 2.3.5.7


[[Comma list]]: 21/20, 243/224
[[Comma list]]: 21/20, 243/224


[[Mapping]]: [{{val| 1 0 -7 -5 }}, {{val| 0 1 6 5 }}]
{{Mapping|legend=1| 1 0 -7 -5 | 0 1 6 5 }}
 
: mapping generators: ~2, ~3
{{Multival|legend=1| 1 6 5 7 5 -5 }}


[[POTE generator]]: ~3/2 = 663.059
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1211.420{{c}}, ~3/2 = 669.369{{c}}
: [[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 }}


{{Val list|legend=1| 9, 20bdd, 29bdd }}
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20bdd, 29bdd }}


[[Badness]]: 0.055623
[[Badness]] (Sintel): 1.41


== Sodium ==
== Sodium ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 21/20, 54/49
[[Comma list]]: 21/20, 54/49


[[Mapping]]: [{{val| 1 1 1 2 }}, {{val| 0 2 5 3 }}]
{{Mapping|legend=1| 1 1 1 2 | 0 2 5 3 }}
 
: mapping generators: ~2, ~7/6
{{Multival|legend=1| 2 5 3 3 -1 -7 }}
 
[[POTE generator]]: ~7/6 = 320.182
 
{{Val list|legend=1| 4, 11, 15b }}
 
[[Badness]]: 0.055814
 
== Oxygen ==
{{see also| Porcupine family }}
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 21/20, 175/162
 
[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -3 -5 -2 }}]
 
{{Multival|legend=1| 3 5 2 1 -5 -9 }}


[[POTE generator]]: ~7/6 = 169.112
[[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 }}


{{Val list|legend=1| 7d, 8 }}
{{Optimal ET sequence|legend=1| 4, 11 }}


[[Badness]]: 0.059866
[[Badness]] (Sintel): 1.41


[[Category:Regular temperament theory]]
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Septisemi temperaments| ]] <!-- main article -->
[[Category:Septisemi temperaments| ]] <!-- main article -->
[[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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