Septisemi temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
+CTE tunings; +error maps; spell out 1\1 in decimal; note the badness metric being used
 
(10 intermediate revisions by 5 users not shown)
Line 1: Line 1:
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.
{{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:  
Line 6: Line 7:
* ''[[Pelogic]]'' (+135/128) → [[Mavila family #Pelogic|Mavila family]]
* ''[[Pelogic]]'' (+135/128) → [[Mavila family #Pelogic|Mavila family]]
* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]]
* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]]
* ''[[Beep]]'' (+27/25) → [[Bug family #Beep|Bug family]]
* [[Beep]] (+27/25) → [[Bug family #Beep|Bug family]]
* ''[[Deflated]]'' (+21/20) → [[Augmented family #Deflated|Augmented family]]
* ''[[Deflated]]'' (+128/125) → [[Augmented family #Deflated|Augmented family]]
* ''[[Gidorah]]'' (+144/125) → [[Gamelismic clan #Gidorah|Gamelismic clan]]
* ''[[Gidorah]]'' (+144/125) → [[Gamelismic clan #Gidorah|Gamelismic clan]]
* ''[[Oxygen]]'' (+175/162) → [[Porcupine family #Oxygen|Porcupine family]]
* ''[[Oxygen]]'' (+175/162) → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]]


Considered below are fluorine and sodium.  
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
{{Mapping|legend=1| 1 0 -7 | 0 1 6 }}
: mapping generators: ~2, ~3
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 666.499
: [[error map]]: {{val| 0.000 -35.456 +12.682 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 661.593
: error map: {{val| 0.000 -40.362 -16.754 }}
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }}
[[Badness]] (Smith): 0.181941
=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Line 39: Line 22:


{{Mapping|legend=1| 1 0 -7 -5 | 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 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 668.748
* [[WE]]: ~2 = 1211.420{{c}}, ~3/2 = 669.369{{c}}
: [[error map]]: {{val| 0.000 -33.207 +26.177 -25.084 }}
: [[error map]]: {{val| +11.420 -21.165 +18.481 -21.980 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 663.059
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 665.210{{c}}
: error map: {{val| 0.000 -38.896 -7.960 -53.531 }}
: error map: {{val| 0.000 -36.745 +4.945 -42.777 }}


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


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


== Sodium ==
== Sodium ==
Line 58: Line 40:


{{Mapping|legend=1| 1 1 1 2 | 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 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/6 = 325.425
* [[WE]]: ~2 = 1207.624{{c}}, ~7/6 = 322.216{{c}}
: [[error map]]: {{val| 0.000 -51.104 +40.813 +7.450 }}
: [[error map]]: {{val| +7.624 -49.898 +32.393 +13.072 }}
* [[POTE]]: ~2 = 1200.000, ~7/6 = 320.182
* [[CWE]]: ~2 = 1200.000{{c}}, ~7/6 = 322.210{{c}}
: error map: {{val| 0.000 -61.591 +14.597 -8.280 }}
: error map: {{val| 0.000 -57.535 +24.737 -2.196 }}


{{Optimal ET sequence|legend=1| 4, 11, 15b }}
{{Optimal ET sequence|legend=1| 4, 11 }}


[[Badness]] (Smith): 0.055814
[[Badness]] (Sintel): 1.41


[[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

Retrieved from "https://en.xen.wiki/index.php?title=Septisemi_temperaments&oldid=217980"