7th-octave temperaments: Difference between revisions

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7th octave temperament ~~occurs through~~ temperament merging ~~any two~~ edos whose greatest common divisor is 7. A comma that frequently appears in 7th-octave temps is [[akjaysma]], which sets 105/64 to be equal to 5\7.

A 7th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 7. The most notable 7th-octave family is the [[whitewood family]] – tempering out [[2187/2048]] and associating 4\7 to [[3/2]].

A comma that frequently appears in 7th-octave temps is [[akjaysma]], which sets [[105/64]] to be equal to 5\7.

Temperaments discussed elsewhere include:

* ''[[Septant]]'' → [[Schismatic family #Septant|Schismatic family]]

* ''[[Brahmagupta]]'' → [[Ragismic microtemperaments #Brahmagupta|Ragismic microtemperaments]]

* ''[[Absurdity]]'' → [[Porwell temperaments #Absurdity|Porwell temperaments]]

* ''Septant →'' [[Schismatic family#Septant|Schismatic family]]

== Nitrogen ==

* ''Brahmagupta →'' [[Ragismic microtemperaments#Brahmagupta|~~Ragismic microtemperaments]]~~

Nitrogen may be described as the {{nowrap| 140 & 1407 }} temperament in the 7-limit. It was named after the 7th element for having a 7th-octave period and also because 140 and 1407 only contain numbers 7 and 14, atomic number and atomic weight of nitrogen respectively. On top of this connection to the number 7, it also reaches the 7th harmonic 7 generators down.

* ''Absurdity'' ''→'' [[Syntonic-~~chromatic equivalence continuum#Absurdity|Syntonic chromatic equivalence continuum]]~~

~~==Nitrogen==~~

[[Subgroup]]: 2.3.5.7

Described as 140 & 1407 temperament in the 7-limit, named after the 7th element for being period-7 and also because 140 and 1407 only contain numbers 7 and 14, atomic number and atomic weight of nitrogen respectively. ~~On top of this connection to the number~~ 7~~, it also reaches 7th harmonic 7 generators down.~~

~~Subgroup~~: ~~2.3.5.~~7

[[Comma list]]: 3955078125/3954653486, {{monzo| 47 -7 -7 -7 }}

~~Comma list~~: ~~3955078125~~/~~3954653486~~, ~~140737488355328~~/~~140710042265625~~

: mapping generators: ~1157625/1048576, ~1029/1024

~~Mapping~~: [{{val|~~7 10 17 20~~}}, {{val|0 ~~22 -15 -7~~}}]

[[Optimal tuning]]s:

* [[WE]]: ~1157625/1048576 = 171.4278{{c}}, ~1029/1024 = 8.5308{{c}}

: [[error map]]: {{val| -0.005 +0.001 -0.002 +0.015 }}

* [[CWE]]: ~1157625/1048576 = 171.4286{{c}}, ~1029/1024 = 8.5308{{c}}

: error map: {{val| 0.000 +0.008 +0.010 +0.030 }}

~~Mapping generators: ~1157625/1048576~~, ~~~1029/1024~~

{{Optimal ET sequence|legend=1| 140, 847, 987, 1127, 1267, 1407, 1547, 2954 }}

~~Optimal tuning~~ (~~CTE~~): ~~~1157625/1048576 =~~ 1~~\7, ~1029/1024 = 8~~.~~531~~

[[Badness]] (Sintel): 1.50

{{~~Optimal ET sequence|legend=1|140, 1407, 1547~~}}~~, ...~~

[[Category:7edo]]

~~[[Category:Rank 2]]~~

~~[[Category:Temperament collections]]~~

@@ Line 1: / Line 1: @@
-th octave temperament occurs through temperament merging any two edos whose greatest common divisor is 7. A comma that frequently appears in 7th-octave temps is [[akjaysma]], which sets 105/64 to be equal to 5\7.
+{{Technical data page}}
+{{Infobox fractional-octave|7}}
+A 7th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 7. The most notable 7th-octave family is the [[whitewood family]] – tempering out [[2187/2048]] and associating 4\7 to [[3/2]].
+A comma that frequently appears in 7th-octave temps is [[akjaysma]], which sets [[105/64]] to be equal to 5\7.
 Temperaments discussed elsewhere include:
+* ''[[Septant]]'' → [[Schismatic family #Septant|Schismatic family]]
+* ''[[Brahmagupta]]'' → [[Ragismic microtemperaments #Brahmagupta|Ragismic microtemperaments]]
+* ''[[Absurdity]]'' → [[Porwell temperaments #Absurdity|Porwell temperaments]]
-* ''Septant →'' [[Schismatic family#Septant|Schismatic family]]
+== Nitrogen ==
-* ''Brahmagupta →'' [[Ragismic microtemperaments#Brahmagupta|Ragismic microtemperaments]]
+Nitrogen may be described as the {{nowrap| 140 & 1407 }} temperament in the 7-limit. It was named after the 7th element for having a 7th-octave period and also because 140 and 1407 only contain numbers 7 and 14, atomic number and atomic weight of nitrogen respectively. On top of this connection to the number 7, it also reaches the 7th harmonic 7 generators down.
-* ''Absurdity'' ''→'' [[Syntonic-chromatic equivalence continuum#Absurdity|Syntonic chromatic equivalence continuum]]
-==Nitrogen==
+[[Subgroup]]: 2.3.5.7
-Described as 140 & 1407 temperament in the 7-limit, named after the 7th element for being period-7 and also because 140 and 1407 only contain numbers 7 and 14, atomic number and atomic weight of nitrogen respectively. On top of this connection to the number 7, it also reaches 7th harmonic 7 generators down.
-Subgroup: 2.3.5.7
+[[Comma list]]: 3955078125/3954653486, {{monzo| 47 -7 -7 -7 }}
-Comma list: 3955078125/3954653486, 140737488355328/140710042265625
+{{Mapping|legend=1| 7 10 17 20 | 0 22 -15 -7 }}
+: mapping generators: ~1157625/1048576, ~1029/1024
-Mapping: [{{val|7 10 17 20}}, {{val|0 22 -15 -7}}]
+[[Optimal tuning]]s:
+* [[WE]]: ~1157625/1048576 = 171.4278{{c}}, ~1029/1024 = 8.5308{{c}}
+: [[error map]]: {{val| -0.005 +0.001 -0.002 +0.015 }}
+* [[CWE]]: ~1157625/1048576 = 171.4286{{c}}, ~1029/1024 = 8.5308{{c}}
+: error map: {{val| 0.000 +0.008 +0.010 +0.030 }}
-Mapping generators: ~1157625/1048576, ~1029/1024
+{{Optimal ET sequence|legend=1| 140, 847, 987, 1127, 1267, 1407, 1547, 2954 }}
-Optimal tuning (CTE): ~1157625/1048576 = 1\7, ~1029/1024 = 8.531
+[[Badness]] (Sintel): 1.50
-{{Optimal ET sequence|legend=1|140, 1407, 1547}}, ...
+{{Navbox fractional-octave}}
 [[Category:7edo]]
-[[Category:Rank 2]]
-[[Category:Temperament collections]]