7th-octave temperaments: Difference between revisions

(9 intermediate revisions by 6 users not shown)

Line 1:

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 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]]

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

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

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

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

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

== Jamesbond ==

This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its [[wedgie]] starts with {{multival| 0 0 7 … }}.

This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its "[[wedgie]]" (a kind of mathematical object representing the temperament) starts with {{multival| 0 0 7 … }} (in fact, it is {{Multival|legend=| 0 0 7 0 11 16 }})

[[Subgroup]]: 2.3.5.7

Line 17:

Line 18:

~~{{Multival|legend=1| 0 0 7 0 11 16 }}~~

[[Optimal tuning]] ([[POTE]]): ~10/9 = 1\7, ~7/4 = 941.861

Line 52:

Line 51:

Badness: 0.023003

==== ~~Septimal~~ ====

==== Austinpowers ====

Subgroup: 2.3.5.7.11.13

Line 73:

Line 72:

[[Mapping]]: [{{val| 7 0 0 47 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -1 }}]

Mapping generators: ~1157625/1048576, ~3, ~5

: Mapping generators: ~1157625/1048576, ~3, ~5

[[POTE generator]]s: ~3/2 = 701.965, ~5/4 = 386.330

Line 80:

Line 79:

=== 11-limit ===

Subgroup: 2.3.5.7.11

Line 87:

Line 85:

Mapping: [{{val| 7 0 0 47 -168 }}, {{val| 0 1 0 -1 10 }}, {{val| 0 0 1 -1 5 }}]

Mapping generators: ~29160/26411, ~3, ~5

: Mapping generators: ~29160/26411, ~3, ~5

POTE generators: ~3/2 = 701.968, ~5/4 = 386.332

Line 94:

Line 92:

== Nitrogen ==

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

Line 117:

Line 115:

: ~~mapping~~ generators: ~32/29, ~3

: Mapping generators: ~32/29, ~3

[[Optimal tuning]] ([[CTE]]): ~32/29 = 1\7, ~3/2 = 701.955 (~24576/24389 = 16.239)

[[Support]]ing [[ET]]s: {{EDOs|7, 77, 70, 147, 224, 84, 63, 301, 217, 371, 56, 161, 91, 378}}

== Profanity ==

Profanity identifies [[11/9]] with 2\7.

[[Subgroup]]: 2.3.11

[[Comma list]]: 19487171/19131876

: Mapping generators: ~1458/1331, ~3

[[Support]]ing [[ET]]s: {{EDOs|7, 49, 56, 63, 70, 77, 133}}

[[Category:7edo]]

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

@@ Line 1: / Line 1: @@
-{{Fractional-octave navigation|7}}
+{{Technical data page}}
-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]].
+{{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]]
+* ''Septant →'' [[Schismatic family#Septant|Schismatic family]]
-* ''Brahmagupta →'' [[Ragismic microtemperaments #Brahmagupta|Ragismic microtemperaments]]
+* ''Brahmagupta →'' [[Ragismic microtemperaments#Brahmagupta|Ragismic microtemperaments]]
-* ''Absurdity'' ''→'' [[Syntonic-chromatic equivalence continuum #Absurdity|Syntonic chromatic equivalence continuum]]
+* ''Absurdity'' ''→'' [[Syntonic&ndash;chromatic equivalence continuum#Absurdity|Syntonic&ndash;chromatic equivalence continuum]]
 == Jamesbond ==
-This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its [[wedgie]] starts with {{multival| 0 0 7 … }}.
+This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its "[[wedgie]]" (a kind of mathematical object representing the temperament) starts with {{multival| 0 0 7 … }} (in fact, it is {{Multival|legend=| 0 0 7 0 11 16 }})
 [[Subgroup]]: 2.3.5.7
@@ Line 17: / Line 18: @@
 {{Mapping|legend=1| 7 11 16 0 | 0 0 0 1 }}
-{{Multival|legend=1| 0 0 7 0 11 16 }}
 [[Optimal tuning]] ([[POTE]]): ~10/9 = 1\7, ~7/4 = 941.861
@@ Line 52: / Line 51: @@
 Badness: 0.023003
-==== Septimal ====
+==== Austinpowers ====
 Subgroup: 2.3.5.7.11.13
@@ Line 73: / Line 72: @@
 [[Mapping]]: [{{val| 7 0 0 47 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -1 }}]
-Mapping generators: ~1157625/1048576, ~3, ~5
+: Mapping generators: ~1157625/1048576, ~3, ~5
 [[POTE generator]]s: ~3/2 = 701.965, ~5/4 = 386.330
@@ Line 80: / Line 79: @@
 === 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 87: / Line 85: @@
 Mapping: [{{val| 7 0 0 47 -168 }}, {{val| 0 1 0 -1 10 }}, {{val| 0 0 1 -1 5 }}]
-Mapping generators: ~29160/26411, ~3, ~5
+: Mapping generators: ~29160/26411, ~3, ~5
 POTE generators: ~3/2 = 701.968, ~5/4 = 386.332
@@ Line 94: / Line 92: @@
 == Nitrogen ==
-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.
+Described as 140 &amp; 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
@@ Line 117: / Line 115: @@
 {{mapping|legend=1| 7 0 34 | 0 1 0 }}
-: mapping generators: ~32/29, ~3
+: Mapping generators: ~32/29, ~3
 [[Optimal tuning]] ([[CTE]]): ~32/29 = 1\7, ~3/2 = 701.955 (~24576/24389 = 16.239)
 [[Support]]ing [[ET]]s: {{EDOs|7, 77, 70, 147, 224, 84, 63, 301, 217, 371, 56, 161, 91, 378}}
+== Profanity ==
+Profanity identifies [[11/9]] with 2\7.
+[[Subgroup]]: 2.3.11
+[[Comma list]]: 19487171/19131876
+{{mapping|legend=1| 7 0 2 | 0 1 2 }}
+: Mapping generators: ~1458/1331, ~3
+[[Support]]ing [[ET]]s: {{EDOs|7, 49, 56, 63, 70, 77, 133}}
+{{Navbox fractional-octave}}
 [[Category:7edo]]
-[[Category:Temperament collections]]