7th-octave temperaments: Difference between revisions

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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]].

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[[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

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=== 11-limit ===

Subgroup: 2.3.5.7.11

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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

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== 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

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: ~~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)

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+{{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]].
@@ Line 73: / Line 74: @@
 [[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 81: @@
 === 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 87: / Line 87: @@
 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 94: @@
 == 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
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 {{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)