Octagar family: Difference between revisions

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~~Octagar temperament is the 7-limit~~ [[~~Planar_Temperament|~~planar temperament]] tempering out 4000/3969. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7 odd limit minimax tuning has fifths and 7s 2.245 cents sharp, with just major thirds.

The '''octagar family''' of temperaments are [[planar temperament]]s tempering out [[4000/3969]]. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7 odd limit minimax tuning has fifths and 7s 2.245 cents sharp, with just major thirds.

=~~==Vital statistics==~~=

= Octagar =

[[~~Comma|~~Comma]] c = 4000/3969

[[Comma]] c = 4000/3969

7-limit minimax: 3 and 7 1/6c sharp, 5 just

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|0 0 1 0>, |5/6 -2/3 1/2 2/3>]

[[Eigenmonzo~~|Eigenmonzos~~]]: 2, 7/6, 5/4

[[Eigenmonzo]]s: 2, 7/6, 5/4

9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp

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|0 0 1 0>, |5/4 -1 3/4 1/2>]

[[Eigenmonzo~~|Eigenmonzos~~]]: 2, 5/4, 9/7

[[Eigenmonzo]]s: 2, 5/4, 9/7

Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605

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Badness: 0.000216

[[~~Projection_pair|~~Projection pair]]s: 5 3969/800 7 27783/4000 to 2.3.7/5

[[Projection pair]]s: 5 3969/800 7 27783/4000 to 2.3.7/5

===[[Hobbits|Hobbit bases]]===

=== [[Hobbits|Hobbit bases]] ===

{2, 3, 7/5} subgroup

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23: 12800000/12252303, 107163/102400

==Nakika==

== Nakika ==

Commas: 100/99, 245/242

Associated linear temperament: [[~~Tetracot_family~~|octacot]]

Associated linear temperament: [[Tetracot family|octacot]]

Lattice basis: 11/7 0.798 22/21 0.906

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Projection pairs: 5 242/49 7 21296/3087 11 234256/21609 to 2.3.11/7

Scales: [[~~nakika12|~~nakika12]]

Scales: [[nakika12]]

[[Category:Theory]]

[[Category:Temperament family]]

~~[[Category:Planar temperament]]~~

[[Category:Octagar]]

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
-Octagar temperament is the 7-limit [[Planar_Temperament|planar temperament]] tempering out 4000/3969. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7 odd limit minimax tuning has fifths and 7s 2.245 cents sharp, with just major thirds.
+The '''octagar family''' of temperaments are [[planar temperament]]s tempering out [[4000/3969]]. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7 odd limit minimax tuning has fifths and 7s 2.245 cents sharp, with just major thirds.
-===Vital statistics===
+= Octagar =
-[[Comma|Comma]] c = 4000/3969
+[[Comma]] c = 4000/3969
 -limit minimax: 3 and 7 1/6c sharp, 5 just
@@ Line 9: / Line 9: @@
 |0 0 1 0&gt;, |5/6 -2/3 1/2 2/3&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 5/4
+[[Eigenmonzo]]s: 2, 7/6, 5/4
 -limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp
@@ Line 16: / Line 16: @@
 |0 0 1 0&gt;, |5/4 -1 3/4 1/2&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 9/7
+[[Eigenmonzo]]s: 2, 5/4, 9/7
 Lattice basis: 63/50 length 0.8966, 21/20 length 1.0605
@@ Line 28: / Line 28: @@
 Badness: 0.000216
-[[Projection_pair|Projection pair]]s: 5 3969/800 7 27783/4000 to 2.3.7/5
+[[Projection pair]]s: 5 3969/800 7 27783/4000 to 2.3.7/5
-===[[Hobbits|Hobbit bases]]===
+=== [[Hobbits|Hobbit bases]] ===
 {2, 3, 7/5} subgroup
@@ Line 39: / Line 39: @@
 : 12800000/12252303, 107163/102400
-==Nakika==
+== Nakika ==
 Commas: 100/99, 245/242
-Associated linear temperament: [[Tetracot_family|octacot]]
+Associated linear temperament: [[Tetracot family|octacot]]
 Lattice basis: 11/7 0.798 22/21 0.906
@@ Line 58: / Line 58: @@
 Projection pairs: 5 242/49 7 21296/3087 11 234256/21609 to 2.3.11/7
-Scales: [[nakika12|nakika12]]
+Scales: [[nakika12]]
 [[Category:Theory]]
 [[Category:Temperament family]]
-[[Category:Planar temperament]]
 [[Category:Octagar]]
+[[Category:Rank 3]]