Metric microtemperaments: Difference between revisions

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These are [[Rank-2 temperament|rank-2]] [[temperament]]s that [[Tempering out|temper out]] the [[meter ~~comma~~]], 703125/702464 = {{monzo| -11 2 7 -3 }}.

These are [[Rank-2 temperament|rank-2]] [[temperament]]s that [[Tempering out|temper out]] the [[meter]], 703125/702464 = {{monzo| -11 2 7 -3 }}.

Temperaments discussed elsewhere include:

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~~{{Multival|legend=1| 29 -49 -95 -145 -232 -82 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8505/8192 = 65.5883

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~~{{Multival|legend=1| 40 10 50 -77 -33 88 }}~~

[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~5/4 = 385.495

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~~{{Multival|legend=1| 26 -25 -41 -100 -138 -25 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 111.453

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== Geb ==

~~The geb temperament (171 & 506, named after the earth god of ancient Egyptian religion) tempers out {{monzo| -31 43 -16 }} (quadla-quadquadgu) in~~ the 5-limit~~; the meter and the euzenius comma, 78125000/78121827 as well as skeetsma (14348907/14336000~~, ~~lalarutrigu) in the 7-limit.~~ [[~~Breedsmic temperaments~~ #~~Osiris|Osiris temperament]]~~ (~~171&670, named after the eldest son of Geb) tempers out the same~~ 5-limit ~~comma as the geb, but with the [[2401/2400|breedsma~~]] ~~rather than the meter tempered out~~.

: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Geb (5-limit)]].''

[[~~Subgroup~~]]~~: 2~~.3.5

The geb temperament (171 & 506, named after the earth god of ancient Egyptian religion) tempers out the meter and the [[euzenius comma]] (78125000/78121827) as well as [[skeetsma]] (14348907/14336000) in the 7-limit. [[Osiris]] (171 & 670, named after the eldest son of Geb) tempers out the same 5-limit comma as the geb, but with the [[2401/2400|breedsma]] rather than the meter tempered out.

~~[[Comma list]]: {{monzo| -31 43 -16 }}~~

~~{{Mapping|legend=1| 1 -3 -10 | 0 16 43 }}~~

~~[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8000/6561 = 343.868~~

~~{{Optimal ET sequence|legend=1| 7, 143c, 150c, 157, 164, 171, 506, 677, 848 }}~~

~~[[Badness]]: 0.118577~~

~~=== 7-limit ===~~

[[Subgroup]]: 2.3.5.7

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~~{{Multival|legend=1| 16 43 111 31 131 137 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8000/6561 = 343.863

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[[Category:Temperament collections]]

[[Category:Pages with mostly numerical content]]

[[Category:Metric microtemperaments| ]]

[[Category:Metric| ]]

[[Category:Rank 2]]

[[Category:Microtemperaments]]

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-These are [[Rank-2 temperament|rank-2]] [[temperament]]s that [[Tempering out|temper out]] the [[meter comma]], 703125/702464 = {{monzo| -11 2 7 -3 }}.
+{{Technical data page}}
+These are [[Rank-2 temperament|rank-2]] [[temperament]]s that [[Tempering out|temper out]] the [[meter]], 703125/702464 = {{monzo| -11 2 7 -3 }}.
 Temperaments discussed elsewhere include:
@@ Line 22: / Line 23: @@
 {{Mapping|legend=1| 1 0 5 8 | 0 29 -49 -95 }}
-{{Multival|legend=1| 29 -49 -95 -145 -232 -82 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8505/8192 = 65.5883
@@ Line 78: / Line 77: @@
 {{Mapping|legend=1| 10 3 20 12 | 0 4 1 5 }}
-{{Multival|legend=1| 40 10 50 -77 -33 88 }}
 [[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~5/4 = 385.495
@@ Line 134: / Line 131: @@
 {{Mapping|legend=1| 1 4 0 -1 | 0 -26 25 41 }}
-{{Multival|legend=1| 26 -25 -41 -100 -138 -25 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 111.453
@@ Line 183: / Line 178: @@
 == Geb ==
-The geb temperament (171 &amp; 506, named after the earth god of ancient Egyptian religion) tempers out {{monzo| -31 43 -16 }} (quadla-quadquadgu) in the 5-limit; the meter and the euzenius comma, 78125000/78121827 as well as skeetsma (14348907/14336000, lalarutrigu) in the 7-limit. [[Breedsmic temperaments #Osiris|Osiris temperament]] (171&amp;670, named after the eldest son of Geb) tempers out the same 5-limit comma as the geb, but with the [[2401/2400|breedsma]] rather than the meter tempered out.
+: ''For the 5-limit version, see [[Syntonic–chromatic equivalence continuum #Geb (5-limit)]].''
-[[Subgroup]]: 2.3.5
+The geb temperament (171 & 506, named after the earth god of ancient Egyptian religion) tempers out the meter and the [[euzenius comma]] (78125000/78121827) as well as [[skeetsma]] (14348907/14336000) in the 7-limit. [[Osiris]] (171 & 670, named after the eldest son of Geb) tempers out the same 5-limit comma as the geb, but with the [[2401/2400|breedsma]] rather than the meter tempered out.
-[[Comma list]]: {{monzo| -31 43 -16 }}
-{{Mapping|legend=1| 1 -3 -10 | 0 16 43 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8000/6561 = 343.868
-{{Optimal ET sequence|legend=1| 7, 143c, 150c, 157, 164, 171, 506, 677, 848 }}
-[[Badness]]: 0.118577
-=== 7-limit ===
 [[Subgroup]]: 2.3.5.7
@@ Line 203: / Line 187: @@
 {{Mapping|legend=1| 1 -3 -10 -29 | 0 16 43 111 }}
-{{Multival|legend=1| 16 43 111 31 131 137 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8000/6561 = 343.863
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 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Metric microtemperaments| ]] <!-- main article -->
 [[Category:Metric| ]] <!-- key article -->
 [[Category:Rank 2]]
 [[Category:Microtemperaments]]