17th-octave temperaments: Difference between revisions

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== Chlorine ==

~~The name~~ of ~~chlorine temperament comes from chlorine~~, ~~the 17th element, and has no relation to~~ the [[~~chlorisma~~]].

Chlorine has a period of 1/17 octave. It tempers out {{monzo| -52 -17 34 }}, the [[septendecima]], by which 17 classical chromatic semitones ((25/24)<sup>17</sup>) exceed an octave. This temperament can be described as 289 & 323 temperament, which tempers out {{monzo| -49 4 22 -3 }} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator.

~~Chlorine~~ temperament has ~~a period of 1/17 octave. It tempers out~~ the [[~~septendecima~~]], {{monzo| -52 -17 34 }}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289 & 323 temperament, which tempers out {{monzo| -49 4 22 -3 }} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator.

The name of this temperament comes from chlorine, the 17th element, and has no relation to the [[chlorisma]].

[[Subgroup]]: 2.3.5

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: mapping generators: ~25/24, ~{{monzo| 26 9 -17 }}

[[Optimal tuning]]s:

* [[~~CTE~~]]: ~25/24 = 70.~~588~~{{c}} ~~(1\17)~~, ~{{monzo| 26 9 -17 }} = 950.~~982~~{{c}}

* [[WE]]: ~25/24 = 70.5887{{c}}, ~{{monzo| 26 9 -17 }} = 950.9807{{c}}

* [[CWE]]: ~25/24 = 70.~~588~~{{c}} ~~(1\17)~~, ~{{monzo| 26 9 -17 }} = 950.~~978~~{{c}}

: [[error map]]: {{val| +0.008 +0.006 -0.027 }}

* [[CWE]]: ~25/24 = 70.5882{{c}}, ~{{monzo| 26 9 -17 }} = 950.9776{{c}}

: error map: {{val| 0.000 -0.000 -0.042 }}

{{Optimal ET sequence|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~25/24 = 70.~~588~~{{c}} ~~(1\17)~~, ~{{monzo| 24 -5 -9 2 }} = 950.~~998~~{{c}}

* [[WE]]: ~25/24 = 70.5880{{c}}, ~{{monzo| 24 -5 -9 2 }} = 950.9962{{c}}

* [[CWE]]: ~25/24 = 70.~~588~~{{c}} ~~(1\17)~~, ~{{monzo| 24 -5 -9 2 }} = 950.~~999~~{{c}}

: [[error map]]: {{val| -0.004 +0.037 -0.030 -0.019 }}

* [[CWE]]: ~25/24 = 70.5882{{c}}, ~{{monzo| 24 -5 -9 2 }} = 950.9990{{c}}

: error map: {{val| 0.000 +0.043 -0.021 -0.013 }}

{{Optimal ET sequence|legend=1| 289, 323, 612, 935, 1547, 3706, 5253 }}

[[Badness]] (Sintel): 1.05

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Optimal tunings:

* ~~CTE~~: ~25/24 = 70.~~588~~{{c}} ~~(1\17)~~, ~693/400 = ~~950~~.~~978~~{{c}}

* WE: ~25/24 = 70.5905{{c}}, ~693/400 = 951.0054{{c}}

* CWE: ~25/24 = 70.~~588~~{{c}} ~~(1\17)~~, ~693/400 = 950.~~975~~{{c}}

* CWE: ~25/24 = 70.5882{{c}}, ~693/400 = 950.9754{{c}}

{{Optimal ET sequence|legend=0| 289, 323, 612, 3349de, 3961de, …, 5797ddee }}

Badness (Sintel): 2.11

@@ Line 73: / Line 73: @@
 == Chlorine ==
-The name of chlorine temperament comes from chlorine, the 17th element, and has no relation to the [[chlorisma]].
+Chlorine has a period of 1/17 octave. It tempers out {{monzo| -52 -17 34 }}, the [[septendecima]], by which 17 classical chromatic semitones ((25/24)<sup>17</sup>) exceed an octave. This temperament can be described as 289 & 323 temperament, which tempers out {{monzo| -49 4 22 -3 }} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator.
-Chlorine temperament has a period of 1/17 octave. It tempers out the [[septendecima]], {{monzo| -52 -17 34 }}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289 &amp; 323 temperament, which tempers out {{monzo| -49 4 22 -3 }} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator.
+The name of this temperament comes from chlorine, the 17th element, and has no relation to the [[chlorisma]].
 [[Subgroup]]: 2.3.5
@@ Line 82: / Line 82: @@
 {{Mapping|legend=1| 17 0 26 | 0 2 1 }}
 : mapping generators: ~25/24, ~{{monzo| 26 9 -17 }}
 [[Optimal tuning]]s:
-* [[CTE]]: ~25/24 = 70.588{{c}} (1\17), ~{{monzo| 26 9 -17 }} = 950.982{{c}}
+* [[WE]]: ~25/24 = 70.5887{{c}}, ~{{monzo| 26 9 -17 }} = 950.9807{{c}}
-* [[CWE]]: ~25/24 = 70.588{{c}} (1\17), ~{{monzo| 26 9 -17 }} = 950.978{{c}}
+: [[error map]]: {{val| +0.008 +0.006 -0.027 }}
+* [[CWE]]: ~25/24 = 70.5882{{c}}, ~{{monzo| 26 9 -17 }} = 950.9776{{c}}
+: error map: {{val| 0.000 -0.000 -0.042 }}
 {{Optimal ET sequence|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}
@@ Line 101: / Line 102: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~25/24 = 70.588{{c}} (1\17), ~{{monzo| 24 -5 -9 2 }} = 950.998{{c}}
+* [[WE]]: ~25/24 = 70.5880{{c}}, ~{{monzo| 24 -5 -9 2 }} = 950.9962{{c}}
-* [[CWE]]: ~25/24 = 70.588{{c}} (1\17), ~{{monzo| 24 -5 -9 2 }} = 950.999{{c}}
+: [[error map]]: {{val| -0.004 +0.037 -0.030 -0.019 }}
+* [[CWE]]: ~25/24 = 70.5882{{c}}, ~{{monzo| 24 -5 -9 2 }} = 950.9990{{c}}
+: error map: {{val| 0.000 +0.043 -0.021 -0.013 }}
-{{Optimal ET sequence|legend=1| 289, 323, 612, 935, 1547 }}
+{{Optimal ET sequence|legend=1| 289, 323, 612, 935, 1547, 3706, 5253 }}
 [[Badness]] (Sintel): 1.05
@@ Line 116: / Line 119: @@
 Optimal tunings:
-* CTE: ~25/24 = 70.588{{c}} (1\17), ~693/400 = 950.978{{c}}
+* WE: ~25/24 = 70.5905{{c}}, ~693/400 = 951.0054{{c}}
-* CWE: ~25/24 = 70.588{{c}} (1\17), ~693/400 = 950.975{{c}}
+* CWE: ~25/24 = 70.5882{{c}}, ~693/400 = 950.9754{{c}}
-{{Optimal ET sequence|legend=0| 289, 323, 612 }}
+{{Optimal ET sequence|legend=0| 289, 323, 612, 3349de, 3961de, …, 5797ddee }}
 Badness (Sintel): 2.11