Xenharmonic Wiki

Undim family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings
Naming of unlit and twilight
 
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Line 19: Line 19:
* [[CWE]]: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.6252{{c}}
* [[CWE]]: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.6252{{c}}
: error map: {{val| 0.000 +0.670 +0.560 }}
: error map: {{val| 0.000 +0.670 +0.560 }}
<!-- * [[CTE]]: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.6754{{c}}
: [[error map]]: {{val| 0.0000 +0.7204 +0.3092 }}
* [[POTE]]: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.6054{{c}}
: error map: {{val| 0.0000 +0.6504 +0.6591 }} -->


{{Optimal ET sequence|legend=1| 12, …, 104, 116, 128, 140, 152, 620, 772, 924c, 1076bc, 1228bc }}
{{Optimal ET sequence|legend=1| 12, …, 104, 116, 128, 140, 152, 620, 772, 924c, 1076bc, 1228bc }}
Line 47: Line 43:
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7528{{c}}
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7528{{c}}
: error map: {{val| 0.000 +0.798 -0.078 +0.894 }}
: error map: {{val| 0.000 +0.798 -0.078 +0.894 }}
<!-- * [[CTE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7948{{c}}
: [[error map]]: {{val| 0.0000 +0.8398 -0.2879 +0.4308 }}
* [[POTE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7362{{c}}
: error map: {{val| 0.0000 +0.7812 +0.0051 +1.0754 }} -->


{{Optimal ET sequence|legend=1| 12, …, 128, 140, 152, 292 }}
{{Optimal ET sequence|legend=1| 12, …, 128, 140, 152, 292 }}
Line 66: Line 58:
* WE: ~25/21 = 299.9389{{c}}, ~3/2 = 702.5455{{c}}
* WE: ~25/21 = 299.9389{{c}}, ~3/2 = 702.5455{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7038{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7038{{c}}
<!-- * CTE: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7433{{c}}
* POTE: ~25/21 = 300.0000{{c}}, ~3/2 = 702.6886{{c}} -->


{{Optimal ET sequence|legend=0| 12, 128e, 140, 152, 292, 444d, 596d }}
{{Optimal ET sequence|legend=0| 12, 128e, 140, 152, 292, 444d, 596d }}
Line 83: Line 73:
* WE: ~25/21 = 299.9476{{c}}, ~3/2 = 702.6135{{c}}
* WE: ~25/21 = 299.9476{{c}}, ~3/2 = 702.6135{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7480{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7480{{c}}
<!-- * CTE: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7792{{c}}
* POTE: ~25/21 = 300.0000{{c}}, ~3/2 = 702.7363{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 128ef, 140, 152f, 292 }}
{{Optimal ET sequence|legend=0| 12f, 128ef, 140, 152f, 292 }}
Line 91: Line 79:


== Unlit ==
== Unlit ==
Unlit tempers out 4375/4374, the [[ragisma]], and may be described as {{nowrap| 152 & 164 }}. This temperament is more faithful to the 5-limit optimal tuning, but comes with the cost of a much higher complexity.  
Unlit tempers out 4375/4374, the [[ragisma]], and may be described as {{nowrap| 152 & 164 }}. This temperament is more faithful to the 5-limit optimal tuning, but comes with the cost of a much higher complexity. It was named by [[Flora Canou]] in 2021 for it is some sort of opposite of [[#Septimal undim|septimal undim]].  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 104: Line 92:
* [[CWE]]: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5716{{c}}
* [[CWE]]: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5716{{c}}
: error map: {{val| 0.000 +0.617 +0.828 +0.607 }}
: error map: {{val| 0.000 +0.617 +0.828 +0.607 }}
<!-- * [[CTE]]: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5556{{c}}
: [[error map]]: {{val| 0.0000 +0.6006 +0.9081 +0.1761 }}
* [[POTE]]: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5764{{c}}
: error map: {{val| 0.0000 +0.6214 +0.8043 +0.7369 }} -->


{{Optimal ET sequence|legend=1| 152, 316, 468, 620, 1088bcd, 1708bccdd }}
{{Optimal ET sequence|legend=1| 152, 316, 468, 620, 1088bcd, 1708bccdd }}
Line 123: Line 107:
* WE: ~1215/1024 = 299.9426{{c}}, ~3/2 = 702.4482{{c}}
* WE: ~1215/1024 = 299.9426{{c}}, ~3/2 = 702.4482{{c}}
* CWE: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5772{{c}}
* CWE: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5772{{c}}
<!-- * CTE: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5582{{c}}
* POTE: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5826{{c}} -->


{{Optimal ET sequence|legend=0| 152, 468, 620 }}
{{Optimal ET sequence|legend=0| 152, 468, 620 }}
Line 140: Line 122:
* WE: ~1215/1024 = 299.9452{{c}}, ~3/2 = 702.4459{{c}}
* WE: ~1215/1024 = 299.9452{{c}}, ~3/2 = 702.4459{{c}}
* CWE: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5703{{c}}
* CWE: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5703{{c}}
<!-- * CTE: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5562{{c}}
* POTE: ~1215/1024 = 300.0000{{c}}, ~3/2 = 702.5741{{c}} -->


{{Optimal ET sequence|legend=0| 152f, 316, 468, 620f, 1088bcdf }}
{{Optimal ET sequence|legend=0| 152f, 316, 468, 620f, 1088bcdf }}
Line 148: Line 128:


== Twilight ==
== Twilight ==
Twilight tempers out 6144/6125, the [[porwell comma]], and may be described as {{nowrap| 152 & 176 }}. It splits the period of undim into 1/8 of an octave, and has a [[ploidacot]] of octaploid monocot.  
Twilight tempers out 6144/6125, the [[porwell comma]], and may be described as {{nowrap| 152 & 176 }}. It splits the period of undim into 1/8 of an octave, and has a [[ploidacot]] of octaploid monocot. It was named by [[Flora Canou]] in 2021 for it splits the period in halves to reconcile the different mappings of [[#Septimal undim|septimal undim]] and [[#Unlit|unlit]].  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 162: Line 142:
* [[CWE]]: ~7168/6561 = 150.0000{{c}}, ~3/2 = 702.5023{{c}}
* [[CWE]]: ~7168/6561 = 150.0000{{c}}, ~3/2 = 702.5023{{c}}
: error map: {{val| 0.000 +0.547 +1.175 +1.192 }}
: error map: {{val| 0.000 +0.547 +1.175 +1.192 }}
<!-- * [[CTE]]: ~7168/6561 = 150.0000{{c}}, ~3/2 = 702.4765{{c}}
: [[error map]]: {{val| 0.0000 +0.5215 +1.3036 +0.9865 }}
* [[POTE]]: ~7168/6561 = 150.0000{{c}}, ~3/2 = 702.5090{{c}}
: error map: {{val| 0.0000 +0.5540 +1.1415 +1.2457 }} -->


{{Optimal ET sequence|legend=1| 152, 328, 480, 1592bccddd }}
{{Optimal ET sequence|legend=1| 152, 328, 480, 1592bccddd }}
Line 181: Line 157:
* WE: ~12/11 = 149.9593{{c}}, ~3/2 = 702.3182{{c}}
* WE: ~12/11 = 149.9593{{c}}, ~3/2 = 702.3182{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 702.5022{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 702.5022{{c}}
<!-- * CTE: ~12/11 = 150.0000{{c}}, ~3/2 = 702.4692{{c}}
* POTE: ~12/11 = 150.0000{{c}}, ~3/2 = 702.5090{{c}} -->


{{Optimal ET sequence|legend=0| 152, 328, 480, 1112bccddee, 1592bccdddeee }}
{{Optimal ET sequence|legend=0| 152, 328, 480, 1112bccddee, 1592bccdddeee }}
Line 198: Line 172:
* WE: ~12/11 = 149.9582{{c}}, ~3/2 = 702.2815{{c}}
* WE: ~12/11 = 149.9582{{c}}, ~3/2 = 702.2815{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 702.4670{{c}}
* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 702.4670{{c}}
<!-- * CTE: ~12/11 = 150.0000{{c}}, ~3/2 = 702.4168{{c}}
* POTE: ~12/11 = 150.0000{{c}}, ~3/2 = 702.4773{{c}} -->


{{Optimal ET sequence|legend=0| 152f, 328, 480f, 808cdeff }}
{{Optimal ET sequence|legend=0| 152f, 328, 480f, 808cdeff }}
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