Garischismic clan: Difference between revisions

+ devitredecimal extensions for heptacot and garitritonic
- "gary comma" (temp name + comma conventionally refers to the comma tempered out in the temp). Stop semantic inflation (good means good). Fix typos
 
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==== Subgroup extensions ====
==== Subgroup extensions ====
Gary can be naturally extended into the no-5's 11-limit with good accuracy by equating (64/63)<sup>2</sup> with 33/32, at the cost of doubling the complexity.  
Gary can be naturally extended into the no-5's 11-limit with good accuracy by equating (64/63)<sup>2</sup> with 33/32 at the cost of doubling the complexity, acting as a temperament of [[olympic clan #Olympian|olympian]] which accurately represents the entire 2.3.7.11 into the chain of fifths. The major third additionally is extremely close to [[19/15]], and is a natural interpretation in extensions with 5 and 19.  


=== 2.3.7.11 subgroup ===
=== 2.3.7.11 subgroup ===
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Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9631{{c}}, ~3/2 = 702.2077{{c}}
* WE: ~2 = 1199.9631{{c}}, ~3/2 = 702.2077{{c}}
: error map: {{val| -0.037 0.216 -0.139 -0.173 }}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2290{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2290{{c}}
: error map: {{val| -0.000 0.274 -0.032 -0.051 }}


{{Optimal ET sequence|legend=0| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}
{{Optimal ET sequence|legend=0| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}
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=== 2.3.5.7.11.13.19 subgroup ===
=== 2.3.5.7.11.13.19 subgroup ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.19


Comma list: 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625
Comma list: 1216/1215, 1716/1715, 2080/2079, 2376/2375, 9633/9625