198edo: Difference between revisions

Line 1:

'''198 equal temperament''' divides the octave into 198 parts of 6.061 cents each. It is contorted in the [[7-limit]], with the same tuning as [[99edo]], but makes for a good 11- and 13-limit system. Like 99, it tempers out [[2401/2400]], [[4375/4374]], [[3136/3125]], [[5120/5103]] and 6144/6125 in the 7-limit; in the [[11-limit]] it tempers 3025/3024, 9801/9800 and [[14641/14580]]; and in the [[13-limit]] [[352/351]], 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079.

'''198 equal temperament''' divides the octave into 198 parts of 6.061 cents each.

It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the 15-limit, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.

== Theory ==

198edo is contorted in the [[7-limit]], with the same tuning as [[99edo]], but makes for a good 11- and 13-limit system. Like 99, it tempers out [[2401/2400]], [[4375/4374]], [[3136/3125]], [[5120/5103]] and 6144/6125 in the 7-limit; in the [[11-limit]] it tempers [[3025/3024]], [[9801/9800]] and [[14641/14580]]; and in the [[13-limit]] [[352/351]], 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079.

It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the [[15-odd-limit]], and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.

== Intervals ==

== Just approximation ==

Line 48:

Line 54:

[[Category:Edo]]

[[Category:99edo]]

[[Category:198edo]]

[[Category:Minthmic]]

[[Category:Misty]]

@@ Line 1: / Line 1: @@
-'''198 equal temperament''' divides the octave into 198 parts of 6.061 cents each. It is contorted in the [[7-limit]], with the same tuning as [[99edo]], but makes for a good 11- and 13-limit system. Like 99, it tempers out [[2401/2400]], [[4375/4374]], [[3136/3125]], [[5120/5103]] and 6144/6125 in the 7-limit; in the [[11-limit]] it tempers 3025/3024, 9801/9800 and [[14641/14580]]; and in the [[13-limit]] [[352/351]], 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079.
+'''198 equal temperament''' divides the octave into 198 parts of 6.061 cents each.
-It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the 15-limit, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.
+== Theory ==
+edo is contorted in the [[7-limit]], with the same tuning as [[99edo]], but makes for a good 11- and 13-limit system. Like 99, it tempers out [[2401/2400]], [[4375/4374]], [[3136/3125]], [[5120/5103]] and 6144/6125 in the 7-limit; in the [[11-limit]] it tempers [[3025/3024]], [[9801/9800]] and [[14641/14580]]; and in the [[13-limit]] [[352/351]], 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079.
+It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the [[15-odd-limit]], and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.
+== Intervals ==
+{{main|Table of 198edo intervals}}
 == Just approximation ==
@@ Line 48: / Line 54: @@
 [[Category:Edo]]
 [[Category:99edo]]
+[[Category:198edo]]
 [[Category:Minthmic]]
 [[Category:Misty]]