159edo: Difference between revisions
→Theory: remove factually wrong additions |
→Commas: Sorry, but I have to say that this (first) section is so crammed with facts that one cannot reach its end without the certainty of having already forgotten most of them. |
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=== Commas === | === Commas === | ||
{{todo|improve readability}} | |||
In the 7-limit it tempers out 1029/1024, 10976/10935, 117649/116640, 235298/234375 and [[Meter comma|703125/702464]] in addition to the 5-limit commas [[32805/32768]], [[15625/15552]], [[amity comma|1600000/1594323]], [[semicomma|2109375/2097152]], and [[vulture comma|10485760000/10460353203]]. This makes it among other things an excellent tuning for [[Schismatic_family#Guiron|guiron]] and [[Gamelismic_clan #Tritikleismic|tritikleismic]] temperaments, as well as a possible tuning for metric temperament. In the 11-limit, it tempers out not only [[385/384]], [[441/440]], [[3025/3024]], [[4000/3993]], [[4375/4356]], and [[6250/6237]], but– in a first for EDOs that are multiples of 53– both [[Nexuma|1771561/1769472]] and [[Quartisma|117440512/117406179]], which, in turn means that [[Symbiosma|19712/19683]] is tempered out as well. In the 13-limit it tempers out [[325/324]], [[364/363]], [[625/624]], [[676/675]], [[1001/1000]], [[1575/1573]], [[2080/2079]], [[cantonisma|10985/10976]] and 13720/13689. In the 17-limit tempers out [[273/272]], 375/374, 595/594, 715/714, [[936/935]], [[1089/1088]], 8624/8619 and 15379/15300. In the 19-limit, it is known to temper out 343/342 and 361/360, but since it is inconsistent in the 19-limit, there are other potential mappings available that temper out different commas. It also provides the [[optimal patent val]] for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament [[Gamelismic_family #Portending|portending]]. | In the 7-limit it tempers out 1029/1024, 10976/10935, 117649/116640, 235298/234375 and [[Meter comma|703125/702464]] in addition to the 5-limit commas [[32805/32768]], [[15625/15552]], [[amity comma|1600000/1594323]], [[semicomma|2109375/2097152]], and [[vulture comma|10485760000/10460353203]]. This makes it among other things an excellent tuning for [[Schismatic_family#Guiron|guiron]] and [[Gamelismic_clan #Tritikleismic|tritikleismic]] temperaments, as well as a possible tuning for metric temperament. In the 11-limit, it tempers out not only [[385/384]], [[441/440]], [[3025/3024]], [[4000/3993]], [[4375/4356]], and [[6250/6237]], but– in a first for EDOs that are multiples of 53– both [[Nexuma|1771561/1769472]] and [[Quartisma|117440512/117406179]], which, in turn means that [[Symbiosma|19712/19683]] is tempered out as well. In the 13-limit it tempers out [[325/324]], [[364/363]], [[625/624]], [[676/675]], [[1001/1000]], [[1575/1573]], [[2080/2079]], [[cantonisma|10985/10976]] and 13720/13689. In the 17-limit tempers out [[273/272]], 375/374, 595/594, 715/714, [[936/935]], [[1089/1088]], 8624/8619 and 15379/15300. In the 19-limit, it is known to temper out 343/342 and 361/360, but since it is inconsistent in the 19-limit, there are other potential mappings available that temper out different commas. It also provides the [[optimal patent val]] for 11-limit guiron and 13-limit tritikleismic, as well as the 13-limit rank three temperament [[Gamelismic_family #Portending|portending]]. | ||