Bird's eye view of temperaments by accuracy: Difference between revisions
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This page | This page serves to document temperaments people deem to be highly valuable, and organizing them broadly by accuracy preference, and then approximately by subgroup focus, that is, what sort of harmonies, broadly speaking, the temperament is targetting. Under each accuracy and subgroup focus is found an incomplete list of temperaments, organized ''approximately'' by complexity (how many notes per octave are required). The complexity given is the note count per octave (or for no-2's, per tritave), with the set of odds used for deriving the complexity given. Sometimes two complexities are given and the average is taken for the purpose of ranking. | ||
'''Importantly: ''do not add a temperament if you do not personally consider it to be unusually valuable''.''' Temperaments here should only be ones that one or more people seriously consider to be "cream of the crop". Therefore, when adding a temperament, ''make sure to include a description of how it works'', ideally one that motivates it as to why someone might want to use it. | |||
'''Importantly:''' the "accuracy" classification of a temperament is the ''maximum error allowed'' on (almost*) ''all'' intervals. {{nowrap|* If there}} is some intervals in the corresponding (thr)odd-limit that violate this bound slightly even in an optimized tuning, they should be noted as "'''Bound-violating intervals:'''" under the header for easy comprehension and consideration, but this should not be abused to attempt to reclassify temperaments, as there should only be one to three such intervals at most (the larger the set of target odds, the more are permissible), and ideally zero. The main exception that justifies more than two bound-violating interval pairs is when a single odd is responsible for all of them (e.g. odd 7 in [[#Buzzard]]). Therefore, most temperaments in a category are more accurate than the bound suggests. | '''Importantly:''' the "accuracy" classification of a temperament is the ''maximum error allowed'' on (almost*) ''all'' intervals. {{nowrap|* If there}} is some intervals in the corresponding (thr)odd-limit that violate this bound slightly even in an optimized tuning, they should be noted as "'''Bound-violating intervals:'''" under the header for easy comprehension and consideration, but this should not be abused to attempt to reclassify temperaments, as there should only be one to three such intervals at most (the larger the set of target odds, the more are permissible), and ideally zero. The main exception that justifies more than two bound-violating interval pairs is when a single odd is responsible for all of them (e.g. odd 7 in [[#Buzzard]]). Therefore, most temperaments in a category are more accurate than the bound suggests. | ||
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'''Also:''' the convention for this page, in contrast to most xen wiki pages, is that if you want to refer to another rank 2 temperament while discussing a rank 2 temperament, you should link to that rank 2 temperament's entry '''on this page''' (unless you are merely discussing competing extensions/don't intend to log that temperament separately on the page) so that the page can be fairly self-contained to avoid intimidating and confusing someone using this page as a reference. The obvious exception is every temperament here may link to its own entry on other pages. Also note that the purpose of using #Temperament to link to something on this page is to indicate that clicking on the link will not take you away from the page and that #Temperament is intended to be logged on the page. | '''Also:''' the convention for this page, in contrast to most xen wiki pages, is that if you want to refer to another rank 2 temperament while discussing a rank 2 temperament, you should link to that rank 2 temperament's entry '''on this page''' (unless you are merely discussing competing extensions/don't intend to log that temperament separately on the page) so that the page can be fairly self-contained to avoid intimidating and confusing someone using this page as a reference. The obvious exception is every temperament here may link to its own entry on other pages. Also note that the purpose of using #Temperament to link to something on this page is to indicate that clicking on the link will not take you away from the page and that #Temperament is intended to be logged on the page. | ||
= Generator tunings = | = Generator tunings = | ||