Bird's eye view of temperaments by accuracy: Difference between revisions
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This page is a work in progress, serving to document temperaments 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. | This page is a work in progress, serving to document temperaments 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:''' the "accuracy" classification of a temperament is the ''maximum error allowed'' on ''all'' intervals. 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 or two such intervals at most, 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. 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 ''all'' intervals. 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 or two such intervals at most, 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 (EG odd 7 in [[#Buzzard]]). Therefore, most temperaments in a category are more accurate than the bound suggests. | ||
The bounds are: '''exotemperament''' (>~18c), '''low or very low''' (<~18c), '''medium or low''' (<12c), '''high or medium''' (<7c), '''very high or high''' (<3.5c), '''microtemperament''' (<1c). | The bounds are: '''exotemperament''' (>~18c), '''low or very low''' (<~18c), '''medium or low''' (<12c), '''high or medium''' (<7c), '''very high or high''' (<3.5c), '''microtemperament''' (<1c). | ||