Survey of efficient temperaments by subgroup: Difference between revisions
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This page highlights those [[rank-2 temperament]]s which recieve the most discussion among theorists and composers. | This page highlights those [[rank-2 temperament]]s which recieve the most discussion among theorists and composers. | ||
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The most common theoretical approach to 12edo is to treat it as a 2.3.5 subgroup temperament, with similar accuracy to '''augmented'''. | The most common theoretical approach to 12edo is to treat it as a 2.3.5 subgroup temperament, with similar accuracy to '''augmented'''. | ||
The second most common approach is to interpret 12edo as a 2.3.17.19 subgroup temperament, with similar accuracy to '''semitonic'''. (Such a temperament would go in the “''2.3.other n''” row of the below | The second most common approach is to interpret 12edo as a 2.3.17.19 subgroup temperament, with similar accuracy to '''semitonic'''. (Such a temperament would go in the “''2.3.other n''” row of the below tables). | ||
So that should provide a helpful point of comparison to measure these other temperaments against. | So that should provide a helpful point of comparison to measure these other temperaments against. | ||
== How to read the | == How to read the tables == | ||
'''Rows''' | '''Rows''' | ||
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Some theorists believe including 13, 17 or higher in a subgroup is pointless because the brain can't register such complex intervals. Others believe these intervals are registered by the brain, perhaps subtly and subconsciously in some instances, but still there. | Some theorists believe including 13, 17 or higher in a subgroup is pointless because the brain can't register such complex intervals. Others believe these intervals are registered by the brain, perhaps subtly and subconsciously in some instances, but still there. | ||
The same temperament may occur multiple times on | The same temperament may occur multiple times on a table if it is good at approximating multiple different subgroups. For example, magic is good at approximating both the 7-limit and the 11-limit, so it is listed under both. | ||
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All of the temperaments listed in | All of the temperaments listed in these tables have low [[badness]] (high relative accuracy), meaning they approximate their target JI subgroup much better than most temperaments with their same amount of needed notes. | ||
That means that for temperaments ''in | That means that for temperaments ''in these tables'', the more notes they require, the more accurate they are. The ones requiring less notes are less accurate, though they are good for their size. (Note that this rule is only true for ''the temperaments in these tables'', it is not true of all temperaments ''in general''.) | ||
== Table of temperaments (5-45 notes per equave) == | == Table of temperaments (5-45 notes per equave) == | ||