Survey of efficient temperaments by subgroup: Difference between revisions
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== Which temperaments should I use to make music? == | == Which temperaments should I use to make music? == | ||
There are many different schools of thought within | There are many different schools of thought within regular temperament theory (RTT). Most would agree that a good temperament is ''efficient'', meaning it approximates some subset of [[just intonation]] relatively accurately with a relatively small number of notes. What they disagree on is ''how'' accurate is "relatively accurate", ''how'' small is "relatively small", and ''which'' JI subsets are interesting enough to be worth approximating. | ||
Most would agree that a good temperament is ''efficient'', meaning it approximates some subset of [[just intonation]] relatively accurately with a relatively small number of notes. | |||
What they disagree on is ''how'' accurate is "relatively accurate", ''how'' small is "relatively small", and ''which'' JI subsets are interesting enough to be worth approximating. | |||
For example: | For example: | ||
* '''Xenharmonicist A''' might argue that an error less than ~15 [[cents]] on most intervals, and less than 5 cents on the really important ones (like the perfect fifth and the octave), is accurate enough, and they might argue that 25 notes per [[equave]] is the most that is practical, any more than that is too cumbersome. They might argue that nobody can hear the harmonic effect of [[prime harmonics]] higher than 11, and they might argue that there is no real reason to use [[subgroup]]s that are missing primes 2 or 3, because those primes are so important to consonance. | |||
* '''Xenharmonicist B''' might argue that the error must be less than ~5 cents on almost all intervals, anything further out than that sounds out of tune to them. They might argue that it is perfectly possible to learn up to 50 notes per equave. They might argue that they can hear the subtle, delicate effect of prime harmonics up to 23, and they might argue that subgroups like 3.5.7.11 and 2.5.7.11 are the most fertile ground for new and exciting musical exploration. | |||
These are not the only possible stances, either: one could imagine a xenharmonicist C, xenharmonicist D, etc. Thousands of differing individual perspectives on what traits are important in a temperament. | |||
To gain more of a grasp on these debates, it may help to compare these temperaments to [[12edo]], a.k.a. the familiar 12-tone equal temperament which most modern music is tuned to by default. 12edo has, of course, 12 notes per equave, which makes it fairly small by temperament standards but not abnormally so. The most common theoretical approach to 12edo is to treat it as a 2.3.5-subgroup temperament, with similar accuracy to [[augmented (temperament)|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 tables). So that should provide a helpful point of comparison to measure these other temperaments against. | |||
To gain more of a grasp on these debates, it may help to compare these temperaments to [[12edo]], a.k.a. the familiar 12-tone equal temperament which most modern music is tuned to by default. 12edo has, of course, 12 notes per equave, which makes it fairly small by temperament standards | |||
The most common theoretical approach to 12edo is to treat it as a 2.3.5 subgroup temperament, with similar accuracy to | |||
The second most common approach is to interpret 12edo as a 2.3.17.19 subgroup temperament, with similar accuracy to | |||
So that should provide a helpful point of comparison to measure these other temperaments against. | |||
== How to read the tables == | == How to read the tables == | ||