12th-octave temperaments
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
12edo is the predominating tuning system in the world today, so some of the 12th octave temperaments have been known for a very long time.
By far the most notable 12th-octave temperament is compton or aristoxenean, associated with the Pythagorean comma, which sets 3/2 to 7\12. Given that the circle of 12 fifths closing was the basis of music in Europe and independently China, it can be argued that the 12th-octave temperaments are the oldest form of musical tradition in history.
Furthermore, 12th-octave temperaments like compton usually temper other intervals to subsets of 12edo, like 9/8 to 6edo whole tone scale, and 5/4 to 3edo.
Another temperament which was hugely known is atomic, stemming from a comma described as the Kirnberger's atom. 3/2 flattened by 32805/32768, the schisma, is extremely close to 7\12.
For temperament data, see:
- Compton - Compton family
- Atomic - Very high accuracy temperaments
Magnesium (5-limit)
- For extensions, see Landscape microtemperaments #Magnesium.
Subgroup: 2.3.5
Comma list: [-157 -24 84⟩
Mapping: [⟨12 2 23], ⟨0 7 2]]
- Mapping generators: 78125/73728 = 1\12, [71 11 -38⟩ = 243.137
Supporting ETs: 84, 360, 528, 612, 696, 864, 1920, ...
Badness: 1.226720