Well temperament
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A well temperament or a circulating temperament is a scale which is regarded as an approximation of an equal-step tuning, has the same equave as that equal-step tuning and preserves the transposability of the equal-step tuning, but is not exactly the equal-step tuning being approximated. Historical well-temperaments were formed by stacking a combination of pure 3/2 and meantone fifths and had 12 nearly equal steps.
One of the advantages of these tunings, is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.
Types
A well temperament may be classified by method as follows:
- Maximally even set in a large edo or another equal-step tuning
- Neji or a quasi-equal detemperament (though not all detemperaments of an edo are well temperaments)
Historical well temperaments
- Kirnberger – Kirnberger temperament
- the fifths are pure, except for
- the C–G, D–A, G–D and A–E fifths are quarter comma meantone
- the F#–Db is the wolf fifth, a schisma flat
- Vallotti – Vallotti/Young temperament
- the fifths are pure, except for
- the C–G, D–A, E–B, F–C, G–D and A–E fifths are 1/6 Pythagorean comma flat.
Other quasi-equal scales
- Cauldron
- Bifrost
- Teleic scales – unit step generator, patent tuning alternating *ed(16/9) and *ed(9/8)
- Kartvelian scales – unit step generator, alternating edf and ed(4/3)
- Well tempered nonet
- Daseian scales - unit step generator, patent tuning alternating edo-edo-*edf