Well Temperament

Temperament is tuning with compromises. There are many criteria, that can't all be satisfied perfectly:

• including many consontant intervals;
• not including too many notes per octave;
• symmetry, where the intervals available from one note are also available from other notes;
• simple paths from a note don't lead to a note that is slightly off the starting point, giving rise to drifting or sounding out of tune.

Well temperament is a class of tunings that allow all twelve key signatures without any sounding too far off. A few years ago I suggested a 12 note subset of 34edo that tempers out the diaschisma rather than the syntonic comma, so it is not too conventional. Lately I have been looking at just tuned diatonic scales. The diaschismic tuning avoids perfect fifths that are too far off, so I had the idea that it could provide a form of well temperament, supporting all twelve key signatures with reasonable diatonic scale shapes.

C Major

An algorithmic example.

G Major

An algorithmic example.

D Major

An algorithmic example.

A Major

An algorithmic example.

E Major

An algorithmic example.

B Major

An algorithmic example.

F# Major

The shapes of the diatonic scales now start to repeat, so their characters will be the same as those already given.

C# Major

Ab Major

Eb Major

Bb Major

F Major