Dear List,

I've been meaning to post this on my website but have a few hurdles to get over before I can do that. Since at least one reader was interested in an aural bearing plan for temperament, I submit the following.

It will yield a temperament which is excellent for all music of the Classical period and earlier. It may also be used for most any Romantic era music or later but may exhibit tonalties which are too strong for some tastes. It can be tried on any modern music including Jazz too and may well be liked over standard Equal Temperament (ET).

It is far easier to get correct than a true ET. For that reason, I use it to teach my apprentices. All comments are welcome.

Tuning a Representative 18th Century Well Tempered Tuning

1. Tune A4 to A-440 pitch source.

2. Tune A3 from A4, a 6:3 octave.
Test for 6:3 octave: play A3 and C4, then C4 and A4. When both intervals beat
exactly the same, the octave is correct.

3. From A3, tune F3, a widened 3rd to beat at 4 beats per second.

4. Tune C4 from F4, a pure 5th. The A3-C4 minor 3rd will beat 1.5 times as fast as
the F3-A3 Major 3rd (6 beats per second).

5. Tune F4 from C4, a pure 4th. This will form a perfect 4:2 octave, F3-F4.

6. Tune Bb3(A#3), a pure 5th from F4. This will also make a pure 4th, F3-Bb(A#3).

7. Tune Eb4(D#4), a pure 4th from Bb3(A#3).

8. Tune Ab3(G#3), a pure 5th from Eb4(D#4).

9. Tune Db4(C#4), a pure 4th from Ab3(G#3).

10. Tune Gb3(F#3), a pure 5th from Db4(C#4).

11. Temporarily tune D4 to A4, a pure 4th.

12. Temporarily tune G3 to D4, a pure 5th.

13. Listen to the G3-C4 4th and notice the strong beating.

14. Sharpen G3 until the G3-C4 4th beats exactly the same as the G3-D4 5th.
15. Sharpen D4 until the A3-D4 4th and the G3-D4 5th beat exactly the same.
16. Tune B3 from G3 so that the G3-B3 3rd beats exactly the same as the
F3-A3 3rd (4 beats per second).
17. Temporarily tune E4, a pure 5th from A3.
18. Notice the resultant beat between E4 and B3.
19. Flatten E4 until the A3-E4 5th and the B3-E4 4th beat exactly the same.
20. The C4-E4 3rd should beat gently, 2-3 beats per second.

Bill Bremmer RPT
Madison WI USA