Rules for Well Temperament

[Paul N. Bailey]

                        Tuning The Historical Temperaments By Ear
                                        OWEN JORGENSEN

pages 246-7-7

1.Each tonality or key center should sound differently and should have its
own
distinct color characteristics or "Affekt." This is in direct opposition to
the ideals of equal temperament in which all tonalities have the same
identical neutral color
except for increasing or decreasing beat speeds. The purpose of well
temperament is to allow harmonic color-change through modulation.

2.The same as in equal temperament, one must be able to modulate freely in
all possible keys without experiencing any unacceptable out-of-tune wolf
sounds. Thus, all twelve tones may be used enharmonically which is
impossible in the class of restricted temperaments including just
temperaments or meantone temperaments.

3. During modulation through a series of fourths or fifths, the color
changes of the
"Affekts" must be consistent and even.

        From a detailed study and evaluation of the beat speeds and
qualities of all the most prominent documented historical temperaments, the
following rules for well temperament are evident:

RULES
1. THE TWELVE SEMITONES OF THE OCTAVE MUST NOT all be of the same size.

2.No fifth , minor sixth, or minor third should be wider than just.

3.No fourth, major sixth, or major third should be narrower than just.

4.No major or minor third and no major or minor sixth should be altered or
tempered from just intonation by more than one syntonic comma.

5.No fourth or fifth should be altered or tempered from just intonation by
more than one half syntonic comma.

6.No octave should be altered at all from just intonation.

7.No major third should be smaller or closer to just intonation than C E.

8. F A must be the same size or larger than  C E.

9. Bb D  must be the same size or larger than  F A. Also,  Bb D just be
larger than 
   C E.

10. Eb G must be the same size or larger than Bb D.

11. Ab C  must be the same size or larger than Eb G.

12. Db F must be the same size or larger than Ab C. Also, Db F must be the
same size or larger than  B D#. (Db F may be the same size, smaller or
larger than Gb Bb. No other major thirds may be larger than Db F and Gb
Bb.)

13. Gb Bb must be the same size or larger than  Ab C.

14. B D#  must be the same size or smaller than  F# A#.

15. E G#  must be the same size or smaller than  B D#.

16. A C#  must be the same size or smaller than  E G#.

17. D F#  must be the same size or smaller than  A C#. Also, D F# must be
larger than      C E.

18. G B  must be the same size or smaller than  D F#.

19. C E  must be the same size or smaller than  G B.

20. No minor third should be larger or closer to just intonation than E G
or A C.
    There are necessary exceptions, but it is definitely preferable that A
C not be larger or closer to just intonation than E G. To have E G larger
than A C is 
considered a fine accomplishment.

21. D F must be the same size or smaller than  A C. Also, D F must be
smaller than  
    E G.

22. G Bb must be the same size or smaller than D F.

23. C Eb must be the same size or smaller than  D F.

24. F Ab must be the same size or smaller than  C Eb. Also, F Ab must be
the same size or smaller than Eb Gb. (F Ab may be the same size, smaller,
or larger than  Bb Db. No other minor thirds may be smaller than  F Ab or
Bb Db.)

25. Bb Db must be the same size or smaller than C Eb.

26. Bb Db must be the same size or smaller than  C Eb.

27. G# B  must be the same size or larger than  D# F#.

28. C# E must be the same size or larger than  G# B.

29. F# A  must be the same size or larger than C# E.

30. B D must be the same size or larger than F# A.

31. E G must be the same size or larger than B D.

32. The following tonalities are found to be more brilliant or richer than
the same tonalities in equal temperament:

        F minor                         Ab major
        Bb minor                        Db major
        Eb minor                        Gb or F# major
        G# minor                        B major

33. The following tonalities are found to be less brilliant or plainer than
the same tonalities in equal temperament:

        E minor                         G major
        A minor                         C major
        D minor                         F major

34. The following tonalities are sometimes found to be quite similar to the
same tonalities in equal temperament:

        C# minor                        E major
        F# minor                        A major
        B minor                         D major
        G minor                         Bb major
        C minor                         Eb major

35.Breaking any of the above 34 rules ruins the evenness of chord-color
progression or the basic tonality of C major. Also, unnecessary extra
beatings or wolf sounds could be introduced.


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Paul Bailey RPT