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. =========================================================================== ============ Paul Bailey RPT
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