HT's worth a try ?

A440A@AOL.COM A440A@AOL.COM
Sun, 25 Jun 2000 09:40:47 EDT


<< O.K., You have talked me into it - I will try a few of your H.T.'s.     
What book do I have to get that shows the beat-rate relationships between the 
various intervals when tuned aurally and which H.T. would you recommend for a 
modern Jazz pianist like myself? 

 

hi Clive, 
     Jorgensen's "Tuning the Historical Temperaments By Ear"  would be the 
best place to start.  It is probably out of print, but some library, 
somewhere will have it.  
I will include a tuning scheme below that will get you started in the unequal 
tunings.  All of the earlier temperments between meantone and ET are really 
the same form, differing in degree of consonance/dissonance relationships.  
Good luck, 
Ed Foote 

TEMPERAMENT  FOR THE 21st CENTURY
 Ed Foote  
                                         
    The following is the 1840 Tuner's Guide Temperament #1 (® Owen Jorgensen 
1991).  It provides a conservative digression between sweet thirds and some 
with "energy".  There are no checks, you will develop a sense of tonal 
comparison after you do it and listen a little. 

1.  tune from the C fork to C5 , then go by the following steps.
2.  C5 - C4   Just
3.  C4 -  G4  temper narrow to approx 1.3 bps
4   G4 - G3  Just
5.  G3 - D4  narrow 1.3 bps
6.  D4 - A4     narrow 1.3
7   A4 - A3  just
8.  A3  - E4    narrow 1.3

Trial chord here is C4-E4-G4-C5 and it should sound beautiful.  The C-E will 
be beating about half normal speed . 

9.    E4 - B4      narrow by .7 BPS,  this is a nicer fifth than those 
previous! 
10   B4 - B3    Just
11.  B3  - F#4    narrow by .7 BPS
12   F#4  -  F#3  just 
13.  F#3 - C#4  narrow  by .7 BPS
14.  C#4  - G#4  Just 
15.  G#4  - G#3  Just
16.  C5  - F4  narrow by 1.3 bps
17.  F4 - Bb3  narrow by 1.3 bps
18.  Bb3  - Bb4 Just
19.   Tune Eb4  to make two identical fifths between Bb-Eb and Ab-Eb.  These 
fifths should be pure, but can stand a little temperament.  

      This tuning provides a varied set of consonances, in the thirds, that 
follow the amount of key signature. If you modulate by fourths, from C, tonic 
thirds should increase in size until you reach F#, at which point it will 
begin heading back toward "home".  The art is in getting a smooth 
progression, with no reversals on the way out or in. 


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