more on this temperament thing

A440A@AOL.COM A440A@AOL.COM
Sat, 27 Oct 2001 17:18:35 EDT


<<I would like to know

how to tune some of these Historical Tuning's aurally. On the List I've only

ever seen cent values for ETD's. Any info, would as always, be appreciated.

Paul Tizzard>>

Hi Paul, 
    Here is a great procedure that will allow you to create any kind of 
temperament you want. 
 
Tuning To Personal Taste (by Owen Jorgensen)

All fourths are wide or Just,  all fifths are narrow or Just

1.   tune C to fork
2.   tune C4-E4 according to taste  (Just or wide)
3.   tune E4 - E3    Just
4.   tune G#3 between E3 & C4 so   Ab-C is 1.25 times as fast as  E-G#

Tune the following intervals Just for Well temperament, (or very slightly 
tempered for Victorian if C-E is beating at least 4 bps).
5.  G#3-C#4
6.  C#4 - F#4
7.  F#4 - F#3  
8.  Ab3 - Eb4
9.  Eb4 - Bb3

10.  tune D4 between Bb3 & F#4 so D -F#  is1.25 times as fast as Bb-D
11.  tune G3 from C4 & D4 so G-C beats 1.3 as fast as G-D
12.  tune A3 from E3 & D4 so A-D beats 1.3 times as fast as E-A
13.  tune B3 between F#3 and E4 so B-E beats 1.3 times as fast as F#-B

    Check 
G3-D4 is slower than A3-E4
G3-C4 is faster than A3-E4
A3-D4 is faster tahn G3-C4

14.  tune F4 from Bb3 & C4 so C-F beats 1.5 times as fast as Bb-F
Beat rates should increase in order from 
E3-B3
Bb3-F4
B3-F#4
B3-E4
E4-A4

    If steps 5 - 9 are tuned in Just intonation, the C-E third controls the 
harmonic balance.  If it is Just, a temperament like Kirnberger(Prinz) 
results.  If C-E is tuned faster than 4 bps and less than7 bps, only F#-A# is 
21.5 cents wide and the results are more "Victorian".  



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