Conrad- here are the beat rates and bearing plan for 1/7 comma syntonic
meantone,
hope it helps.
Don't fear the diminished fourth wolves (F#-Bb, C#-F, G#-C and
B-D#) ; they're
barely 1 cent wider than the 'pythagorean' thirds in the same keys in many
well temperaments.
Paul Bailey
.....from TUNING THE HISTORICAL TEMPERAMENTS BY EAR by Owen Jorgensen
pg.194.TUNING THE THEORETICALLY CORRECT JEAN BAPTISTE ROMIEU 1/7 SYNTONIC
COMMA MEANTONE TEMPERAMENT IN THE ACOUSTIC TONALITY OF C MAJOR AND A MINOR
THERE ARE SIXTEEN musically usable major and minor triads to the octave.
There
are also three extra second inversion minor triads which are usable. The
major triads contain excellent proportional beating sonorities. Each fifth
is narrowed by 1/7 syntonic comma. The bearing octave is E below middle C
to E above middle C. Major sixths, fourths, major thirds, and small minor
thirds are wide. Fifths and minor thirds are narrow. This is a complete
temperament with no tuning done except for octaves which are the only pure
intervals. When the lower tone of a fourth is also the lower tone of a
fifth, then the fourth beats approximately
1 1/3 times as fast as the fifth. When the upper tone of a fourth is also
the upper tone of a fifth, then the fourth beats approximately 1 1/2 times
as fast as the fifth.
TEMPERAMENT STEPS
1. Tune middle C to the tuning fork.
2. Temper E above middle C from middle C so that the major third CE is wide
and beating at 7.0 beats per second.
3. Tune G below middle C roughly pure to E above middle C and then proceed
to lower G until the major sixth GE beats at exactly the same speed as the
major
third CE. GE should be wide.
4. Test the following intervals for the purpose of finding possible
mistakes
which should be corrected. The figures above....( musical notation of the
sixth GE, 7bps, third CE also 7bps, and the fourth GC, 1.4 bps.)
....(when it's right) proceed....
5. Temper A below middle C from E above middle C so that the fifth AE is
narrow and beating at 1.2 beats per second, a minute amount slower than the
fourth GC.
6. Tune D above middle C roughly pure to A below middle C and then proceed
to
raise D until the fourth AD beats approximately 1 1/2 times as fast as the
fifth GD and also the fourth AD beats approximately 1 1/3 times as fast as
AE. AD should be wide and GE should be narrow.
7. Test the following intervals:
G3-D4: 1.0 bps A3-E4:1.2 bps
G3-C4:1.4 bps A3-D4: 1.6 bps
C4-E4: 7 bps G3-E4: 7.0 bps
A3-C4: 4.3 bps.
8. Tune E below middle C pure to E above middle middle C.
9. Test the following intervals:
E4-E3: 0.0 bps
E3-G3: 7.0 bps
G3-E4: 7.0 bps
E3-A3 1.2 bps
G3-C4: 1.4 bps
E3-G3 7.0 bps
A3-C4 4.3 bps
10. Temper Bb3from D4 so Major 3rd Bb D is wide and beating at 6.2
bps.
11. Test following intervals
Bb3-D4 6.2 bps
C4-E4 7.0
E3-G3 7.0
G3-Bb3 8.3
A3-C3 9.3
12. Tune f3 roughly pure to D4 and then lower F until the major sixth
F3-D4 beats
at exactly the same speed as the major third Bb3-D4. F3-D4 should
be wide.
13. Thest the following intervals:
F3-D4 6.2bps
Bb3-D4 6.2
F3-C4 0.9
G3-D4 1.0
E3-A3 1.2
F3-Bb3 1.3
G3-C4 1.4
F3-A3 4.7
Bb3-D4 6.2
F3-D4 6.2
G3-E4 7.0
14. Temper B3 from G3 so the major third G3-B3 beats 5.2 bps.
15. Tests:
E3-B3 0.9bps
F3-C4 0.9+
A3-D4 1.6 bps
B3-E4 1.8
F3-A3 4.7bps
G3-B3 5.2
Bb3-D4 6.2
A3-C4 9.3
B3-D4 10.4
16. Temper C#4 so the major sixth E3-C#4 is wide and beaating at 5.9
bps.
and also so that the major third A3-C#4 beats exactly the same
speed as the
major sixth E3-C#4.
17. Tests:
G3-B3 5.2 bps
A3-C#4 5.4
Bb3-D4 6.2
A3-C#4 5.9
E3-C#4 5.9
F3-D4 6.2
Bb3-C#4 20.6
B3-D4 10.4
C#4-E4 11.7
18. Tune F#3 roughly pure to B3 and then proceed to lower F# until the
fourth F#3-B3 beats approximately 1 1/2 times as fast as the fifth
E3-B3 and
also the fourth F#3-B3 beats approximately 1 1/3 times as fast as
the fifth
F#3-C#4. F#3-B4 should be wide and F#3-C#4 should be narrow.
19. Test intervals:
F3-C4 0.9 bps
F#3-C#4 1.0
G3-D4 1.0+
F3-Bb3 1.2 bps
F#3-B3 1.3
G3-C4 1.4
E3-G3 7.0
F#3-A3 7.8
G3-Bb3 8.3
F#3-Bb3 12.1 (wolf)
20. Temper G#3 from E3 so that the major third E3-G#3 is wide and beats
at 4.4 bps.
21. Tests:
G3-C4 1.4 bps
G#3-C#4 1.5
A3-D4 1.6
E3-G#3 4.4 bps
F3-A3 4.7
F3-G#3 15.4 bps
Bb3-C#4 20.6
G3-Bb3 8.3 bps
G#-3-B3 8.8
A3-C4 9.3
F#3-Bb3 12.1 bps (wolf)
G#3-C4 13.6 (wolf)
22. Temper Eb4 from Bb3 so the fourth Bb3-Eb4 is wied and beating at
1.7 bps.
23. Test the following intervals sa a complete test for all the
intervals
between E3 and E4.
E3-E4 pure
(narrow fifths)
E3-B3 0.9
F3-C4 0.9
F#3-C#4 1.0
G3-D4 1.0+
A3-E4 1.2
(wide fourths)
E3-A3 1.2
F3-Bb3 1.2
F#3-B3 1.3
G3-C4 1.4
G#3-C#4 1.5
A3-D4 1.6
Bb3-Eb4 1.7
B3-E4 1.8
(wide major thirds)
E3-G#3 4.4
F3-A3 4.7
G3-B3 5.2
A3-C#4 5.9
Bb3-d4 6.2
C4-E4 7.0
(wide major sixths)
E3-C#4 5.4
F3-D4 6.2
G3-E4 7.0
(narrow augmented seconds, or small minor thirds)
F3-G#3 15.4
Bb3-C#4 20.6
(narrow regular minor thirds)
E3-G3 7.0
F#3-A3 7.8
G3-Bb3 8.3
G#3-B3 8.8
A3-C4 9.3
B3-D4 10.4
C4-Eb4 11.1
C#4-E4 11.7
(diminished sixth)
G#3-Eb4 3.7 (wolf)
(diminished fourths)
F#3-Bb3 12.1 (wolf)
G#3-C4 13.6 (wolf)
B3-Eb4 16.2 (wolf)
The theoretically correct Jean Baptiste Romieu 1/7 syntonic comma
meantone temperament can be converted into the theoretically
correct
17 syntonic comma well temperament by retuning Bb, Eb, Ab,and Db
each in
turn by a series of pupre fourths and fifths all pure from F.
This PTG archive page provided courtesy of Moy Piano Service, LLC