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.
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