Tuning Vallotti by ear

Try Vallotti by ear like this:

A from the tuning fork.

A down to tenor A, below middle C.

A to F major third in tenor, wide about 3 beats per second. (A tempo you can memorize from a piece of music.)

All pure fifths or fourths: F - Bb - Eb - Ab - Db - Gb - Cb.

To establish F-C-G-D-A as evenly tempered fifths and fourths, use the technique that I mentioned last week:

C fourth under tenor F temporarily pure. D fifth under tenor A temporarily pure.

Use that C and that D to set tenor G evenly balanced by quality. (If you want to check it by beats: the D-G fourth is triplets against the C-G fifth’s duplets.) This step is placing G halfway between F and A. Your C-G and your D-G will both sound rough, 1/3 comma, but don’t worry. The next steps will take care of that.

Use F and G to correct the C to where it really belongs: same quality from both of them, which means slightly lower in pitch than the temporary C built earlier.

Use G and A to correct the C to where it really belongs: same quality from both of them, which means slightly higher than the earlier temporary D.

Check that all of F-C-G-D-A are smoothly the same quality.

Get middle C and middle D as octaves, plus the F and G, and check that everything is still smoothly even with them in the qualities of F-C-G-D-A.

Everything is now done except for E. Balance your E evenly against A and the B (Cb) that are already done. This quality of the fifths and fourths is the same: F-C-G-D-A-E-B.

And all the other fifths and fourths are pure, as done earlier.

This same F-C-G-D-A-E-B can be used to build a complete 1/6 Pythagorean meantone, or whatever.

If you want to make it Bach/Lehman…

Raise the B to be pure from E. Make E-B-F#-C# all pure from there.

Make C#-G# nearly pure, very slightly narrow.

Make G#-D# nearly pure, very slightly narrow.

Make A# slightly lower than the point where it would have been pure from both D# and F. Scarcely enough to notice that D#-A# is narrow, and A#-F is wide.

Play your music.

Bradley Lehman

Thanks a lot, Brad. I was trying to follow instructions on Carey Beebe’s website. I have now saved your post and I will try it.

Dom

Bradley: Do you mean “Use G and A to correct the [D]…”?

-Nick

Nick: Yes, good catch, thank you! (Where I copied/pasted that sentence from the previous one, and forgot to update one occurrence of C to D…)

“Use G and A to correct the D to where it really belongs: same quality from both of them, which means slightly higher than the earlier temporary D.”

You can use the web interface to edit and correct posts. That is better than posting errata (altho of course the corrections don’t go out by email.) The web interface is the reference source, not email.

I tried that first, but it wouldn’t let me edit any of the original post here on the website. That was because it had been moved out to a separate thread, not in original position.

Is anybody getting this by-ear method into their fingers? How about the technique of checking octaves with the characters of fourths and fifths?