Pianos and JI tuning

Dave asks:
> Is it always risky to a piano to occasionally
>move all the Abs by 40 cents or all the Ebs by 40 cents so as to move the
>wolf in mean tone around?

Not always. An old instrument may exhibit a lot of wire breakage, but new
ones should be able to take it.
The most highly stressed part of the wire is where it goes around bends,
and the tuning pin's first wrap has to flex quite a bit to go 40 cents worth.
Pianos that have been played real hard often show fatigue breakage at the end
of the speaking length.
It will probably destabilize the strings to move a note 40 cents, but
usually, you would be moving the note no more than 20 cents from its normal ET
position, (unless you want to change from one meantone to another).
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.

Jon Catler, quoted by Johnny Reinhard, wrote

>"The difference between the frequencies of the two notes being sounded
>produces a third note below the range of the first two, called a
>difference tone. By playing through a _descending_ harmonic series with
>two notes and keeping a "B" on top, we can see that the difference tone
>line creates an _ascending_ minor scale that corresponds exactly to the
>Undertone Series created earlier from mirror-imaging.

The wording here is unclear -- anyone know what Jon meant by "playing
through a _descending_ harmonic series with
two notes and keeping a "B" on top"? Judging from the results, he
probably meant something like "playing through a series of
superparticular ratios, with the upper note fixed at "B", and the lower
note descending."

Anyway, I had written a 22tET guitar piece which demonstrates something
similar. Two notes are played at a time; the upper one is held constant,
while the lower one forms approximate simple ratios with the upper one:

7/8:1/1 (4/22)
6/7:1/1 (5/22)
5/6:1/1 (6/22)
4/5:1/1 (7/22)
7/9:1/1 (8/22)
3/4:1/1 (9/22)

With distortion, one need not rely on the ear's production of difference
tones, which only works at very loud volumes. Distortion creates
difference tones that can be heard at any volume. Tube distortion is
especially nice for this purpose, as it is more forgiving of temperament
that transistor distortion. The single 15'' speaker on my tube amp is
especially conducive to bringing out low difference tones. Playing the
intervals above, one hears a series of roots, all subharmonics of the
top note:

1/8
1/7
1/6
1/5
2/9
1/4

By actually playing the following notes on the lower strings, I
reinforce those difference tones:

1/4
2/7
1/3
1/5
2/9
1/4

The result (with rhythmic fanciness, and two extra measures of
tonic/dominant stuff) is, according to some of my friends, the most
effective demonstration of what microtones can contribute to music that
they have heard (and believe me, I've played them a lot of microtonal
music).

Note that the simultaneities in both my and Catler's examples are always
otonal chords.