Single/triple unisons, 8ve 5

[FSSturm@aol.com]

Dear Jim,

Thanks for clarifying the issue. I guess I'll bow to your judgement and
experimental data on this one. I figured I probably would when I first raised
the question, but wanted to hear the full story first. I still think this has
a very limited application in real world tuning, but I may find myself
hedging a bit sharp to compensate just to be on the safe side.

You are correct in stating that aural unisons for bass and midrange can equal
or surpass "machine" unisons. I was thinking about 8ves 5 - 7 when I wrote
that I didn't beleive it was possible to tune aural unisons within a .1 cent
tolerance. Oviously I forgot to be specific - the written word is extremely
unforgiving.

I still believe that the crux of Virgil's assertion about unisons, which
started this conversation, is not difference in pitch between single and
triple stringed unisons, but rather the "problem of octave five". Somehow
that area of the piano is a troublesome one to tune. When I tuned exclusively
aurally, I often went back to alter 8ve 5 after I saw how 8ves 6 and 7 wanted
to be tuned (a good reason to strip mute the whole piano). After I started
using the SAT about a year ago, I noticed that it also has trouble placing
that octave.

Since 8ves 4, 5, and 6 are all tuned and read at 8ve 6, it is possible to
compare partials by simply looking at the numbers in the cents window. For
8ve 4 we are looking at the 4th partial, for 8ve 5 at the 2nd, and for 8ve 6
at the 1st. So if we compare the numbers for, say F4, F5, and F6, we can see
whether the F4/F5 4:2 8ve will be expanded, contracted, or pure, and by how
much. It turns out that for most FAC input numbers, the 4:2 8ve between 8ves
4 and 5 begin to be contracted just above C4/C5, though in a few cases they
remain expanded until B4/B5. The 4:1 double 8ves between 8ves 4 and 5 are
always expanded or pure, but the amount varies from 0 to about 1.0 cents. I
won't go into great detail, but it is useful to scroll through some figures
before tuning 8ves 5 and 6, so you know what you are dealing with.

I think the source of the inconsistencies lies in the fact that the FAC
program tries to produce double octaves that are fairly evenly wide
throughout the scale (and does this quite successfully - amazing what Dr. Al
was able to get out of only three numeric inputs. Quite an accomplishment).
While this produces a very good, clean, conservative tuning, it has a few
quirks as it applies this template to a variey of pianos.

When tuning the majority of pianos, in which the FAC program starts to narrow
the 4:2 8ves between 8ves 4 and 5, I have decided after some experimentation
that it is better to make the 4:2 octaves begin to narrow somewhat higher in
the scale, usually around F#5, and the way I do this is quite simple: when I
get to B4, I scroll up to B5 and note the discrepancy between the two numbers
(for B4 and B5). Then I go to C5 and scroll down to C4, noting that
difference as well. Depending on what I have just noted, I begin to tune 8ve
5 to the 8ve 4 numbers (the SAT says C4, but I tune C5), adding about .3
cents to C4 and C#4, decreasing the amount added to each successive note
(maybe .2 cents added to D4 and D#4, etc) until F#4, after which I begin
gradually decreasing each number. When I get to B5 (B4 in the window) I want
the figure to be no more than about 1.0 to 1.5 cents larger than the number
the machine calculated (otherwise my double octaves are too wide for my
taste). I also check each note aurally with its lower octave and double
octave, to see that those intervals are not becoming overly wild.

Octave 6 and above are tuned by playing notes below: double octave, double
octave fifth, and triple octave, and coming up with the best compromise for
the given piano. Having tuned 8ve 5 somewhat sharp, the 2:1 octaves are not
as objectionable between 8ves 5 and 6, and the double 8ves between 8ves 5 and
7 are closer to the triple 8ves between 8ves 4 and 7.

I said it was simple, but looking back over what I have written, it looks
clear as mud, like most writing about electronic tuning. Sorry about that.
Hope this is of interest to at least some out there. Otherwise, help is just
a delete button away (now he tells me!)

Fred Sturm,
Albuquerque, NM