[CAUT] Stretch

[Fred Sturm]

On Feb 3, 2007, at 11:14 AM, David Porritt wrote:

> This discussion of wide and narrow stretch is difficult using plain  
> English.  Frankly RCT stretch numbers are to me just as obscure.   
> We can discuss particulars in terms of partial ratios (4:2, 8:4  
> etc.) and that is a little more revealing.  Or if one at least has  
> an ETD of some kind we can talk of the stretch of C8 in numbers.   
> For example in tuning a Steinway “D” my C8 ends up at 43.92 cents  
> and on a “B” 34.76 cents.  That means something to me.  I’ve heard  
> of people using a stretch that gets to 75 cents at C8 and that  
> seems pretty s-t-r-e-t-c-h-e-d to me.
>
> Revealing where C8 ends up might make this a little clearer.
>
> dave____________________
>
> David M. Porritt, RPT
>
> dporritt at smu.edu
Hi Dave,
	For my part, I end up with C8 at +65¢. This may be misleading,  
however, as C6 is about 5, C7 about 18, far more "conservative"  
figures. Partials I use to arrive at this for the concert grand are  
12:1. (I would look at 16:1 as well, but the 16th partial is pretty  
weak. 16:1 closely follows 12:1 almost all the way). This means  
beatless 26ths (triple octave +5th), throughout the piano. I found  
that that was pretty much what I had already, tuning aurally in a  
relatively conservative fashion, A0 to C6. I matched that using ETD  
when I started using one 12 years ago. A few years ago I decided to  
see experiment with extending that partial match to C7, then, later,  
all the way to C8. I liked the results. 12:1 mirrors 8:1 and 6:1  
fairly consistently and only begins to diverge widely around G6. So I  
have a fairly steep curve, if you will, upward from G6 to C8.
	Note I have mentioned nothing of 2:1, 4:2, 6:3, 8:4 octave sizes.  
They are not what I, personally, focus on. I let them fall where they  
may at this point. Granted, in getting to this point, I paid plenty  
of attention to them, fussing and fretting, and tearing hair out when  
facing various models of piano where things I thought I had figured  
out simply wouldn't work. But essentially I would say that all my  
single octaves from A0 to at least C6 "sound relatively beatless" and  
are wide of 4:2. The top octaves definitely beat, but it isn't very  
noticeable to most ears. And it _is_ noticeable (to my ear) that the  
triple octaves and quads and 19ths and 26ths don't beat. To my ear,  
that is more important than the individual octaves, for reasons I  
have stated in earlier posts. It is also very nice to have those  
highest notes sounding "musically" closer to where the human ear  
wants to hear them.
	On smaller pianos, I follow 6:1 and 8:1, abandoning them where there  
are big inharmonicity breaks and picking them up later in the scale.  
Typical C8s range usually from 35 to 55 in my tunings (occasionally  
as low as 20-25 on bizarre pianos). For a Steinway B, typical is  
50-55. I have two, in our piano prof's studio, that hits 65, per his  
request for more stretch (I had it at 55 when he asked for more). I  
don't mind the sound of his pianos.
	For mid-range, typically my octaves are wide 4:2, bass wide 6:3  
(where mid-range changes to bass varies somewhat in smaller pianos).  
In the bass I am, again, more concerned with 6:1 and 8:1 than with  
octave size per se, though the octave size tends to end up pretty  
consistent.
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu



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