[pianotech] Cents deviation & tuning charts

[Ron Nossaman]

On 4/30/2012 11:47 AM, Jason Kanter wrote:
> All right, let me weigh in here briefly. I really like the metaphors of
> using a micrometer to measure a marshmallow, or finding the best tape to
> stick the wind to a shadow. Sure, the physical world does not provide us
> the ability for that much precise control. But the design of
> temperaments is a mathematical thing before it is a practical activity,
> and while it remains in the realm of math, the additional precision
> helps make things "work out" theoretically. I doubt anyone who designs
> temperaments has the conviction that the degree of precision actually
> makes it into the instrument for more than perhaps five seconds per
> interval, if that.
>
> That said, the math itself can be really beautiful. I have been working
> on finding temperamental relationships that provide a high degree of
> "beat synchrony" -- that is, for example, when you play a major triad,
> the inner thirds (major third and minor third) beat in time with each
> other, either 1:1 or 2:1 or 3:2, creating a very pleasing tremolo-like
> pulsing sound. I'm sure you all have experienced this by happenstance
> with some chords, and it is in fact possible to design a temperament in
> which this phenomenon happens a lot.  But the math goes to two decimal
> points (at least) to find this exactitude, and I don't dream that the
> phenomenon will remain for long or even be noticeable much. Still, the
> intellectual beauty is worth pondering. And in my experience, a
> sensitive artist can be very deeply moved by the quality of the tuning,
> hearing musical depths that he or she never before experienced.

Sure, I understand, and well put. And if you didn't take it to two 
decimal places, someone would surely complain.

I had no problems with this at all.
Ron N