[sdiy] Interesting article on top octave generators.

[Donald Tillman]

That quote from the manual is misleading.

In string instruments the harmonics of the note run slightly sharp.  This is because the endpoints are a little less flexible than the rest of the string.  Just plug an electric guitar into an oscilloscope and it's pretty easy to see the harmonic frequencies scooting to the left of the fundamental.

So pianos are stretch tuned so that, if you're playing octaves, the harmonics of the lower notes are in tune with the fundamentals of the higher notes.  The amount of stretch depends on the string length, tension, and physical characteristics, so each instrument model is different, and so traditionally they come with a chart like that.

And the effect is similar for electric pianos with tines (Rhodes) or reeds (Wurlitzer).  But not for organs.

So stretch tuning in the synth world would only make sense if you could generate slightly sharp harmonics.  Other than physical modeling, say a Karplus-Strong model tweaked for less flexibility at the endpoints, I don't see how that would work.

https://en.wikipedia.org/wiki/Stretched_tuning

  -- Don
--
Donald Tillman, Palo Alto, California
https://till.com

> On Jan 4, 2025, at 9:09 AM, Ben Stuyts via Synth-diy <synth-diy at synth-diy.org> wrote:
> 
> All this discussion about tuning and temperaments reminded me of the Fender Rhodes service manual, where they take a dive into stretch-tuning. See https://www.fenderrhodes.com/org/manual/ch5.html#5-3 
> 
> Quote: "Stretch tuning is a procedure widely followed by the piano tuning profession. It recognizes a phenomenon of the human ear whereby tones in the upper range of a keyboard will sound "flat" even though they are calibrated with extreme precision. Fortunately for all, a consensus has long since been agreed upon as to the exact amount of stretching. A piano so tuned creates the impression of great tonal brilliance."
> 
> With this chart:
> 
> <Stretch Tuning Chart.jpeg>
> 
> This obviously can never be done with the divide by 2 approach.
> 
> But are there any analog VCO’s (or synths) that actually implement some sort of stretch tuning? (Aside from the unwanted flattening in the high end which is opposite from stretch tuning.)
> 
> Ben
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