In another thread, Ian Russell spoke of, and linked to, Colin Pykett's discussion of widening and narrowing the octave.

http://www.pykett.org.uk/impureoctaves.htm#Summary

We've often discussed temperaments that widen the octave to achieve equal beating octaves and M5's here. And the well temperaments create M3's that are closer to just in some keys than M3's in ET. Meantone, of course, places more emphasis on M3's being closer to just, too.

But has anyone tried working with narrowing the octave to create less wide M3's for an ET or quasi-ET, per Pykett? (The UT's and meantone assume at least a pure octave and often, in practice, a stretch to a 2:1 or wider octave, yes?) Is it possible to narrow the octave and slowly stretch in expanding past the temperament? Would the M5's just beat too much against the octave? (Not sure what intervals, if any, could be made to be beat equally.) And, clearly, the 2nd partial of the lower octave note will beat against the fundamental of the higher note, so inharmonicity would be an immediate problem. Jeff--an insurmountable problem?

(Bill--My first thought was that such a temperament would that take us in the direction of a temperament ordinaire--a meantone that tried for better M5's. But even a temperament ordinaire starts with the assumption of a "perfect" octave.)

Greetings,
Many years ago, a studio tuning was done with no stretch, (bass player/producer wanted to see if that would solve the problem that inharmonicity causes with tuning for other instruments). We often tune a very tight bass on recording studio pianos so that the bass can tune with the piano and not disagree with the electronic tuners that so many guitar players use. Somebody mentioned that it was easier to tune to a Rhodes than an acoustic piano....
The piano sounded as dead as can be. Regardless of what happens to the thirds, the totally unstretched octaves are more noticeable than anything else.
Regards,

You'd have to shrink the octaves too drastically to get a noticeable effect on the thirds.

Kees

Remember Colin Pykett had organs and other instruments in mind as well as pianos.

What he said!

I'd lump this under "subtle, but noticeable to some"...

Those of you that have read "Grand Obsession" will remember the author's quest to recapture a tuning - one that ended up being built on a narrow temperament octave and then stretched out from there to make up the difference so the piano still had "life" as opposed to Ed's experiment from above.

How much narrow? Well, a "normal" approach to that size piano would have the temperament octave a bit wide or using a pure 4:2 octave match. (4th partial of A3 matching with the 2nd partial of A4) Instead the temperament octave in the book was a bit narrow of a 4:2 octave...

"Calm, yet resonant" are some of the terms used to express this type of tuning.

Ron Koval