# Tuning and what the piano should sound like as an instrument



## David Pinnegar (Jan 16, 2019)

In doing some more research on the battle of concepts of the scale, an important article on minimum entropy scales http://www.scielo.br/scielo.php?pid=S1806-11172016000100410&script=sci_arttext has a very helpful diagram







One major assumption of the authors of that concept is demonstrated by that particular chord - it's not one we see often in music - the tuning that derives from its logic is a theoretician's rather than a musician's scale.

The result of the stretched octave logic tunes the instrument's scale to its own inharmonicity. The inharmonicity is what takes the instrument into the realms of the metallic. This might be the sound that piano manufacturers want but it's not the sound through which to express meaningful music, or rather music meant to convey meaning.

We can see the logic of stretching the scale so that that E above middle C has both the red and the purple harmonic coinciding. And then actually the major third C-E becomes wider and more harsh. Who's been jibing at wide thirds in Unequal Temperaments? This concept makes them worse, universally so none are sweet.

If instead we start out from the concept of Kirnberger III which has a perfect C-E third, and we don't stretch the middle three octaves at all, and we tune Tenor C downwards harmonically - that's C2 downwards, then for the chord of C major we have perfect C2E2, C3E3, C4E4, beatless. We have C1 tuned so that its 4 harmonic falls on C3 and the 5th harmonic on E3 and 3rd and 6th harmonics very near to their respective G2 and G3. The sound is wonderfully pure and resonant. When we shift up to C# then with a perfect fifth on C#G# the even harmonics add up, and the 3rd coincides too, and the 5th harmonic is so shifted from F3 it's not associated with it at all. This means that we remove it from resonating with the sustaining pedal down. So at once we remove confusion in the sound, allowing Chopin and Beethoven pedalling to be sustaining passages for many bars, and as the pantalon, and we make the sound more coherent in the technical sense, more resonant. And as we slip from one key to another we really do get a different timbre in the built up chords, chromatically, as in a spectrum that we see in the rainbow.





is in Kirnberger III temperament. This genre of temperament has much to give the instrument both musically and in improvement to its tonality, and the modern instrument likewise.

Best wishes

David Pinnegar


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