Please forgive me for starting a specific thread on how to tune historic temperaments, some of which having been mentioned before.
But on a recent tuning I did some measurements with the aid of some rather helpful graphics which I believe help rather a lot from the software recommended by some here, Easy Piano Tuner, and I hope will help others to tune in the temperaments, even those who haven't had good experiences before.
It's quite apparent that some people such as Fred and I recall one or two others had become quite disillusioned by tunings in unequal temperaments and potentially we might be seeing a good reason why results might not have been as good in the past as potentially we're able to achieve now.
As I suspected, there's a great deal of distortion of the scale by stretching. Down at Tenor C I found that in contrast to the Easy Piano Tuner regular stretched scale on a Wendl & Lung 161 I was tuning around 5 or 6 cents sharp, and by the C above Treble C, 5 or 6 cents flat.
So over the three octave section compared to a standard octave stretched tuning, there was a 10-12 cent contraction, so around 4 cents per octave. The stretched scale of Equal Temperament produces stretched thirds not much more, worse, than a Kellner temperament to the exact unstretched scheme, tuning the inner central three octaves of the piano as a harpsichord or an organ.
This becomes interesting as then we focus on strict mathematical relationships of intervals within the scale set out by the unequal temperament, and we're using stretching above and below this region to provide the normal supporting resonance of the piano. So then we get the best of both worlds, the harmony of the historic concept of the unequal temperament together with the bringing into line the inharmonicity of the piano outside the central region.
Attached are four screens showing the way in which Pianoteq Bechstein simulation follows the standard recommended stretching curve, although is a little flatter than the curve in the bass, and three tunings, one a Steinway C, another an 1885 Bechstein (7ft or so), and the Wendl & Lung 161 referred to.
A great pianist friend of mine has experimented with me and when faced with the Pianoteq unequal temperament simulations complained to me that some chords aren't as nice as they should be. This isn't the fault of Pianoteq but simply according with inharmonic stretched current tuning practice.
The other photos show the tuning of the notes at the two ends of the three octave range during tuning showing the CTS5 giving me the flat no-stretch baseline, next to the standard curve recommended by the Easy Tuner and showing the cent deviations from the curve.
I hope that this thread may be helpful for those doing similar experiments and potentially able to make measurements of deviations from the standard curve on other instruments.
Best wishes
David P
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David Pinnegar BSc ARCS
Curator and House Tuner - Hammerwood Park, East Grinstead, Sussex UK
antespam@gmail.comSeminar 6th May 2019 -
http://hammerwood.mistral.co.uk/tuning-seminar.pdf "The Importance of Tuning for Better Performance"
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