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I thought that an ETD stretch curve is a plot of the offsets for the particular partials being used for tuning each note. It is thus a "tuning curve" and will only be concurrent with a Railsback curve if the partial happens to be the fundamental. That is usually the case for the upper octaves I think from what little I know about ETDs.

Working back from a tuning curve to a produce a Railsback curve requires a prior knowledge of the IH values.

The question I have is whether a Railsback curve is P1 or P0?

I assume that when we talk about stretch, it is always relative to the first partial, whether or not one can hear that partial. This means that the stretch produced by an ETD listening to the 6th partial, is calculated backward from the measured iH, in spite of the fact that no ETD, of which I am aware, applies offsets to the individual partials of a given note to correct for the anomalies in the bass due to bridge motion (and who knows whatever else). This is of no concern to the tuner, but the stretch value has little meaning when related to the first partial in the low bass.

Am I wrong about this? Do any ETDs display the stretch relative to the partial it uses for tuning? I know they show the stretch of the individual partials in cents, but if you look at the iH coefficient entries in TuneLab pro for example, it is just the single value.

Am I making any sense? I'm confused.

Tunelab displays the difference from theoretical no-inharmonicity of each partial that is used for measuring the pitch (which is never 1 in the bass). You can set them all to 1 to see the theoretical fundamental (which may not actually be audible).

Each string has one IH value, which determines the relative positions of the partials according to a modified Young model which was fitted to measured partials. This has nothing directly to do with stretch.

Kees

I will play around with TuneLab. What I would like to be able to do is, using my own pre-determined set of first partial frequencies that satisfy my temperament and stretch requirements, use some ETD to tune those frequencies.

The problem is that my calculations correct for anomalies in the partial distribution such that a single first partial basis for tuning will yield the desired/correct beat speeds for all the intervals. If I can get TuneLab to listen only to the first partial, it should work. I don't want it telling me, by listening to the sixth partial, what the frequency of the first partial is, since, in my case, it would be incorrect. Any ideas?

You mention that the placement of the partials is based on a modified Young model. I could not reference the formula. Is it Robert Scott's lookup table to replace n^2?