I have been rigorously testing the intonation of my whistles while playing tuns for almost two years now. It just dawned on me that I can improve my measurement, and thus the family of whistles, by changing how I measure their intonation.
Basically, I should test the whistles in a way that will show me if my whistles are changing regardless of changes in the temperature of my shop. Of course it would be best to control the temperature of my shop, but lacking that solution, what is the next best improvement I can make.
For the moment, my question is simplified in order to make a specific decision:
Is it preferable, when measuring intonation as measured with RTTA to
A) set the whistle to the same length regardless of ambient conditions
B) tune a note to it's desired frequency ?
I think I can answer this with some spreadsheet work regarding speed of sound vs. temp in the spreadsheet.
First I developed a metric that ignored absolute pitch but would be a good representation of relative pitch of the note of my whistle. That being the Sigma of cents off target for each note. Cents is used because the ear detects pitch differences linearly if expressed in cents. 10 cents being noticable to an untrained ear, and 5 to a trained ear. And Sigma is used because it is based on the difference from the average error of all the tones, thus ignoring average pitch change due to ambient conditions or tuning slide movement.
The crux of the question is the linear movement of all tone holes (moving the slide) vs. the proportional movement of the pitch with temperature (not moving the slide.) Since absolute tone is not a factor in my metric, I'm looking for the best way to measure the intonation of the whistle regardless of temperature. My intuition says leave the tuning slide alone.
Starting with a calculated D whistle at 80F (typical A/C session conditions plus a little warm breath) I thought I'd calculate the cents off for temps to from 90F to 40F in ten degree increments if I left the tuning slide alone and then again if I adjusted the slide to bring one note into tune.
Here are the plots:
So, if I've done the spreadsheet properly, (I calculated a cent as 1/200th of true D to true E) I'm going to have a larger sigma for my intonation if I tune the whistle to some specific note than if I set it at a fixed length. But without other calculations I won't really have a number that represents the intonation of the whistle at 80F, chief among these is the tempering effect of the breath on the air that is vibrating vs. the ambient air. But because of the that tempering effect, I should see less error in measured intonation than indicated by the charts above.
So then I wondered, if I found the Sigma due to temperature effects, could I subtract that from my calculated value and be left with the error from the whistle? (Using variance when subtracing of course)
Hmm... I could, but I need to include other effects such the temperature of the mixed ambient air and breath air, CO2 and water vapor in the mix. Since I believe my current calculated sigma from the spreadsheets is overstated due to ignoring these effects, I would be blaming too much of the error on the temperature.
But for now I think I've convinced myself that I should set the whistle up for play in a comfortable air conditioned space and use that same length for each RTTA test I do out in the shop.
Thanks to Terry McGee and Grame Roxbury for the RTTA technology.