This tool simulates a choir performing a piece of choir music, predicting how a real choir might drift out of tune over the piece, revealing the spots in the piece for a choir director to fix.
I have spent many years in choirs and acapella groups, and have noticed that ensembles drifting out of tune is a common problem. I was curious how much of this was a result of bad technique, and how much was just a result of the mathematics of musical tuning.
This tool simulates a choir performance of a piece according to the system Henry Klumpenhouwer described in his 1992 paper "The Cartesian Choir", tuning their pitches based on certain "Cartesian" just intonated intervals from previous pitches.
How we built it
When testing the tool on the piece "Carmina Chromatico" from "Prophetiae Sibyllarum" by Orlando di Lasso, the piece used in Klumpenhouwer's paper, its analysis differed from Klumpenhouwer's. Assuming this was due to a bug, I investigated, which revealed that it was due to errors in Klumpenhouwer's analysis of the piece and differences between his score and most editions.
The mathematics of tuning have never previously been accessible enough to be understood and compensated for by ensembles. With this tool, ensemble directors can know what adjustments to intervals they need to tell their performers, and composers can compose for or against tuning drift.
What we learned
This tool could easily be extended to generate tuning diagrams similar to the one in Klumpenhouwer's paper, highlight moments when voices in a piece go out of tune, and even suggest tuning corrections that could be made by performers to keep a piece in tune.
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