Quantitative Evaluation of Musical Scale Tunings
Donald Elliott Hall · American Journal of Physics · 1974
The acoustical and mathematical basis of the problem of how best to tune the twelve-tone chromatic scale is reviewed, with emphasis on understanding why there cannot exist any perfect solution. A quantitative measurement is devised to show how well any tuning succeeds in providing just intonation for any specific piece of music. Application of this measurement to a number of musical examples with a simple computer program is discussed, with results that clarify the reasons for certain historical tuning practices.