Revising the musical equal temperament

Haye Hinrichsen
2016 Revista Brasileira de Ensino de Física  
Western music is predominantly based on the equal temperament with a constant semitone frequency ratio of 21/12. Although this temperament has been in use since the nineteenth century and in spite of its high degree of symmetry, various musicians have repeatedly expressed their discomfort with the harmonicity of certain intervals. Recently it was suggested that this problem can be overcome by introducing a modified temperament with a constant but slightly increased frequency ratio. In this
more » ... we confirm this conjecture quantitatively. Using entropy as a measure for harmonicity, we show numerically that the harmonic optimum is in fact obtained for frequency ratios slightly larger than 21/12. This suggests that the equal temperament should be replaced by a harmonized stretched temperament as a new standard.
doi:10.1590/s1806-11173812105 fatcat:5qk53v5v65gmri4lftcc5rmnoq