Music and the Making of Modern Science

262 Chapter 17

that in certain specific passages such as his first example and especially in the older reper-

tory (such as his Sch ü tz example; figure 17.2 ), natural tuning is important to the musical

effect intended by the composer and also comes naturally to the singers. In general, though,

“ modern vocal music relies almost completely on tempered tuning ... through habituation

to hearing tempered intervals. ”^20

This was arguably the first really surprising result Planck had obtained in his research

career so far, for his result contradicted that of Helmholtz, the great authority in the field,

as well as Planck ’ s own expectations. The whole episode was significant enough that he

included it in his scientific autobiography: “ These studies brought me the discovery,

unsuspected to a certain degree, that the tempered scale was positively more pleasing to

the human ear, under all circumstances, than the ‘ natural, ’ untempered scale. Even in a

harmonic major triad, the natural third sounds feeble and inexpressive in comparison with

the tempered third. Indubitably, this fact can be ascribed ultimately to a habituation through

Figure 17.4

Planck ’ s second test composition, whose tonic should rise about five syntonic commas (about a half step), using

natural tuning ( ♪ sound examples 17.4, 17.5).