The Development of the Equal Temperament Scale

Evolution or Radical Change?

Conclusion

Specifically answering the question for this thesis, equal temperament was a radical change in tuning.  However, the analysis also showed that every tuning could be described as a radical change from its predecessor because no trends were evident.  Equal temperament could be seen as an acquired taste with its adoption as a standard much later than its invention.  It could also be seen as a last resort, saved until music surpassed the limitations of all other possible methods.  Either way, favoring a tonality system in the eighteenth century and keeping it as a standard for over two hundred years is a radical change considering the amount of variability throughout the previous three centuries.

With the knowledge that our current tuning system is mathematically based, it is interesting that mathematicians often invented other systems.  For example, mathematician Leonard Euler (1707-1783 CE) invented a tuning method in 1739 CE (103 years after Mersenne’s Harmonie Universelle).  This method was a version of “just” intonation and deviated far from equal temperament (mean deviation of 15.3 cents and standard deviation of 19.1 cents).  Since Euler wrote extensively on the mathematical evaluation of consonance and “just” intonation is built from consonant intervals, it is not surprising he experimented with this tuning.[i]  He later became an advocate for equal temperament, stating that his theories of consonance still held true because the difference between the tempered ratios and the ratios studied in his work were “almost imperceptible.” [ii]

This highlights the conundrum for those who tried to perfect the tuning system for fixed pitch instruments.  Different types of mathematical perfection are all possible, just not at the same time.  Some mathematicians and musicians focused on the perfection of the interval and harmony itself, while others focused on expanding the possibilities for key signatures and modulation.  The fact that these two searches lead to very different answers explains the variability in tunings throughout the time period analyzed by this research.

This study only provides evidence that the transition to equal temperament was not a natural one, but was driven by necessity.  It does not answer any questions as to the impact of equal temperament on our society.  Many of those currently arguing against the use of equal temperament look to the past for the “ideal” tuning method, but just as early composers wrote music within the context of historic tunings, today’s composers write for equal temperament.  For this reason, it is hard to imagine going back to an earlier method.

Equal temperament was a compromise that took almost two hundred years for Western civilization to accept for fixed pitch instruments.  Now that generations of people have been exposed to this tonality structure, the current perceptions of consonance and dissonance might have been altered.  Future studies are needed to assess the impact of equal temperament on the human interpretation of intervals and harmony.  These studies can help to decide if and how the tuning of fixed pitch instruments could be improved with new technology.

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Last modified: November 19, 2005