The Development of the Equal Temperament Scale

Evolution or Radical Change?

Introduction

A debate exists in the music community about the current method in which fixed pitched instruments such as pianos are tuned.  This debate dates back to the mid seventeenth century when equal temperament tuning was first invented.  Some in the music community believe the equal tempered scale has lessened the effectiveness of harmony and that harmony has been compromised by the invention.  Even the first Western European to publish it, Marin Mersenne (b. 1588), developed other tunings besides equal temperament.

On the other side of the debate, many have pointed out the great benefits of equal tempered tuning.  Composers now write music that would have been impossible to enjoy without the tempered scale.  Instruments have also advanced with more mechanical assistance available for wind and string performers.  Most importantly, our society has (unknowingly) accepted the equal tempered scale as the norm.  Switching back to any of the historic systems of tuning would be quite noticeable to most of the public and would force musicians and composers to alter their techniques.

This thesis does not argue for either side of the debate.  Instead, it examines the developments that preceded the acceptance of the equal tempered scale as a standard tuning for western music.  The question to be answered is not if the tuning is good or bad; the question is whether the Equal Temperament Scale is part of a natural progression over time, or a discovery that made radical changes to the accepted tuning of the day.  Although this will not resolve any arguments, it may shed light on reasons for the debate’s existence. 

The first section of the thesis explains and gives examples of the connections between mathematics and pitch.   The formulas and units of measure are also laid out to help explain the debate.  The second section outlines the history from ancient Greece, when it is believed people first explored the relationship between harmony and mathematics, to eighteenth century Europe, when the equal temperament scale was first applied to Western music.  The most popular tuning methods throughout this time period are described in detail.  These methods are chosen for analysis in the third section.

The third section explains the research completed for this study.  Data organization, methods of analysis, and results are outlined both in this section and in the attached charts, graphs, and tables.   Important trends, correlations, and anomalies are explored.  In addition to the visual aids, I have also assembled musical excerpts so the reader may hear tuning methods as they are explained and analyzed.

In the last section, the research and analysis are used to answer the question posed by this thesis.  This question is an important one because the equal temperament scale has changed our lives.  A person, who has heard nothing but equal temperament, listening to the older tuning methods is similar to a modern English speaking person listening to “old” English.  Although there is some familiarity, the words and phrases sound foreign.  The older tunings also sound familiar to a modern listener, but sound out of tune because the relationships between pitches are not exactly the same as those contained in the music we have been exposed to since childhood. 

It would be remarkable to discover that the modern English language came to be without a progression of small changes over time; evidence to the contrary can be found in literature published throughout the centuries.  It would also be remarkable if the underlying structure of music underwent a sudden change as opposed to an evolutionary process.  The first sections of this paper describe a conflict between the goals of those who tried to “perfect” the musical scale and the reality of nature and sound.  This conflict could have been the impetus for sudden change.  Sudden change could be the cause for debate.

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Last modified: November 21, 2005