Musical Offerings, Fall 2018

Musical Offerings ⦁ 2018 ⦁ Volume 9 ⦁ Number 2 61 Musical Offerings 9, no. 2 (2018): 61–74 ISSN 2330-8206 (print); ISSN 2167-3799 (online) © 2018, Timothy M. True, licensed under CC BY-NC-ND ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ) The Battle Between Impeccable Intonation and Maximized Modulation Timothy M. True Cedarville University qual temperament represents a way of completing the musical circle and systematically compensating for the Pythagorean comma—a fundamental inconsistency in harmony and tuning. Pythagoras discovered this acoustical problem around 550 B.C. Since that time, music theorists have debated how to deal with it. The acoustical problem is that 12 perfect fifths and 7 octaves are different intervals. Unfortunately, no perfect solution exists to this problem— something must be compromised. Four of the major compromises are Pythagorean intonation, just intonation, equal temperament, and meantone temperament. However, understanding these systems requires a basic knowledge of acoustics and harmony. Throughout the course of history, musicians used the tuning or temperament that made their own music sound best. Eventually, they traded true intonation for the ability to play in any key at any time. While equal temperament is now universally hailed as the standard tuning system, it is not perfect. Rather, it represents a compromise designed to best accommodate the needs of tonal music since the Baroque era. What is temperament? To answer this question, one must first understand the basics of musical harmony. Scientifically, a single note, or pitch, represents a sound wave of a specific frequency. 1 Each note corresponds to a particular frequency. For instance, many orchestras tune to the frequency of 440 Hz. Frequency measures the number of vibrations per second; thus, a frequency of 440 Hz means that the sound waves move 440 times every second. The higher the frequency, the higher the note— the lower the frequency, the lower the note. When two different pitches are played simultaneously, the frequency relationship between the notes 1 John Fauvel, Raymond Flood, and Robin J. Wilson, Music and Mathematics: From Pythagoras to Fractals (New York: Oxford University Press, 2003), 13. E