The practice of using period instruments in Early Music has facilitated a general awareness of how Baroque pitch is about a semitone lower than modern pitch. Less commonly known are developments in temperament, tuning and pitch over the course of history. Their implications go beyond the concert experience. In many profound and surprising ways, they have influenced why composers wrote the music that they did.
Tuning, temperament and pitch are not interchangeable.
Pitch is the simplest to understand. It is the frequency at which sound waves move, when referred to in a musical context. Pitch can be measured in the SI unit Hertz (Hz). The modern definition of “A” is defined as 440 Hz.
Tuning can refer to a specific pattern or system of tuning or, secondarily, to two or more pitches that are perfectly synchronized. “When this happens,” as Robert Kerner, period instrument builder and retired keyboard curator at the Eastman School of Music, explains, “any discernible tuning beats are eliminated.”
Temperament is closely related to tuning. When intervals are purposely de-tuned, they are “tempered” from their pure form.
Pythagorean tuning, the first major tuning system used in Western music, is based on mathematical ratios found in the natural world. Perfect fifths sound gloriously pure in this tuning as they are the favoured tuning interval (the only interval used while tuning). Triads, however, are only possible in a few keys. Beyond those few keys, the thirds that result from the tuning of the contiguous fifths that make up the octave become unbearably out of tune.
Pythagorean tuning only works in music consisting of a single melody, parallel fifths and a few triads in a limited number of keys. Accompanied early chant, also known as monody, fits like a glove with this tuning.
Moving on to Temperaments
The idea of purposely de-tuning intervals just a little here and there became more attractive as musicians tried to transcend the constraints of Pythagorean tuning. Kerner explains: “Musicians and theorists began experimenting with tuning systems that require the tempering of one or more of the otherwise pure fifths in the tuning scheme in order to increase the harmony range of the system and allow the music to modulate into more useable keys.”
The first historically significant temperament is mean-tone temperament. It came in countless versions through the three centuries of its popularity, and its use even overlapped with later temperaments well into the 19th century.
Mean-tone temperament favoured pure thirds at the expense of perfect fifths. Every usable triad thus sounded the same. By focusing on thirds, however, another interval became unbearable: tweaking all those fifths created intervals called “wolf tones,” so named because its out-of-tune sound evoked the howling of wolves. Furthermore, just as before, not all keys were usable.
Many Renaissance and early Baroque keyboard pieces were conceived using this temperament. The thirds-centric approach of this temperament directly influenced the upsurge of thirds and sixths in place of the parallel fifths that were more prevalent in the music of the preceding era. Modern listeners can get a taste of mean-tone temperament from recordings of Buxtehude or Italian music on period organs.
Many musicians and theorists experimented with developing beyond mean-tone temperament.
“What we call well temperament nowadays was better known as ‘new temperament,’ of which there were many [types],” Kerner says. “This is a generic phrase referring to any of the unrestricted and irregular ‘unequal’ temperaments of the late Baroque and Classical era.
“In these systems, the circle of fifths is ‘closed’ [all the fifths are usable and either pure or slightly tempered], and the major thirds of the various keys are of differing sizes – some are pure and others much wider than pure. As a result, no two triads in well temperament sound exactly alike. This is what gives each individual key its distinct character.
“We also know that Bach and others were well aware of the system of equal temperament [the common temperament from the 20th century until present day], and that it was not preferred, probably because all of its major thirds were equally wide or pure, and there was no distinguishing character of any particular triad.”
All high Baroque music favored equal temperament. Interested readers can hear this temperament in most harpsichord recordings of Baroque music. The booklet notes usually state which temperament is used.
Many more temperaments were developed through the ages, leading eventually to equal temperament at the turn of the 20th century. This temperament is perhaps the easiest to understand. Simply take a pure octave and divide it into twelve equal parts. Whereas earlier temperaments were based on a pure tuning which then got adjusted here and there, equal temperament throws everything out the window. It has no basis in naturally occurring overtones and requires no adjustment of old models. Instead, it just calculates everything cold.
The compositions that resulted from equal temperament no longer have tendency tones, so composers could truly compose in any key equally. Atonality, which would not have worked with earlier temperaments, burst forth. To hear what this temperament was conceived to facilitate, listen to how dreamy and ambiguous the whole tone scales feel in say, Debussy’s piano works.
The future is an exciting time as music and tuning systems across the world cross-pollinate with Western models. Whatever happens, it is important to keep in mind that the modern temperament that we take for granted is actually very young and still open to change, just as so many tuning systems have been through the ages. It’s not as absolute as one might think!