Musical tuning

Musical tuning serves two primary purposes in the world of sound. First, it refers to the practical act of adjusting an instrument or voice. This process ensures that pitches establish correct intervals between one another. Second, tuning refers to tuning systems. These are the mathematical frameworks used to define the spacing and number of pitches in music.

Without these systems, musicians would lack a shared way to organize sound.

In practice, tuning involves adjusting a pitch to match a fixed reference. A common standard is setting the note A to 440 Hz. If a note is higher than this reference, it is called sharp. If it is lower, it is called flat.

Instruments can drift out of tune due to temperature, humidity, or physical damage. To fix this, musicians use different mechanical methods. String players turn pegs to change string tension. A harp or piano requires a wrench for this task. A violin player can adjust pegs by hand. Wind and brass players modify the length or width of their instrument's tube. A brass player might move a tuning slide to reach the correct pitch.

Musicians often use auditory methods to achieve precision. They may listen for interference beats to measure accuracy. These beats are rhythmic pulses heard when two pitches are slightly different. As the pitches approach a harmonic relationship, the frequency of these beats decreases. For a unison or octave, the goal is to reduce the beating until it is undetectable.

Some musicians use a tuning fork or electronic device. In an orchestra, the principal oboist or clarinetist usually provides the pitch. The ensemble then tunes to that single note.

This ensures that everyone is playing in the same key.

Sometimes, musicians use non-standard tunings called scordatura. This means the instrument is tuned differently than its usual setting. Composers use scordatura to change the instrument's tone or ease certain parts.

In the 17th and 18th centuries, Antonio Vivaldi and Johann Sebastian Bach used these methods. Bach's Fifth Suite for Unaccompanied Cello requires lowering the A string to G. Mozart also raised the solo viola strings in his Sinfonia Concertante. This gave the viola a brighter tone. In the 19th and 20th centuries, composers like Niccolò Paganini and Béla Bartók continued this tradition. Bartók used a specific G♯-D-A-E♭ tuning to play tritones on open strings.

String instruments also rely on open strings, which are the fundamental notes played without pressing the string down. A violin is typically tuned in fifths. A guitar is usually tuned in fourths.

Musicians can also use scordatura for folk music or heavy metal. American folk players in the Appalachians often use alternate tunings for ballads. In heavy metal, electric guitarists frequently use down-tuning. This means they deliberately lower the pitch of the strings. This is different from pitch shifting, which is an electronic change to frequency.

Beyond practice, tuning systems provide the theoretical basis for music. A system defines the frequency values and their spacing. This is complicated because musicians want many different tones. As more tones are added, conflicts arise in how they combine. For example, a tone vibrating at twice the frequency of another creates a natural octave. A ratio of 3:2 creates a perfect fifth.

However, it is mathematically impossible to tune a twelve-note chromatic scale so that every interval is pure. For instance, three pure major thirds do not perfectly equal an octave. This creates a need for compromise methods.

One major method is just intonation. This system uses simple numeric ratios to define notes. A C major scale might use ratios like 1/1, 9/8, and 5/4. While these intervals sound natural, they create problems like the "comma pump." This occurs when stacking intervals causes the pitch to spiral upward. Another method is Pythagorean tuning. This system derives all note ratios from the 3:2 ratio.

Because no single system is perfect, musicians must choose which intervals to prioritize. This choice shapes the entire sound of a musical era.