Musical temperamentA musical temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. These pure intervals are based on a perfect fifth that has an exact 3:2 pitch ratio, but tempering narrows or widens them to accommodate a broader range of tuning needs. Temperaments are especially important for fixed-pitch instruments such as keyboards and guitars, which lack any way to easily make fine pitch adjustments during performance.
SemitoneIn Western music theory, a semitone (also called a half step or half tone) is one of two parts into which a whole tone is divided. Semitones are the smallest intervals commonly harmonically and melodically used in Western music, and are among the most dissonant intervals when sounded harmonically. A progression of semitones forms a chromatic scale, which informs the layout of many fixed-pitch instruments.Zhu ZaiyuZhu Zaiyu (Chinese: 朱載堉; 1536 – 19 May 1611) was a Chinese scholar, mathematician and music theorist. He was a prince of the Chinese Ming dynasty. In 1584, Zhu innovatively described the equal temperament via accurate mathematical calculation.OctaveIn music, an octave (from Latin octavus 'eighth') or perfect octave (sometimes called the diapason) is an interval between two tones, one having twice the frequency of vibration of the other. For instance, the interval between C4 and C5 (in scientific pitch notation) is an octave. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems".Just intonationJust intonation is the tuning of a musical interval without beats. The result is an acoustically pure sound that resonates within the harmonic series. The simplest relationship between pitches in this series can be expressed as small whole number ratios. Musicians around the world instinctively perform in just intonation. Just intonation also describes any musical tuning system containing five or more pure intervals within an octave.Twelfth root of twoThe twelfth root of two or 2 12 {\displaystyle {\sqrt[{12}]{2}}} (or equivalently 2 1 / 12 {\displaystyle 2^{1/12}} ) is an algebraic irrational number approximately equal to 1.0594631. It is important in Western music theory, where it represents the frequency ratio (musical interval) of a semitone () in 12-tone equal temperament. This number was first proposed in relation to musical tuning in the 16th and 17th centuries.
Simon StevinSimon Stevin (Dutch: [ˈsimɔn steːˈvɪn]; 1548–1620), sometimes called Stevinus, was a Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical.
Logarithmic scaleA logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences among the magnitudes of the numbers involved.
Concert pitchConcert pitch is the pitch reference to which a group of musical instruments are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over time. The ISO defines international standard pitch as A440, setting 440 Hz as the frequency of the A above middle C. Frequencies of other notes are defined relative to this pitch. The written pitches for transposing instruments do not match those of non-transposing instruments.
Classical musicBroad tradition of Western art musicMembers of a youth orchestra standing to acknowledge applause after performing.Classical music is a tradition of art music in the Western world, considered to be distinct from Western folk music or popular music. It is sometimes distinguished as Western classical music, as the term "classical music" can also be applied to non-Western art musics.
A440 (pitch standard)A440 (also known as Stuttgart pitch) is the musical pitch corresponding to an audio frequency of 440 Hz, which serves as a tuning standard for the musical note of A above middle C, or A4 in scientific pitch notation. It is standardized by the International Organization for Standardization as ISO 16.Musical tuningIn music, there are two common meanings for tuning: Tuning practice, the act of tuning an instrument or voice.Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases.Tuning practiceTuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as A = 440 Hz.*As an Amazon Associate I earn from qualifying purchases.