Musical temperament in the context of "E♭ (musical note)"

A regular temperament is any tempered system of musical tuning such that each frequency ratio is obtainable as a product of powers of a finite number of generators, or generating frequency ratios. For instance, in 12-TET, the system of music most commonly used in the Western world, the generator is a tempered fifth (700 cents), which is the basis behind the circle of fifths.

When only two generators are needed, with one of them the octave, this is sometimes called a "linear temperament". The best-known example of linear temperaments are meantone temperaments, where the generating intervals are usually given in terms of a slightly flattened fifth and the octave. Other linear temperaments include the schismatic temperament of Hermann von Helmholtz and miracle temperament.

An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same. This system yields pitch steps perceived as equal in size, due to the logarithmic changes in pitch frequency.

In classical music and Western music in general, the most common tuning system since the 18th century has been 12 equal temperament (also known as 12 tone equal temperament, 12 TET or 12 ET, informally abbreviated as 12 equal), which divides the octave into 12 parts, all of which are equal on a logarithmic scale, with a ratio equal to the 12th root of 2, (${\textstyle {\sqrt[{12}]{2}}}$ ≈ 1.05946). That resulting smallest interval, ⁠1/12⁠ the width of an octave, is called a semitone or half step. In Western countries the term equal temperament, without qualification, generally means 12 TET.

In music, an electronic tuner is a device that detects and displays the pitch of musical notes played on a musical instrument. "Pitch" is the perceived fundamental frequency of a musical note, which is typically measured in hertz. Simple tuners indicate—typically with an analog needle or dial, LEDs, or an LCD screen—whether a pitch is lower, higher, or equal to the desired pitch. Since the early 2010s, software applications can turn a smartphone, tablet, or personal computer into a tuner. More complex and expensive tuners indicate pitch more precisely. Tuners vary in size from units that fit in a pocket to 19" rack-mount units. Instrument technicians and piano tuners typically use more expensive, accurate tuners.

The simplest tuners detect and display tuning only for a single pitch—often "A" or "E"—or for a small number of pitches, such as the six used in the standard tuning of a guitar (E, A, D, G, B, E). More complex tuners offer chromatic tuning for all 12 pitches of the equally tempered octave. Some electronic tuners offer additional features, such as pitch calibration, temperament options, the sounding of a desired pitch through an amplifier plus speaker, and adjustable "read-time" settings that affect how long the tuner takes to measure the pitch of the note.

In music, 72 equal temperament, called twelfth-tone, 72 TET, 72 EDO, or 72 ET, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps (equal frequency ratios). Play Each step represents a frequency ratio of √2, or ⁠16+2/3⁠ cents, which divides the 100 cent 12 EDO "halftone" into 6 equal parts (100 cents ÷ ⁠16+2/3⁠ = 6 steps, exactly) and is thus a "twelfth-tone" (Play). Since 72 is divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72, 72 EDO includes all those equal temperaments. Since it contains so many temperaments, 72 EDO contains at the same time tempered semitones, third-tones, quartertones and sixth-tones, which makes it a very versatile temperament.

This division of the octave has attracted much attention from tuning theorists, since on the one hand it subdivides the standard 12 equal temperament and on the other hand it accurately represents overtones up to the twelfth partial tone, and hence can be used for 11 limit music. It was theoreticized in the form of twelfth-tones by Alois Hába and Ivan Wyschnegradsky, who considered it as a good approach to the continuum of sound. 72 EDO is also cited among the divisions of the tone by Julián Carrillo, who preferred the sixteenth-tone (96 EDO) as an approximation to continuous sound in discontinuous scales.

A schismatic temperament is a musical tuning system that results from tempering the schisma of 32805:32768 (1.9537 cents) to a unison. It is also called the schismic temperament, Helmholtz temperament, or quasi-Pythagorean temperament.