Equal temperament in the context of "12 equal temperament"

A piano is a keyboard instrument that produces sound when its keys are depressed, activating an action mechanism where hammers strike strings. Modern pianos have a row of 88 black and white keys, tuned to a chromatic scale in equal temperament. A musician who specializes in piano is called a pianist.

There are two main types of piano: the grand piano and the upright piano. The grand piano offers better sound and more precise key control, making it the preferred choice when space and budget allow. The grand piano is also considered a necessity in venues hosting skilled pianists. The upright piano is more commonly used because of its smaller size and lower cost.

In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 (Play), 1.5, and may be approximated by an equal tempered perfect fifth (Play) which is 2 (about 1.498). If the A above middle C is 440 Hz, the perfect fifth above it would be E, at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz.

Ratios, rather than direct frequency measurements, allow musicians to work with relative pitch measurements applicable to many instruments in an intuitive manner, whereas one rarely has the frequencies of fixed pitched instruments memorized and rarely has the capabilities to measure the changes of adjustable pitch instruments (electronic tuner). Ratios have an inverse relationship to string length, for example stopping a string at two-thirds (2:3) its length produces a pitch one and one-half (3:2) that of the open string (not to be confused with inversion).

Microtonality is the use in music of microtones — intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls "between the keys" of a piano tuned in equal temperament.

A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor seventh. However, a variety of sevenths may be added to a variety of triads, resulting in many different types of seventh chords.

In its earliest usage, the seventh was introduced solely as an embellishing or nonchord tone. The seventh destabilized the triad, and allowed the composer to emphasize movement in a given direction. As time passed and the collective ear of the western world became more accustomed to dissonance, the seventh was allowed to become a part of the chord itself, and in some modern music, jazz in particular, nearly every chord is a seventh chord. Additionally, the general acceptance of equal temperament during the 19th century reduced the dissonance of some earlier forms of sevenths.

E is the third note and the fifth semitone of the C major scale, and mi in fixed-do solfège. It has enharmonic equivalents of F♭ [(F-flat) which is by definition a diatonic semitone above E♭] and D (D-double sharp), amongst others.

When calculated in equal temperament with a reference of A above middle C as 440 Hz, the frequency of Middle E (E₄) is approximately 329.628 Hz. See pitch (music) for a discussion of historical variations in frequency.

Harry Partch (June 24, 1901 – September 3, 1974) was an American composer, music theorist, and creator of unique musical instruments. He composed using scales of unequal intervals in just intonation, and was one of the first 20th-century composers in the West to work systematically with microtonal scales, alongside Lou Harrison. He built his own instruments in these tunings on which to play his compositions, and described the method behind his theory and practice in his book Genesis of a Music (1947).

Partch composed with scales dividing the octave into 43 unequal tones derived from the natural harmonic series; these scales allowed for more tones of smaller intervals than in standard Western tuning, which uses twelve equal intervals to the octave. To play his music, Partch built many unique instruments, with such names as the Chromelodeon, the Quadrangularis Reversum, and the Zymo-Xyl. Partch described his music as "corporeal" (emphasizing its physical/visceral elements), and distinguished it from abstract music, which he perceived as the dominant trend in Western music since the time of J.S. Bach, whose seminal book of preludes and fugues called The Well-tempered Clavier (in German, Das wohltemperierte Klavier) is often cited as the pivot point beyond which older mean-tone and ancient just intonation tunings were abandoned (in the late-18th century) and the then-future of Western Classical (and popular) instruments were (and most are still) based, for exploitation of all 24 theoretical key signatures. Partch's earliest compositions were small-scale pieces to be intoned with simple folkloric-like string instrumental backing; his later works were large-scale (like a fusion of theater and music decidedly related to but quite apart from Wagnerian opera), they were integrated theater productions in which he expected each of the performers to sing, dance, speak, and play instruments in a "corporeal apotheosis". Ancient Greek theatre and Japanese Noh and kabuki heavily influenced Harry Partch's music theatre.

In music theory, the tritone is defined as a musical interval spanning three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B.

Narrowly defined, each of these whole tones must be a step in the scale, so by this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. More broadly, a tritone is also commonly defined as any interval with a width of three whole tones (spanning six semitones in the chromatic scale), regardless of scale degrees. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B (from F to the B above it, also called augmented fourth) and B–F (from B to the F above it, also called diminished fifth, semidiapente, or semitritonus); the latter is decomposed as a semitone B–C, a whole tone C–D, a whole tone D–E, and a semitone E–F, for a total width of three whole tones, but composed as four steps in the scale. In twelve-equal temperament, the tritone divides the octave exactly in half as 6 of 12 semitones or 600 of 1,200 cents.

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music, drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that.

One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, melodic inversion, and complementation. Some theorists apply the methods of musical set theory to the analysis of rhythm as well.