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  2. Interval (music) - Wikipedia

    en.wikipedia.org/wiki/Interval_(music)

    The size of an interval between two notes may be measured by the ratio of their frequencies.When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (), 2:1 (), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third).

  3. The Virtuoso Pianist in 60 Exercises - Wikipedia

    en.wikipedia.org/wiki/The_Virtuoso_Pianist_in_60...

    The exercises are divided in three parts: Exercises 1 - 20: Labeled "preparatory exercises", these are also the most famous exercises, and are used to develop finger strength and independence. Each exercise contains a sequence of 8 semiquavers, beginning on C, which is then repeated starting on D, and so on across two octaves. The exercise is ...

  4. Ear training - Wikipedia

    en.wikipedia.org/wiki/Ear_training

    As a process, ear training is in essence the inverse of reading music, which is the ability to decipher a musical piece by reading musical notation. Ear training is typically a component of formal musical training and is a fundamental, essential skill required in music schools and the mastery of music.

  5. Arban's Complete Conservatory Method for Trumpet - Wikipedia

    en.wikipedia.org/wiki/Arban's_Complete...

    Arban's Complete Conservatory Method for Trumpet is a method book for students of trumpet, cornet, and other brass instruments.The original edition, Grande méthode complète de cornet à pistons et de saxhorn), was written and composed by Jean-Baptiste Arban (1825-1889) and published in Paris by Léon Escudier in 1864. [1]

  6. Transformational theory - Wikipedia

    en.wikipedia.org/wiki/Transformational_theory

    Transformational theory is a branch of music theory developed by David Lewin in the 1980s, and formally introduced in his 1987 work, Generalized Musical Intervals and Transformations. The theory—which models musical transformations as elements of a mathematical group—can be used to analyze both tonal and atonal music.

  7. Inversion (music) - Wikipedia

    en.wikipedia.org/wiki/Inversion_(music)

    An interval is inverted by raising or lowering either of the notes by one or more octaves so that the higher note becomes the lower note and vice versa. For example, the inversion of an interval consisting of a C with an E above it (the third measure below) is an E with a C above it – to work this out, the C may be moved up, the E may be lowered, or both may be moved.

  8. Music and mathematics - Wikipedia

    en.wikipedia.org/wiki/Music_and_mathematics

    In western music, a division into twelve intervals is commonly assumed unless it is specified otherwise. For the chromatic scale, the octave is divided into twelve equal parts, each semitone (half-step) is an interval of the twelfth root of two so that twelve of these equal half steps add up to exactly an octave. With fretted instruments it is ...

  9. Perfect fifth - Wikipedia

    en.wikipedia.org/wiki/Perfect_fifth

    In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.. In classical music from Western culture, a fifth is the interval from the first to the last of the first five consecutive notes in a diatonic scale. [2]