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Pseudo-octave
In music theory, a pseudo-octave, pseudooctave, or paradoxical octave is an interval whose ratio of frequencies is not exactly expected for perfectly harmonic pitches, but slightly wider or narrower in pitch – for example , , or even as large as The pseudo-octave is never-the-less perceived as if it were equivalent to the conventional 2:1 harmonic ratio, and consequently is treated the same: Pitches separated by a pseudo-octave appropriate for a given instrument are considered equivalent to each other just as with normal ''"pitch classes"'' (which are typically explained only in terms of the idealized 2:1 octave). Stretched octave The stretched octave, for example rather than (an 8.6  cent pitch difference), sounds ''out of tune'' when played with ideal harmonic overtones, but ''in tune'' when played with lower notes whose overtones are themselves naturally stretched by an equivalent amount. In piano tuning, stretched octaves are commonly encou ...
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Octave And Septimal Chromatic Semitone On C
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. 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". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' (), ''8va bassa'' (, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing this mark above or below the staff. Exp ...
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Inharmonicity
In music, inharmonicity is the degree to which the frequency, frequencies of overtones (also known as Harmonic series (music)#Partial, partials or partial tones) depart from Integer, whole multiples of the fundamental frequency (harmonic series (music), harmonic series). Acoustically, a note perceived to have a single distinct pitch in fact contains a variety of additional overtones. Many percussion instruments, such as cymbals, tam-tams, and Tubular bells, chimes, create complex and inharmonic sounds. Music harmony and intonation depends strongly on the harmonicity of tones. An ideal, homogeneous, infinitesimally thin or infinitely flexible string or column of air has exact harmonic modes of vibration. In any real musical instrument, the resonant body that produces the music tone—typically a string, wire, or column of air—deviates from this ideal and has some small or large amount of inharmonicity. For instance, a very thick string behaves less as an ideal string and m ...
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Interval (music)
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In Western music, intervals are most commonly differences between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic fr ...
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Piano Tuning
Piano tuning is the process of adjusting the tension of the strings of an acoustic piano so that the musical intervals between strings are in tune. The meaning of the term 'in tune', in the context of piano tuning, is not simply a particular fixed set of pitches. Fine piano tuning requires an assessment of the vibration interaction among notes, which is different for every piano, thus in practice requiring slightly different pitches from any theoretical standard. Pianos are usually tuned to a modified version of the system called equal temperament. (See Piano key frequencies for the theoretical piano tuning.) In all systems of tuning, every pitch may be derived from its relationship to a chosen fixed pitch, which is usually A440 (440 Hz), the note A above middle C. For a classical piano and musical theory, the middle C is usually labelled as C4 (as in scientific pitch notation); However, in the MIDI standard definition this middle C (261.626 Hz) is labelled C3. In pr ...
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Octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. 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". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' (), ''8va bassa'' (, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing this mark above or below the staff. ...
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Piano Acoustics
Piano acoustics is the set of physical properties of the piano that affect its sound. It is an area of study within musical acoustics. String length, mass and tension The strings of a piano vary in diameter, and therefore in mass per length, with lower strings thicker than upper. A typical range is from for the lowest bass strings to , string size 13, for the highest treble strings. These differences in string thickness follow from well-understood acoustic properties of strings. Given two strings, equally taut and heavy, one twice as long as the other, the longer will vibrate with a pitch one octave lower than the shorter. However, if one were to use this principle to design a piano, i.e. if one began with the highest notes and then doubled the length of the strings again and again for each lower octave, it would be impossible to fit the bass strings onto a frame of any reasonable size. Furthermore, when strings vibrate, the width of the vibrations is related to the string len ...
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Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the Crystal structure, atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubber elasticity, rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be Prop ...
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Harmonics
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st harmonic''; the other harmonics are known as ''higher harmonics''. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a '' harmonic series''. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50  Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz. In music, harmonics are used on string instruments and ...
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Fundamental Frequency
The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), is defined as the lowest frequency of a Periodic signal, periodic waveform. In music, the fundamental is the musical pitch (music), pitch of a note that is perceived as the lowest Harmonic series (music)#Partial, partial present. In terms of a superposition of Sine wave, sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as 0, indicating the lowest frequency Zero-based numbering, counting from zero. In other contexts, it is more common to abbreviate it as 1, the first harmonic. (The second harmonic is then 2 = 2⋅1, etc.) According to Benward and Saker's ''Music: In Theory and Practice'': Explanation All sinusoidal and many non-sinusoidal waveforms repeat exactly over time – they are per ...
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Hertz (unit)
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base units is 1/s or s−1, meaning that one hertz is one per second or the reciprocal of one second. It is used only in the case of periodic events. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. For high frequencies, the unit is commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of the e ...
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Timbre
In music, timbre (), also known as tone color or tone quality (from psychoacoustics), is the perceived sound of a musical note, sound or tone. Timbre distinguishes sounds according to their source, such as choir voices and musical instruments. It also enables listeners to distinguish instruments in the same category (e.g., an oboe and a clarinet, both woodwinds). In simple terms, timbre is what makes a particular musical instrument or human voice have a different sound from another, even when they play or sing the same note. For instance, it is the difference in sound between a guitar and a piano playing the same note at the same volume. Both instruments can sound equally tuned in relation to each other as they play the same note, and while playing at the same amplitude level each instrument will still sound distinctive with its own unique tone color. Musicians distinguish instruments based on their varied timbres, even instruments playing notes at the same pitch and volume ...
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Partial (music)
The harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a ''fundamental frequency''. Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. As waves travel in both directions along the string or air column, they reinforce and cancel one another to form standing waves. Interaction with the surrounding air produces audible sound waves, which travel away from the instrument. These frequencies are generally integer multiples, or harmonics, of the fundamental and such multiples form the harmonic series. The fundamental, which is usually perceived as the lowest partial present, is generally perceived as the pitch of a musical tone. The musical timbre of a steady tone from such an instrument is strongly affected by the relative strength of each harmonic. Terminology Partial, harmonic, f ...
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