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An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, which gives an equal perceived step size as pitch is perceived roughly as the logarithm of frequency.
A harmonic series is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency.
In music, harmony is the process by which individual sounds are joined together or composed into whole units or compositions. Often, the term harmony refers to simultaneously occurring frequencies, pitches, or chords. However, harmony is generally understood to involve both vertical harmony (chords) and horizontal harmony (melody).
A harmonic is a wave with a frequency that is a positive integer multiple of the fundamental frequency, the frequency of the original periodic signal, such as a sinusoidal wave. The original signal 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.
In music, timbre, also known as tone color or tone quality, is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables listeners to distinguish different instruments in the same category.
Pitch is a perceptual property of sounds that allows their ordering on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.
A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth is the fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones.
In jazz and blues, a blue note is a note that—for expressive purposes—is sung or played at a slightly different pitch from standard. Typically the alteration is between a quartertone and a semitone, but this varies depending on the musical context.
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be perceived between successive notes.
In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term limit was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name.
Xenharmonic music is music that uses a tuning system that is unlike the 12-tone equal temperament scale. It was named by Ivor Darreg, from Xenia, hospitable, and Xenos foreign. He stated that it was "intended to include just intonation and such temperaments as the 5-, 7-, and 11-tone, along with the higher-numbered really-microtonal systems as far as one wishes to go."
The Bohlen–Pierce scale is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal-tempered diatonic scale.
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer and music theorist Paul Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.
In music, 19 Tone Equal Temperament, called 19 TET, 19 EDO, 19-ED2 or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps. Each step represents a frequency ratio of 19√2, or 63.16 cents.
Genesis of a Music is a book first published in 1949 by microtonal composer Harry Partch (1901–1974).
A regular diatonic tuning is any musical scale consisting of "tones" (T) and "semitones" (S) arranged in any rotation of the sequence TTSTTTS which adds up to the octave with all the T's being the same size and all the S's the being the same size, with the 'S's being smaller than the 'T's. In such a tuning, then the notes are connected together in a chain of seven fifths, all the same size which makes it a Linear temperament with the tempered fifth as a generator.
An isomorphic keyboard is a musical input device consisting of a two-dimensional grid of note-controlling elements on which any given sequence and/or combination of musical intervals has the "same shape" on the keyboard wherever it occurs – within a key, across keys, across octaves, and across tunings.
Dynamic tonality is a paradigm for tuning and timbre which generalizes the special relationship between just intonation and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic timbres.
Paul Erlich is a guitarist and music theorist living near Boston, Massachusetts. He is known for his seminal role in developing the theory of regular temperaments, including being the first to define pajara temperament and its decatonic scales in 22-ET. He holds a Bachelor of Science degree in physics from Yale University.
In music, 23 equal temperament, called 23-TET, 23-EDO, or 23-ET, is the tempered scale derived by dividing the octave into 23 equal steps. Each step represents a frequency ratio of 23√2, or 52.174 cents. This system is the largest EDO that has an error of at least 20 cents for the 3rd (3:2), 5th (5:4), 7th (7:4), and 11th (11:8) harmonics. The lack of approximation to simple intervals makes the scale notable among those seeking to break free from conventional harmony rules.
References
- ↑ R. Plomp and W. J. M. Levelt (October 1965). "Tonal Consonance and Critical Bandwidth". Journal of the Acoustical Society of America. 38 (4): 548–560. Bibcode:1965ASAJ...38..548P. doi:10.1121/1.1909741. hdl: 2066/15403 . PMID 5831012. S2CID 15852125.
- ↑ Sethares, William (September 1993). "Local consonance and the relationship between timbre and scale". Journal of the Acoustical Society of America. 94 (3): 1218–1228. Bibcode:1993ASAJ...94.1218S. doi:10.1121/1.408175.
- ↑ Sethares, William (September 1992). "Relating Tuning and Timbre". Experimental Musical Instruments. IX (2).
- ↑ Sethares, William (January 1998). Tuning, Timbre, Spectrum, Scale (1st ed.). New York: Springer. ISBN 978-3-540-76173-0.
- ↑ Sethares, William (November 2004). Tuning, Timbre, Spectrum, Scale (2nd ed.). New York: Springer. ISBN 978-1-85233-797-1.
- ↑ Luca Turin (September 2004). "The sound of impossible objects". NZZ Folio.
- ↑ Scott, X. J. "nonoctave.com / tuning / book reviews" . Retrieved 2009-09-20.
- ↑ Musica Facta: http://musicafacta.org
