Dynamic tonality - AbsoluteAstronomy.com

Dynamic tonality is tonal music

Tonality

Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...

which uses real-time changes in tuning

Musical tuning

In music, there are two common meanings for tuning:* Tuning practice, the act of tuning an instrument or voice.* Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases.-Tuning practice:...

and timbre

Timbre

In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...

to perform new musical effects such as polyphonic tuning bends, new chord progressions, and temperament modulations, with the option of consonance

Consonance

Consonance is a stylistic device, most commonly used in poetry and songs, characterized by the repetition of the same consonant two or more times in short succession, as in "pitter patter" or in "all mammals named Sam are clammy".Consonance should not be confused with assonance, which is the...

. The performance of dynamic tonality requires an isomorphic keyboard

Isomorphic keyboard

An isomorphic keyboard is a musical input device consisting of a two-dimensional array 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...

driving a music synthesizer

Synthesizer

A synthesizer is an electronic instrument capable of producing sounds by generating electrical signals of different frequencies. These electrical signals are played through a loudspeaker or set of headphones...

which implements dynamic tuning and dynamic timbres. Dynamic tonality was discovered by Andrew Milne, William Sethares

William Sethares

William A. Sethares is an American music theorist and professor of Electrical engineering and who is known primarily for his contributions to music theory, including dynamic tonality and a formalization of the source of consonance....

, and Jim Plamondon.

Isomorphic keyboards and tuning invariance

Isomorphic keyboards have the unique properties of transpositional invariance and tuning invariance when used with rank-2

Rank of an abelian group

In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines the size of the largest free abelian group contained in A. If A is torsion-free then it embeds into a vector space over the...

temperaments

Regular temperament

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...

of just intonation

Just intonation

In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...

. That is, they expose a given musical interval with "the same shape" in every octave of every key of every tuning of such a temperament. For example, a given tonal scale and its chords will have the same shape, and hence consistent fingering, all across the tuning range of the syntonic temperament

Syntonic temperament

The syntonic temperament is a system of musical tuning in which the frequency ratio of each musical interval is a product of powers of an octave and a tempered perfect fifth, with the width of the tempered major third being equal to four tempered perfect fifths minus two octaves and the width of...

. Of the various isomorphic keyboards (e.g., the Bosanquet, Janko

Janko keyboard

The Jankó keyboard is a musical keyboard layout for a piano designed by Paul von Jankó in 1882.Based on the premise that the hand can barely stretch more than a 9th on the piano, and that all scales are fingered differently, Jankó's new keyboard had two interlocking 'manuals' with three...

, Fokker

Adriaan Fokker

Adriaan Daniël Fokker , was a Dutch physicist and musician.Fokker was born in Buitenzorg, Dutch East Indies ; he was a cousin of the aeronautical engineer Anthony Fokker...

, and Wesley), the Wicki

Wicki-Hayden note layout

In music, the Wicki-Hayden note layout is a key layout for musical instruments that offers some advantages over the traditional keyboard layout.-History:...

keyboard is optimal for dynamic tonality.

Dynamic tuning

On a tuning invariant keyboard, any given musical structure—a scale

Musical scale

In music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...

, a chord

Chord (music)

A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...

, a chord progression

Chord progression

A chord progression is a series of musical chords, or chord changes that "aims for a definite goal" of establishing a tonality founded on a key, root or tonic chord. In other words, the succession of root relationships...

, or an entire song

Song

In music, a song is a composition for voice or voices, performed by singing.A song may be accompanied by musical instruments, or it may be unaccompanied, as in the case of a cappella songs...

-- has exactly the same fingering in every tuning of a given temperament. This allows a performer to learn to play a song in one tuning of a given temperament and then to play it with exactly the same finger-movements, on exactly the same note-controlling buttons, in every other tuning of that temperament. For example, one could learn to play Rodgers and Hammerstein's

Rodgers and Hammerstein

Richard Rodgers and Oscar Hammerstein II were a well-known American songwriting duo, usually referred to as Rodgers and Hammerstein. They created a string of popular Broadway musicals in the 1940s and 1950s during what is considered the golden age of the medium...

Do-Re-Mi

"Do-Re-Mi" is a show tune from the 1959 Rodgers and Hammerstein musical The Sound of Music. Within the story, it is used by Maria to teach the notes of the major musical scale to the Von Trapp children who learn to sing for the first time, even though their father has disallowed frivolity after...

in its original 12-tone equal temperament

Equal temperament

An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...

(12-tet) and then play it with exactly the same finger-movements, on exactly the same note-controlling buttons, while smoothly changing the tuning in real time across the syntonic temperament

Syntonic temperament

's tuning continuum.

Piano keyboard

The piano keyboard is one-dimensional, and therefore cannot present the intervals of a rank-2 (two-dimensional) temperament isomorphically. As it is not isomorphic, the piano keyboard is also not tuning invariant, and hence cannot control dynamic tuning with consistent fingering. Without consistent fingering, a pianist would have to change a given interval's fingering constantly as the tuning changed, which would be impractical. Whereas an isomorphic keyboard's tuning invariance makes dynamic tonality easy to control, the piano keyboard's lack of tuning invariance makes it impractical.

New musical effects

Dynamic tuning enables musical effects which require a change in tuning, such as

polyphonic tuning bends, in which the pitch of the tonic remains fixed while the pitches of all other notes change to reflect changes in the tuning, with notes that are close to the tonic in tonal space
Pitch space
In music theory, pitch spaces model relationships between pitches. These models typically use distance to model the degree of relatedness, with closely related pitches placed near one another, and less closely related pitches placed farther apart. Depending on the complexity of the relationships...

changing pitch only slightly and those that are distant changing considerably;
new chord progressions that start in a first tuning, change to second tuning (to progress across a comma which the second tuning tempers out but the first tuning does not), optionally change to subsequent tunings for similar reasons, and then conclude in the first tuning; and
temperament modulations, which start in a first tuning of a first temperament, change to a second tuning of the first temperament which is also a first tuning of a second temperament (a "pivot tuning"), change note-selection among enharmonics to reflect the second temperament, change to a second tuning of the second temperament, then optionally change to additional tunings and temperaments before returning through the pivot tuning to the first tuning of the first temperament.

Polyphonic tuning bends are demonstrated in this video.

Tonality and timbre

The consonance

Consonance and dissonance

In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...

of musical intervals

Interval (music)

In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

is maximized when the partials of a given timbre

Timbre

(which for harmonic timbres

Harmonic series (music)

Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...

are also called harmonics or overtones) align with the notes of a given tuning. Many cultures' tuning systems can be seen as attempts to maximize the consonance of music played with the timbres of their dominant instruments. For example, the non-tonal tuning systems of Indonesia, Thailand, and Mandinka Africa maximize the consonance of their dominant instruments' timbres (gongs, ranats, and balafons. respectively).

Likewise, the West's system of tonality can be seen as arising from an attempt to maximize consonance with its dominant instruments' timbres, which are almost universally harmonic

Harmonic series (music)

. The system of tuning that most closely aligns fundamentals with harmonic partials is Just Intonation

Just intonation

.

However, the benefits of consonance are not the only consideration in tonality. The utility of being able to modulate

Modulation (music)

In music, modulation is most commonly the act or process of changing from one key to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest...

freely among keys is also highly valued, and attaining this benefit—especially on fixed-pitch instruments such as the piano

Piano

The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...

-- requires tempering

Musical temperament

In musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of just intonation in order to meet other requirements of the system. Most instruments in modern Western music are tuned in the equal temperament system...

a tuning away from Just Intonation. Such tempering moves notes out of alignment with their corresponding harmonics, thereby reducing consonance. This reduction in consonance has been vigorously opposed by many musicians and music theorists throughout history, and this opposition continues today.

Dynamic timbre

One solution to the problem of temperament is to temper a timbre's partials to align with a tempered tuning's notes. The laws of physics make it difficult for acoustic instruments to temper their partials in real time, but acoustically-produced timbres can be tempered electronically in real time, and electronic music synthesis can be used to generate tempered timbres in real time, too.

The tempering of timbres to match tunings can be seen as a generalization of the relationship between Just Intonation and the Harmonic Series—the relationship from which all of tonality arguably springs—to a much wider range of 'pseudo-tonal' tunings and their related 'pseudo-harmonic' timbres. As such, it can be seen as a general solution to the problem of temperament

Musical temperament

, at least for music that is produced or processed electronically.

Dynamic sonance

The ability to control tuning and timbre together does not preclude their independent control. For example, the one can independently control sonance -- i.e., the degree of a timbre's alignment with the current tuning—in real time. Using dynamic sonance, one can (for example) shift the tonic triad from consonance to dissonance and back, or the tritone from dissonant to consonant and back, as a means of controlling tension and relief.

Tension (music)

In music, tension is the perceived need for relaxation or release created by a listener's expectations. For example, dissonance may give way to consonance...

vs. Microtonality

While microtonal music

Microtonal music

Microtonal music is music using microtones—intervals of less than an equally spaced semitone. Microtonal music can also refer to music which uses intervals not found in the Western system of 12 equal intervals to the octave.-Terminology:...

usually involves a single fixed tuning that is something other than 12-tone equal temperament (12-tet), dynamic tuning involves a real-time change among two or more tunings of which one may be 12-tet. Further, Wikipedia's entry for microtonal music states that "the following systems are not microtonal: a diatonic scale in any meantone tuning...", whereas the syntonic temperament's tonally-valid tuning range includes all of the meantone tunings, facilitating the use of the diatonic scale (or any other) therein through its consistent fingering on an isomorphic keyboard.

Tuning invariance facilitates the exploration of static microtonal tunings, while dynamic tuning incorporates microtonality's static tunings into tuning continua along which tuning can be changed dynamically in real time.

Example: C2ShiningC

An example of Dynamic Tonality can be heard in "C to Shining C" C2ShiningC (composed and recorded by William Sethares

William Sethares

in April 2008).
This sound example contains only one chord, Cmaj

Major chord

In music theory, a major chord is a chord having a root, a major third, and a perfect fifth. When a chord has these three notes alone, it is called a major triad...

, played throughout, yet a sense of harmonic tension

Tension (music)

In music, tension is the perceived need for relaxation or release created by a listener's expectations. For example, dissonance may give way to consonance...

is imparted by a tuning progression and a timbre progression:

Cmaj 19-tet/harmonic -> Cmaj 5-tet/harmonic -> Cmaj 19-tet/consonant -> Cmaj 5-tet/consonant

The timbre progresses from a harmonic timbre (with partials following the harmonic series
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...

) to a 'pseudo-harmonic' timbre (with partials adjusted to align with the notes of the current tuning) and back again.
Twice as rapidly, the tuning progresses (via polyphonic tuning bends), within the syntonic temperament
Syntonic temperament
The syntonic temperament is a system of musical tuning in which the frequency ratio of each musical interval is a product of powers of an octave and a tempered perfect fifth, with the width of the tempered major third being equal to four tempered perfect fifths minus two octaves and the width of...

, from an initial tuning in which the tempered perfect fifth (P5) is 695 cents wide (19-tone equal temperament, 19-tet) to a second tuning in which the P5 is 720 cents wide (5-tet), and back again.

As the tuning changes, the pitches of all notes except the tonic

Tonic (music)

In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

change, and the widths of all intervals

Interval (music)

In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

except the octave

Octave

In music, an octave is the interval between one musical pitch and another with half or double its frequency. 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"...

change; however, the relationships among the intervals, as defined by the temperament's

Musical temperament

comma sequence, remain constant throughout. This consistency among a temperament's interval relationships is what makes tuning invariance possible (Milne, 2007).

In the syntonic temperament

Syntonic temperament

, the tempered major third

Major third

In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...

(M3) is as wide as four tempered perfect fifth

Perfect fifth

In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...

s (P5's) minus two octaves -- so the M3's width changes across the tuning progression

from 380 cents in 19-tet (P5 = 695), where the Cmaj triad's M3 is very close in width to its just
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...

width of 386.3 cents,
to 480 cents in 5-tet (P5 = 720), where the Cmaj triad's M3 is close in width to a slightly flat perfect fourth
Perfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...

of 498 cents, making the Cmaj
Major chord
In music theory, a major chord is a chord having a root, a major third, and a perfect fifth. When a chord has these three notes alone, it is called a major triad...

chord sound rather like a Csus4
Suspended chord
A suspended chord is a chord in which the third is omitted, replaced usually with either a perfect fourth or a major second , although the fourth is far more common...

.

Thus, the tuning progression's widening of the Cmaj's M3 from a nearly-just major third

Major third

in 19-tet to a slightly flat perfect fourth

Perfect fourth

In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...

in 5-tet creates harmonic tension

Tension (music)

In music, tension is the perceived need for relaxation or release created by a listener's expectations. For example, dissonance may give way to consonance...

, which is relieved by the return to 19-tet.

External links

Dynamic tonality related news, multimedia, and software, including a synthesizer and sequencer.

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.