Tonality is a system of music in which certain hierarchical pitch relationships are based on a key "center" or tonic. The term tonalité originated with Alexandre Choron (1810) and was borrowed by François-Joseph Fétis in 1840 (Reti, 1958; Simms 1975, 119; Judd, 1998; Dahlhaus 1990). Although Fétis used it as a general term for a system of musical organization and spoke of types de tonalités rather than a single system, today the term is most often used to refer to Major-Minor tonality (also called diatonic tonality or functional tonality), the system of musical organization of the common practice period and most popular music in much of the world today.

History
Carl Dahlhaus (1990) lists the characteristic schemata of tonal harmony, "typified in the compositional formulas of the 16th and early 17th centuries," as the "complete cadence" (vollständige Kadenz), I-IV-V-I, I-IV-I-V-I, or even I-ii-V-I; the circle of fifths progression: I-IV-vii-iii-vi-ii-V-I, and the "major-minor parallelism", minor: v-i-VII-III = major: iii-vi-V-I or minor: III-VII-i-v = major: I-V-vi-iii.
David Cope (1997) considers key, consonance or relaxation and dissonance or tension, and hierarchical relationships to be the three most basic concepts in tonality. In describing these tenets of tonal music, several known terms are used to refer to various elements of tonal

Terms
Main article: Diatonic scale.
Music is considered to be tonal if it includes the following five descriptions of tonality: (1) it uses a Major or minor (diatonic) scale system (2) it contains triadic harmonies (three note chords) (3) it has a tonic (central tone) (4) it has a leading tone (7th scale degree) (5) resolution of dissonance (that is: if a chord or note is played (like a leading tone 7th scale degree) that doesn't sound final, the final sounding chord is played after it (like the tonic) to resolve the piece)
Since the mid-18th century, tonal music has been increasingly composed of a 12-note chromatic scale in a system of equal temperament. Tonal music makes reference to "scales" of notes selected as a series of steps from the chromatic scale. Most of these scales are of 5, 6 or 7 notes with the vast majority of tonal music pitches conforming to one of four specific seven-note scales: major, natural minor, melodic minor, and harmonic minor.
C major scale:

A natural minor scale:

Other scales or modes are often introduced for variety within the context of a major-minor tonal system without disturbing the diatonic nature of the work. The major scale predominates and the melodic minor contains nine pitches (seven with two alterable). The seven basic notes of a scale are notated in the key signature, and whether the piece is in the major or minor key is either stated in the title or implied in the piece (there is a major and minor key for each key signature). While other scales and modes are used in tonal music, particularly after 1890, these two scales are the reference point for most tonal music and its vocabulary.
Other important scales include the other church modes, the blues scale, the whole tone scale used by many Russian composers, pentatonic scale and the chromatic scale. Since none of these are the major or minor diatonic scales, music written exclusively with them is, by the definition above, not tonal.
Tone-centric music composed in other scale systems may be microtonal, and while microtonal music theory may draw from tonal theory, it is generally treated separately in textbooks and other works on music. However, within the tonal system, notes "between" the chromatic system are used in various contexts, including quarter tones and various effects such as portamento or glissando, where the instrumentalist moves between established notes of the diatonic scale. These are usually thought of as being for "colour" rather than harmonic function, and do not disturb the fundamental (diatonic) scale being used.
Chords are built from notes of a diatonic scale, or secondarily on chromatic notes treated as variations or embellishments of the basic scale. The identity of the scale is important in that the scale's steps used as roots determine the system of chord relationships. At any given time one scale degree is heard as the most important (the "tonic"), and the chord built on it, always a major or minor triad, is heard as the most forceful closure.

Tonality
Main article: Scale degree.
In notation, each note or degree of the scale is often designated by a Roman numeral, or, less commonly, solfege:

Roman numerals
Main article: Chord (music).
These numerals also may indicate chords which are built upon the indicated degree. This degree is then known as the root of that chord. Thus "I" describes the tonic chord, the chord built on the tonic note, at a given time. These chords are generally all triads (having three notes, built from thirds, and having a diatonic function).

The degree of a scale is both the pitch (frequency) of that note and that pitch's diatonic function (role), which is why chords are named by scale degree. Thus the notes of a chord do not have to be sounded simultaneously, and one to two notes may function as, or imply, a three (or more) note chord. Thus a chord described as "V" is based on the fifth note of the prevailing tonic scale (V-VII-II). In C Major, that would be a triad based on G, and would be the G Major triad (G-B-D). To describe a chord progression, the Roman numerals of the chords are listed. Thus IV-V-I describes a chord progression of a chord based on the fourth note of a scale, then one based on the fifth note of the scale, and then one on the first note of the scale.
Chords are then further named according to their quality or makeup, determined by the scale notes which lie a third and fifth (two thirds) above the degree a chord is built upon. Capital Roman numerals refer to the major chord, and lower-case Roman numerals refer to the minor chord. Quality is generally not as important as the chord's root.
This means that in the traditional major scale, the ii, iii and vi are minor chords, where as I, IV, V are major. The chord on the seventh note is a diminished triad and is written vii with a degree sign. Numbers attached to a chord indicate additional notes, and one of the most important chords in tonal harmony is the V7 chord, which is a four note chord that includes the fourth note of the tonic scale. The "7" refers to a note seven diatonic steps up from the fundamental note of the chord, not the seventh note of the tonic scale.

Inversion
Main article: form.
The traditional form of tonal music begins and ends on the tonic of the piece, and many tonal works move to a closely related key, such as the dominant of the main tonality (for example sonata form). Establishing a tonality is traditionally accomplished through a cadence which is two chords in succession which give a feeling of completion or rest - the most common being V7-I cadence. Other cadences are considered to be less powerful. The cadences determines the form of a tonal piece of music, and the placement of cadences, their preparation and establishment as cadences, as opposed to simply chord progressions, is central to the theory and practice of tonal music.

Form
Main article: Harmony.
Most tonality uses "functional harmony", which is a term used to describe music where changes in the predominate scale or additional notes to chords are explainable by their place in stabilizing or destabilizing a tonality. This is a complex way of saying that it is possible to explain why a particular note was included, and what that note means in relation to the tonic chord. Harmony with a large number of notes which do not have clear structural function is called "nonfunctional" harmony, which is not to imply "dysfunctional", but merely that the additional notes are not to be played or heard as restricting or advancing the harmonic progression.

Harmony
Main article: Consonance and dissonance.
In the context of tonal organization a chord or a note is said to be "consonant" when it implies stability, and "dissonant" when it implies instability. This is not the same as the ordinary use of the words consonant and dissonant. A dissonant chord is in tension against the tonic, and implies that the music is distant from that tonic chord. "Resolution" is the process by which the harmonic progression moves from dissonant chords to consonant chords and follows counterpoint or voice leading. Voice leading is a description of the "horizontal" movement of the music, as opposed to chords which are considered the "vertical".
Traditional tonal music is described in terms of a scale of notes. On the notes of that scale are built chords. Chords in order form a progression. Progressions establish or deny a particular chord as being the tonic chord. The cadence is held to be the sequence of chords which establishes one chord as being the tonic chord; more powerful cadences create a greater sense of closure and a stronger sense of key. Chords have a function when it can be explained how they lead the music towards or away from a particular tonic chord. When the sense of which tonic chord is changed, the music is said to have "changed key" or "modulated". Roman numerals and numbers are used to describe the relationship of a particular chord to the tonic chord.
The techniques of accomplishing this process, are the subject of tonal music theory and compositional practice.

Consonance and dissonance
Tonality allows for a great range of musical materials, structures, meanings, and understandings. It does this through establishing a tonic, or central chord based on a pitch which is the lowest degree of a scale, and a somewhat flexible network of relations between any pitch or chord and the tonic similar to perspective in painting. This is what is meant by tonality having a hierarchical relationship, one triad, the tonic triad, is the "center of gravity" to which other chords are supposed to lead. Changing which chord is felt to be the tonic triad is referred to as "modulation". As within a musical phrase, interest and tension may be created through the move from consonance to dissonance and back, a larger piece will also create interest by moving away from and back to the tonic and tension by destabilizing and re-establishing the key. Distantly related pitches and chords may be considered dissonant in and of themselves since their resolution to the tonic is implied. Further, temporary secondary tonal centers may be established by cadences or simply passed through in a process called modulation, or simultaneous tonal centers may be established through polytonality. Additionally, the structure of these features and processes may be linear, cyclical, or both. This allows for a huge variety of relations to be expressed through dissonance and consonance, distance or proximity to the tonic, the establishment of temporary or secondary tonal centers, and/or ambiguity as to tonal center. Music notation was created to accommodate tonality and facilitates interpretation.
The majority of tonal music assumes that notes spaced over several octaves are perceived the same way as if they were played in one octave or octave equivalency. Tonal music also assumes that scales have harmonic implication or diatonic functionality. This is generally held to imply that a note which has different places in a chord will be heard differently, and that therefore there is not enharmonic equivalency. In tonal music chords which are moved to different keys, or played with different root notes are not perceived as being the same, and thus transpositional equivalency and far less still inversional equivalency are not generally held to apply.
A successful tonal piece of music, or a successful performance of one, will give the listener a feeling that a particular chord — the tonic chord — is the most stable and final. It will then use musical materials to tell the musician and the listener how far the music is from that tonal center, most commonly, though not always, to heighten the sense of movement and drama as to how the music will resolve the tonic chord. The means for doing this are described by the rules of harmony and counterpoint (some influential theorists prefer the term "thoroughbass" instead of harmony, but the concept is the same). Counterpoint is the study of linear resolutions of music, while harmony encompasses the sequences of chords which form a chord progression.
Though modulation may occur instantaneously without indication or preparation, the least ambiguous way to establish a new tonal center is through a cadence, a succession of two or more chords which ends a section and/or gives a feeling of closure or finality, or series of cadences. Traditionally cadences act both harmonically to establish tonal centers and formally to articulate the end of sections, just as the tonic triad is harmonically central, a dominant-tonic cadence will be structurally central. The more powerful the cadence, the larger the section of music it can close. The strongest cadence is the perfect authentic cadence, which moves from the dominant to the tonic, most strongly establishes tonal center, and ends the most important sections of tonal pieces, including the final section. This is the basis of the "dominant-tonic" or "tonic-dominant" relationship. Common practice placed a great deal of emphasis on the correct use of cadences to structure music, and cadences were placed precisely to define the sections of a work. However, such strict use of cadences gradually gave way to more complex procedures where whole families of chords were used to imply particular distance from the tonal center. Composers, beginning in the late 18th Century began using chords (such as the Neapolitan, French or Italian Sixth) which temporarily suspended a sense of key, and by freely changing between the major and minor voicing for the tonic chord, thereby making the listener unsure whether the music was major or minor. There was also a gradual increase in the use of notes which were not part of the basic 7 notes, called chromaticism, culminating in post-Wagnerian music such as that by Mahler and Strauss and trends such as impressionism and dodecaphony.
One area of disagreement, going back to the origin of the term tonality, is whether, and to what degree, tonality is "natural" or inherent in acoustical phenomena, and whether, and to what degree, it is inherent in the human nervous system, or a psychological construct and, if the latter, whether it is inborn or learned, or some combination of these possibilities (Meyer 1967, 236). A viewpoint held by many theorists since the third quarter of the 19th century holds that diatonic scales and tonality arise from natural overtones (Riemann 1872, 1875, 1882, 1893, 1905, 1914–15; Schenker 1906–35; Hindemith 1937–70), following the publication in 1862 of the first edition of Helmholtz's On the Sensation of Tone (Helmholtz 1877).
There is archaeological evidence of the existence of diatonic scales in ancient times. A still playable 9,000 year old flute was found among many flutes unearthed at Jiahu, China, with 8 notes, including the octave. (Nature Journal, Sept, 1999, 1.) Assyrian cuneiform artifacts, roughly 3,500 years old described a Pythagorean tuning for the diatonic scale, and contain the oldest known written music. (Kilmer, 1976, 15-17. West, 1994.) Much older than both of these is the heavily disputed "flute" found at Divje Babe dating to 50,000 years ago, which one musicologist claims used a diatonic scale.

Effect of tonality

Atonality
History of music
Schenkerian analysis
Peter Westergaard's tonal theory