1- a basic cause or idea.
2- the root of a number is another number that, when multiplied by itself a particular number of times, equals that number. For example, 3 is the square root of 9 and the cube root of 27.
3- the note that forms the base of a chord in music
Called also fundamental note, generator, and ground note. (1) A note which besides its own sound gives overtones or harmonics. (2) That note from amongst whose overtones any chord may be selected, i.e., the chord of CGE, is produced from the vibration of the lowest note C, therefore C is said to be the root of this chord.
An attempt to reduce chords to their roots forms the chief part of many treatises on harmony, but almost insuperable difficulties are met with in consequence of certain overtones being omitted in our scale and other sounds being introduced which can only be obtained by a minute subdivision of the monochord. The flat seventh and the eleventh of nature are unused, and various notes are arbitrarily inserted in the modern scale in order to obtain more or less of temperament. Some authors derive all their chords, or rather all those called fundamental (which constitute but a very small number of the chords actually in use), from three roots - the tonic, subdominant, and dominant. Others, again, insist on only two roots, the tonic and dominant. Not a few modern musicians use the word root without reference to any mathematical laws, and only as describing a note on which, when either expressed or implied, a chord is built up. [A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]
In music theory, the concept of root is the idea that a chord can be represented and named by one of its notes. It is linked to harmonic thinking—to the idea that vertical aggregates of notes can form a single unit, a chord. It is in this sense that one speaks of a "C chord" or a "chord on C"—a chord built from "C" and of which the note (or pitch) "C" is the root. When a chord is referred to in Classical music or popular music without a reference to what type of chord it is (either major or minor, in most cases), it is assumed a major triad, which for C contains the notes C, E and G. The root needs not be the bass note, the lowest note of the chord: the concept of root is linked to that of the inversion of chords, which is derived from the notion of invertible counterpoint. In this concept, chords can be inverted while still retaining their root.
In tertian harmonic theory, that is in a theory where chords can be considered stacks of third intervals (e.g. in common practice tonality), the root of a chord is the note on which the subsequent thirds are stacked. For instance, the root of a triad such as C Major is C, independently of the vertical order in which the three notes (C, E and G) are presented. A triad can be in three possible positions, a "root position" with the root in the bass (i.e., with the root as the lowest note, thus C, E, G or C, G, E, from lowest to highest notes), a first inversion, e.g. E, C, G or E, G, C (i.e., with the note which is a third interval above the root, E, as the lowest note) and a second inversion, e.g. G, C, E or G, E, C, in which the note that is a fifth interval above the root (G ) is the lowest note.
Regardless of whether a chord is in root position or in an inversion, the root remains the same in all three cases. Four-note seventh chords have four possible positions. That is, the chord can be played with the root as the bass note, the note a third above the root as the bass note (first inversion), the note a fifth above the root as the bass note (second inversion), or the note a seventh above the root as the bass note (third inversion). Five-note ninth chords know five positions, etc., but the root position always is that of the stack of thirds, and the root is the lowest note of this stack [see also Factor (chord]. Wikipedia, Root (chord)
The System of Musical Sounds might be sketched as follows : - Three different notes having the simplest relations to each other, when combined, form a chord; and three of these chords, the one built up above the other, form the system.
Three times three are nine; this would give nine notes; but as the top of the first chord serves for the root of the second one, and the top of the second for the root of the third, in this way these three chords of three notes each are formed from seven different notes.
The middle one of these three chords is called the tonic; the chord above is called the dominant; and the chord below is called the subdominant. The order in which these three chords contribute to form the octave scale is as follows : - The first note of the scale is the root, of the tonic; the second is the top of the dominant; the third is the middle of the tonic; the fourth is the root of the subdominant; the fifth is the top of the tonic; the sixth is the middle of the subdominant; the seventh is the middle of the dominant; and the eighth, like the first, is the root of the tonic.
In the first six chords of the scale the tonic is the first of each two. The tonic chord alternating with the other two produces an order of twos, as - tonic dominant, tonic subdominant, tonic subdominant. The first three notes of the octave scale are derived from the root, the top, and the middle of the tonic dominant and tonic; the second three are derived from the root, top, and middle of the subdominant, tonic, and subdominant. The roots, tops, and middles of the chords occurring as they do produce an order of threes, as - root, top, middle; root, top, middle. The first, third, fifth, and eighth of the scale are from the tonic chord; the second and seventh from the dominant; and the fourth and sixth from the subdominant. In the first two chords of the scale the tonic precedes the dominant; in the second two, the subdominant; and in the third two the tonic again precedes the subdominant; and as the top of the subdominant chord is the root of the tonic, and the top of the tonic the root of the dominant, this links three chords together by their roots and tops. The second chord has the top of the first, the third has the root of the second, the fourth has the root of the third, the fifth has the top of the fourth, and the sixth has the root of the fifth; and in this way these successive chords are woven together. The only place of the octave scale where there are two middles of chords beside each other is at the sixth and seventh. The seventh note of the octave scale is the middle of the dominant, and the sixth is the middle of the subdominant. These two chords, though both united to the tonic, which stands between them, are not united to each other by having a note in common, inasmuch as they stand at the extremities of the system; and since they must be enabled to succeed each other in musical progression, Nature has a beautiful way of giving them a note in common by which to do so - adding the root of the subdominant to the top of the dominant, or the top of the dominant to the root of the subdominant, and this gives natural origin to compound chords. The tonic chord, being the centre one of the three chords, is connected with the other two, and may follow the dominant and subdominant; and either of these chords may also follow the tonic; but when the dominant follows the subdominant, as they have no note in common, the root of the subdominant is added to the dominant chord, and this forms the dominant seventh; and when the subdominant follows the dominant, the top of the dominant is added to the subdominant, and this forms the subdominant sixth. The sixth and seventh of the octave scale is the only place where these two compound chords are positively required; but from their modifying and resolvable character they are very generally used. When the dominant is compounded by having the root of the subdominant, its specific effect is considerably lower; and when the subdominant is compounded by having the top of the dominant, its specific effect is considerably higher. In the octave scale the notes of the subdominant and dominant chords are placed round the notes of the tonic chord in such a way as to give the greatest amount of contrast between their notes and the tonic notes. In the tonic chord the note which has the greatest amount of specific gravity is its root; and in the octave scale it has below it the middle and above it the top of the dominant, the two notes which have the greatest amount of specific levity. Again, in the tonic chord, the top has the greatest amount of specific levity; and in the octave scale it has above it the middle and below it the root of the subdominant - the two notes which have the greatest amount of specific gravity. The third note of the scale, the middle of the tonic chord, is the centre of the system, and is the note which has the least tendency either upwards or downwards, and it has above it the root of the subdominant, the note which has the greatest amount of specific gravity, and it has below it the top of the dominant, the note which has the greatest amount of specific levity. Thus the root of the subdominant is placed above, and the top of the dominant below, the centre of the system; the specific gravity of the one above and in the specific levity of the one below cause them to move in the direction of the centre. [Scientific Basis and Build of Music, pages 96-98]