Main article:Added tone chord

Suspended chord(sus2) and added tone chord (add9) both with D (ninth=second), distinguished by the absence or presence of the third (E).[34]An added tone chord is a triad chord with an added, non-tertiannote, such as the commonly added sixth as well as chords with an added second (ninth) or fourth (eleventh) or a combination of the three. These chords do not include "intervening" thirds as in an extended chord. Added chords can also have variations. Thusmadd9,m4andm6are minor triads with extended notes.

Sixth chordscan belong to either of two groups. One is first inversion chords and added sixth chords that contain a sixth from the root.[35]The other group is inverted chords in which the interval of a sixth appears above a bass note that is not the root.[36]The major sixth chord (also called,sixthoradded sixthwith the chord notation6, e.g., "C6") is by far the most common type of sixth chord of the first group. It comprises a major triad with the addedmajor sixthabove the root, common in popular music.[7]For example, the chord C6 contains the notes C-E-G-AIn the 1897 workPaul Dukas'sThe Sorcerer's Apprentice, we hear a rising repetition in fourths, as the tireless work of out-of-control walking brooms causes the water level in the house to "rise and rise". Quartal harmony in Ravel'sSonatineandMa mre l'oyewould follow a few years later.

20th- and 21st-century classical music[edit]Composers who use the techniques of quartal harmony includeClaude Debussy,Francis Poulenc,Alexander Scriabin,Alban Berg,Leonard Bernstein,Arnold Schoenberg,Igor Stravinsky, andAnton Webern(Herder 1987, 78).

Schoenberg[edit]Arnold Schoenberg'sChamber Symphony Op. 9(1906) displays quartal harmony. The work begins not from tonal harmony, but instead begins with a fictitious[clarification needed]tonal centre: the first measures construct a five-part fourth chord with the notes C F B E Adistributed over several instruments. The composer then picks out this vertical quartal harmony in a horizontal sequence of fourths from the horns, eventually leading to a passage of triadic quartal harmony (i.e., chords of three notes, each layer a fourth apart).[citation needed]

Six-note horizontal fourth chord in Arnold Schoenberg's Chamber Symphony Op. 9

Vertical quartal-harmony in the opening measures of Arnold Schoenberg's Chamber Symphony Op. 9

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Schoenberg was also one of the first to write on the theoretical consequences of this harmonic innovation. In hisTheory of Harmony(Harmonielehre) of 1911 he wrote: "The construction of chords by superimposing fourths can lead to a chord that contains all the twelve notes of the chromaticscale; hence, such construction does manifest a possibility for dealing systematically with those harmonic phenomena that already exist in the works of some of us: seven, eight, nine, ten, eleven, and twelve-part chords... But the quartal construction makes possible, as I said, accommodation of all phenomena of harmony" (Schoenberg 1978, 406407). Other examples of quartal harmony appear in Schoenberg'sString Quartet No. 1.

augmented sixth chord resolves to) or to a tonic chord in second inversion (a tonic triad with the fifth doubled for the same purpose). In this case, the tonic note of the key is included in the chord, sometimes along with an optional fourth note, to create one of the following (illustrated here in the key of C major):

Italian augmented sixth: A, C, F French augmented sixth: A, C, D, F German augmented sixth: A, C, E, FThe augmented sixth family of chords exhibits certain peculiarities. Since they are not based on triads, as are seventh chords and other sixth chords, they are not generally regarded as having roots (nor, therefore, inversions), although onere-voicingof the notes is common (with the namesake interval inverted to create a diminished third).[37]The second group of sixth chords includes inverted major and minor chords, which may be calledsixthchords in that thesix-three(6/3) andsix-four(6/4) chords contain intervals of a sixth with the bass note, though this is not the root. Nowadays this is mostly for academic study or analysis (see figured bass) but theneapolitan sixth chordis an important example; a major triad with a flat supertonic scale degree as its root that is called a "sixth" because it is almost always found in first inversion. Though a technically accurate Roman numeral analysis would be II, it is generally labelled N6. In C major, the chord is notated (from root position) D, F, A. Because it uses chromaticallyaltered tonesthis chord is often grouped with the borrowed chords (see below) but the chord is not borrowed from the relative major or minor and it may appear in both major and minor keys.