claim: Phoenix, Arizona is in the southwestern United States.
evidence: In music , a triad is a set of three notes -LRB- or `` pitches '' -RRB- that can be stacked vertically in thirds .. music. music. pitches. pitch ( music ). The term `` harmonic triad '' was coined by Johannes Lippius in his Synopsis musicae novae -LRB- 1612 -RRB- .. Johannes Lippius. Johannes Lippius. When stacked in thirds , notes produce triadic chords .. The triad 's members , from lowest-pitched tone to highest , are called  :. the root. root. root ( chord ). the third -- its interval above the root being a minor third -LRB- three semitones -RRB- or a major third -LRB- four semitones -RRB-. root. root ( chord ). minor third. minor third. major third. major third. major. Major chord. minor. minor chord. the fifth -- its interval above the third being a minor third or a major third , hence its interval above the root being a diminished fifth -LRB- six semitones -RRB- , perfect fifth -LRB- seven semitones -RRB- , or augmented fifth -LRB- eight semitones -RRB- .. root. root ( chord ). minor third. minor third. major third. major third. diminished fifth. diminished fifth. perfect fifth. perfect fifth. augmented fifth. augmented fifth. major. Major chord. minor. minor chord. diminished. diminished triad. augmented. augmented triad. Perfect fifths are the most commonly used interval above the root in Western classical , popular and traditional music .. music. music. root. root ( chord ). classical. classical music. popular. popular music. traditional music. traditional music. -LRB- Note  : The notes of a triad do not have to use the root as the lowest note of the chord , due to the principle of inversion .. root. root ( chord ). inversion. inversion ( music ). A triad can also use the third or fifth as the lowest note of the chord .. Inverting a chord does not change the root note . -RRB-. root. root ( chord ). Some twentieth-century theorists , notably Howard Hanson and Carlton Gamer , expand the term to refer to any combination of three different pitches , regardless of the intervals amongst them .. pitches. pitch ( music ). Howard Hanson. Howard Hanson. Carlton Gamer. Carlton Gamer. The word used by other theorists for this more general concept is `` trichord '' .. trichord. trichord. Others , notably Allen Forte , use the term to refer to combinations apparently stacked of other intervals , as in `` quartal triad '' .. Allen Forte. Allen Forte. quartal. Quartal and quintal harmony. In the late Renaissance music era , and especially during the Baroque music era -LRB- 1600 -- 1750 -RRB- , Western art music shifted from a more `` horizontal '' contrapuntal approach -LRB- in which multiple , independent melody lines were interwoven -RRB- toward chord progressions , which are sequences of chords .. music. music. Renaissance music. Renaissance music. Baroque music. Baroque music. contrapuntal. contrapuntal. The chord progression approach , which was the foundation of the Baroque-era basso continuo accompaniment , required a more `` vertical '' approach , thus relying more heavily on the triad as the basic building block of functional harmony .. chord progression. chord progression. basso continuo. basso continuo. functional harmony. Diatonic function#Functional harmony. The root tone of a triad , together with the degree of the scale to which it corresponds , primarily determine a given triad 's function .. root. root ( chord ). Secondarily , a triad 's function is determined by its quality  : major , minor , diminished or augmented .. major. Major chord. minor. minor chord. diminished. diminished triad. augmented. augmented triad. Major and minor chords are the most commonly used chord qualities in Western classical , popular and traditional music .. music. music. classical. classical music. popular. popular music. traditional music. traditional music. minor. minor chord. In standard tonal music , only major and minor chords can be used as a tonic in a song or some other piece of music .. music. music. major. Major chord. minor. minor chord. tonal music. tonal music. tonic. tonic ( music ). That is , a song or other vocal or instrumental piece can be in the key of C major or A minor , but a song or some other piece can not be in the key of B diminished or F augmented -LRB- although songs or other pieces might include these chords within the chord progression , typically in a temporary , passing role -RRB- .. chord progression. chord progression. major. Major chord. minor. minor chord. diminished. diminished triad. augmented. augmented triad. Three of these four kinds of triads are found in the major -LRB- or diatonic -RRB- scale .. major. Major chord. In popular music and 18th-century classical music , major and minor triads are considered to be consonant and stable , and diminished and augmented triads are considered to be dissonant and unstable .. music. music. classical. classical music. popular. popular music. major. Major chord. minor. minor chord. diminished. diminished triad. augmented. augmented triad. consonant. consonance ( music ). dissonant. dissonance ( music )