In contrast, regular tunings have equal intervals between the strings,[20] and so they have symmetrical scales all along the fretboard. This makes it simpler to translate chords. For the regular tunings, chords may be moved diagonally around the fretboard. The diagonal movement of chords is especially simple for the regular tunings that are repetitive, in which case chords can be moved vertically: Chords can be moved three strings up (or down) in major-thirds tuning and chords can be moved two strings up (or down) in augmented-fourths tuning. Regular tunings thus appeal to new guitarists and also to jazz-guitarists, whose improvisation is simplified by regular intervals.
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As already stated, the perfect-fifths (P5) interval is the most harmonious, after the unison and octave intervals. An explanation of human perception of harmony relates the mechanics of a vibrating string to the musical acoustics of sound waves using the harmonic analysis of Fourier series. When a string is struck with a finger or pick (plectrum), it vibrates according to its harmonic series. When an open-note C-string is struck, its harmonic series begins with the terms (C,C,G,C,E,G,B♭,C). The root note is associated with a sequence of intervals, beginning with the unison interval (C,C), the octave interval (C,C), the perfect fifth (C,G), the perfect fourth (G,C), and the major third (C,E). In particular, this sequence of intervals contains the thirds of the C-major chord {(C,E),(E,G)}.[4]
Minor chords arise as the tonic notes of minor keys that share the same key signature with major keys. From the major key's I-ii-iii-IV-V-vi-viio progression, the "secondary" (minor) triads ii-iii-vi appear in the relative minor key's corresponding chord progression as i-iv-v (or i-iv-V or i-iv-V7): For example, from C's vi-ii-iii progression Am-Dm-Em, the chord Em is often played as E or E7 in a minor chord progression.[24] Among basic chords, the minor chords (D,E,A) are the tonic chords of the relative minors of the three major-keys (F,G,C):
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