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r = root of the chord (while the root is widely used in classical music, pop music and rock music chord voicings, in jazz, the root is often omitted by the chord-playing performer(s)) ♠2 = minor second = 1 semitone (half step) above the root; 2 = major second = 2 semitones above root ♯ 2 = augmented second = 3 semitones above the root
There are two ways to show that a chord is an added tone chord, and it is very common to see both methods on the same score. One way is to simply use the word 'add', for example, C add 9. The second way is to use 2 instead of 9, implying that it is not a seventh chord, for instance, C 2.
The shifting of chords is especially simple for the regular tunings that repeat their open strings, in which case chords can be moved vertically: Chords can be moved three strings up (or down) in major-thirds tuning, [3] and chords can be moved two strings up (or down) in augmented-fourths tuning. Regular tunings thus appeal to new guitarists ...
Two other kinds of semitones are produced by 5 limit tuning. A chromatic scale defines 12 semitones as the 12 intervals between the 13 adjacent notes, spanning a full octave (e.g. from C 4 to C 5). The 12 semitones produced by a commonly used version of 5 limit tuning have four different sizes, and can be classified as follows:
Here, the first chord—stretching two octaves from D 2 to D 4 —is a diatonic (so-called white-note) cluster, indicated by the natural sign below the staff. The second is a pentatonic (so-called black-note) cluster, indicated by the flat sign; a sharp sign would be required if the notes showing the limit of the cluster were spelled as sharps.
The standard tempered fifth has a frequency ratio of 2 7/12:1 (or about 1.498307077:1), approximately two cents narrower than a justly tuned fifth. Ascending by twelve justly tuned fifths fails to close the circle by an excess of approximately 23.46 cents , roughly a quarter of a semitone , an interval known as the Pythagorean comma .
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