tends to" be considered to "sound serious or melancholic," at least to contemporary Western ears. Minor keys are sometimes said to have a more interesting, possibly darker sound than plain major scales. Harry Partch considers minor as, "the immutable faculty of ratios, which in turn represent an immutable faculty of the human ear." The minor key and scale are also considered less justifiable than the major, with Paul Hindemith calling it a "clouding" of major, and Moritz Hauptmann calling it a "falsehood of the major". Changes of mode, which involve the alteration of the third, and mode mixture are often analyzed as minor changes unless structurally supported because the root and overall key and tonality remain unchanged. This is in contrast with, for instance, transposition. Transposition is done by moving all intervals up or down a certain constant interval, and does change the key but not the mode, which requires the alteration of intervals. The use of triads only available in the minor mode, such as the use of A-major in C major, is relatively decorative chromaticism, considered to add color and weaken the sense of key without entirely destroying or losing it. Intonation and tuning Musical tuning of intervals is expressed by the ratio between the pitches' frequencies. Simple fractions can sound more harmonious than complex fractions; for instance, an octave is a simple 2:1 ratio and a fifth is the relatively simple 3:2 ratio. The table below gives approximations of a scale to ratios that are rounded to be as simple as possible. {| class="wikitable" |- ! C !! D !! E !! F !! G !! A !! B !! C |- | 1 |||||||||||||| 2 |} In just intonation, a minor chord is often (but not exclusively) tuned in the frequency ratio 10:12:15 (). In 12-tone equal temperament (12-TET), which is now the most common tuning system in the West, a minor chord has 3 semitones between the root and third, 4 between the third and fifth, and 7 between the root and fifth. In 12-TET, the perfect fifth (700 cents) is only about two cents narrower than the just-tuned perfect fifth (3:2, 702.0 cents), but the minor third (300 cents) is noticeably (about 16 cents) narrower than the just minor third (6:5, 315.6 cents). Moreover, the minor third (300 cents) more closely approximates the 19-limit (Limit (music)) minor third (19:16 , 297.5 cents, the nineteenth