diff options
| -rw-r--r-- | index.html | 28 |
1 files changed, 15 insertions, 13 deletions
@@ -457,22 +457,24 @@ </p> <p> - Tuning systems must weigh the harmony of pure intervals against - musical versatility. A Pythagorean tuning system made from pure - fractions will include many different "fifths" and "thirds" at - different points in the scale, which makes each musical key sound - highly distinctive. Some intervals are extremely dissonant and harsh, - rendering certain keys unplayable. + Tuning systems must weigh the purity of thirds and fifths. A + Pythagorean tuning system made from pure fractions will include many + different "fifths" and "thirds" at different points in the scale, + especially when using basic ratios to determine a 12-tone scale. Each + musical key sounds highly distinctive, and some intervals may be + considered dissonant or harsh. </p> <p> - 12-tone equal temperament enables musicians to play in any key by - bending all of the notes slightly out of tune. This process invokes - irrational numbers, and creates in-between intervals which do not - exist anywhere in the Lambdoma, no matter how far out you go. - Equal-tempered semitones are separated by a ratio of the 12th root of - 2 (1:<super>12</super>√2). Irrationals are real numbers, and these can - only be approximated by fractions made up of natural numbers. + In a sense, 12-tone equal temperament "bends" all of the notes such + that the fifths are more consisent, making it easier to modulate + between keys, though other intervals (like thirds) are far from a pure + interval. This process invokes irrational numbers, and creates + in-between intervals which do not exist anywhere in the Lambdoma, no + matter how far out you go. Equal-tempered semitones are separated by a + ratio of the 12th root of 2 (1:<super>12</super>√2). Irrationals are + real numbers, and these can only be approximated by fractions made up + of natural numbers. </p> <p> |