ditone การใช้
- A ditone may precede or follow [ a pycnon ] in ascent or descent.
- A ditone ( or major third ) is an interval formed by two major tones.
- The size of a ditone varies according to the sizes of the two tones of which it is compounded.
- Two tones make a " ditone ", a dissonantly wide major third, ratio 81 / 64.
- The ditone differs from the just major third ( 5 / 4 ) by the syntonic comma ( 81 / 80 ).
- Two Dittons appear in the Domesday Book of 1086 and were written as " Ditone " and " Ditune ".
- The older concept of a ditone ( two 9 : 8 major seconds ) made a dissonantly wide major third with the ratio 81 : 64 ( ).
- Rarely, the term ditone is also used to indicate an interval spanning two whole tones ( for example, a major third ), or more strictly as a synonym of major third.
- In Pythagorean tuning, a major tone has a size of about 203.9 cents ( frequency ratio 9 : 8 ), thus a Pythagorean ditone is about 407.8 cents.
- Interestingly, despite its name, a semiditone ( 3 semitones, or about 300 cents ) can hardly be viewed as half of a ditone ( 4 semitones, or about 400 cents ).
- Notice that the terms " ditone " and " semiditone " are specific for Pythagorean tuning, while " tone " and " tritone " are used generically for all tuning systems.
- Following the strict definition found in Nicola Vicentino's " L'antica musica ridotta alla moderna prattica " ( 1555 ), all intervals larger than the major third ( or ditone ) are necessarily composite.
- The largest is the Pythagorean ditone, with a ratio of 81 : 64, also called a comma-redundant major third; the smallest is the interval with a ratio of 100 : 81, also called a comma-deficient major third.
- "The major third that appears commonly in the [ Pythagorean ] system ( C E, D F, etc . ) is more properly known as the Pythagorean ditone and consists of two major and two minor semitones ( 2M + 2m ).
- Thus the major third is considered not a third but a ditone, literally " two tones ", and is ( 9 : 8 ) 2 = 81 : 64, rather than the independent and harmonic just 5 : 4 = 80 : 64 directly below.
- Aristides Quintilianus ( writing probably in the 3rd century AD ) enumerates the incomposite intervals : " the smallest, so far as their use in melody is concerned, is the enharmonic diesis, followed to speak rather roughly by the semitone, which is twice the diesis, the tone, which is twice the semitone, and finally the ditone, which is twice the tone ".
- :: INCOMPOSIT Ditone of the Enharmonic Genus is the excess of a fourth tone above half a tone major, or 3??8 root 2, which is 202 ? + 4f + 17絤, or 202.00393 ? + 4f + 17絤, whose common logarithm is . 9006375.2462, and its Euler's log . = . 330076, and it contains 18.41741 major commas.
- After chapters on'litterae'( letter notation ), monochord, nine'consonant'intervals ( unison, semitone, whole tone, ditone, semiditone, diatessaron, diapente, semitone-plus-diapente, whole-tone-plus-diapente ), the Perfect System ( systema teleion ) of Greeks, musical modes ( including a chapter on their ethos ), and the composition of chant, the treatise includes one chapter most of interest to contemporary scholars : a detailed description of how to compose organum.
- As late as the 13th century the half step was experienced as a problematic interval not easily understood, as the irrational remainder between the perfect fourth and the ditone \ left ( \ begin { matrix } \ frac { 4 } { 3 } \ end { matrix } / ^ 2 } = \ begin { matrix } \ frac { 256 } { 243 } \ end { matrix } \ right ) . In a melodic half step, no tendency was perceived of the lower tone toward the upper, or of the upper toward the lower.