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The size of an interval between two notes may be measured by the ratio of their frequencies.When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (), 2:1 (), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third).
For instance, the limit of the just perfect fourth (4:3) is 3, but the just minor tone (10:9) has a limit of 5, because 10 can be factored into 2 × 5 (and 9 into 3 × 3). There exists another type of limit, the odd limit , a concept used by Harry Partch (bigger of odd numbers obtained after dividing numerator and denominator by highest ...
An interval is said to be bounded, if it is both left- and right-bounded; and is said to be unbounded otherwise. Intervals that are bounded at only one end are said to be half-bounded. The empty set is bounded, and the set of all reals is the only interval that is unbounded at both ends. Bounded intervals are also commonly known as finite ...
Warmup (10-20 minutes) Get warm by riding at a comfortable pace. Add in some high-effort intervals of 5-10 seconds to prep the legs. Main set. 90 secs @ zone 5. 90 secs recovery (easy effort) 1 ...
A specific scale is defined by its characteristic interval pattern and by a special note, known as its first degree (or tonic). The tonic of a scale is the note selected as the beginning of the octave, and therefore as the beginning of the adopted interval pattern. Typically, the name of the scale specifies both its tonic and its interval pattern.
The major tone may be derived from the harmonic series as the interval between the eighth and ninth harmonics. The minor tone may be derived from the harmonic series as the interval between the ninth and tenth harmonics. The 10:9 minor tone arises in the C major scale between D & E and G & A, and is "a sharper dissonance" than 9:8.
Equally spaced values on a logarithmic scale have exponents that increment uniformly. Examples of equally spaced values are 10, 100, 1000, 10000, and 100000 (i.e., 10 1, 10 2, 10 3, 10 4, 10 5) and 2, 4, 8, 16, and 32 (i.e., 2 1, 2 2, 2 3, 2 4, 2 5). Exponential growth curves are often depicted on a logarithmic scale graph.
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, to check intonation, or to compare the sizes of comparable intervals in different tuning systems. For humans, a single cent is too small ...