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The harmonic seventh interval, also known as the septimal minor seventh, [2] [3] or subminor seventh, [4] [5] [6] is one with an exact 7:4 ratio [7] (about 969 cents). [8] This is somewhat narrower than and is, "particularly sweet", [ 9 ] "sweeter in quality" than an "ordinary" [ 10 ] just minor seventh , which has an intonation ratio of 9:5 ...
Comparison between tunings: Pythagorean, equal-tempered, quarter-comma meantone, and others.For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fifths; as in each of these tunings except just intonation all fifths are of the same size, the tunings appear as straight lines, the slope indicating the relative tempering with respect to ...
In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 ( Play ⓘ ), 1.5, and may be approximated by an equal tempered perfect fifth ( Play ⓘ ) which is 2 7/12 (about 1.498).
Interval graphs are chordal graphs and perfect graphs. They can be recognized in linear time, and an optimal graph coloring or maximum clique in these graphs can be found in linear time. The interval graphs include all proper interval graphs, graphs defined in the same way from a set of unit intervals.
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).
When one contrasts this with a dissonant interval such as a tritone (not tempered) with a frequency ratio of 7:5 one gets, for example, 700 − 500 = 200 (1st order combination tone) and 500 − 200 = 300 (2nd order). The rest of the combination tones are octaves of 100 Hz so the 7:5 interval actually contains four notes: 100 Hz (and its ...
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There is no 'interval class 7' therefore, since counting down five semitones can describe the perfect fifth more parsimoniously that counting up seven semitones can. A visual way to do determine an unordered pitch-class interval is to place the pitch-classes on a clockface and measure clockwise or counter-clockwise, whichever distance is smaller.