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The ratio type takes its name from the fact that measurement is the estimation of the ratio between a magnitude of a continuous quantity and a unit of measurement of the same kind (Michell, 1997, 1999). Most measurement in the physical sciences and engineering is done on ratio scales.
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 measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in degree Celsius or degree Fahrenheit), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different ...
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).
The base ratio is then multiplied by a negative or positive power of 2, as large as needed to bring it within the range of the octave starting from C (from 1:1 to 2:1). For instance, the base ratio for the lower left cell ( 1 / 45 ) is multiplied by 2 6, and the resulting ratio is 64:45, which is a number between 1:1 and 2:1.
Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different measurements defined ...
Below is a comparison between the first 31 harmonics and the intervals of 12-tone equal temperament (12TET), octave displaced and compressed into the span of one octave. Tinted fields highlight differences greater than 5 cents ( 1 ⁄ 20 of a semitone), which is the human ear's " just noticeable difference " for notes played one after the other ...
Comparison of equal-tempered (black) and Pythagorean (green) intervals showing the relationship between frequency ratio and the intervals' values, in cents. Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths [ 2 ] which are " pure " or perfect , with ...