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A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio: = An amplifier or filter may be stated to have a frequency response of ±6 dB per octave over a particular frequency range, which signifies that the power gain changes by ±6 decibels (a factor of 4 in power), when the frequency changes by a factor of 2.
An octave band is a frequency band that spans one octave (Play ⓘ).In this context an octave can be a factor of 2 [1] [full citation needed] or a factor of 10 0.301. [2] [full citation needed] [3] [full citation needed] An octave of 1200 cents in musical pitch (a logarithmic unit) corresponds to a frequency ratio of 2 / 1 ≈ 10 0.301.
A cent is a unit of measure for the ratio between two frequencies. An equally tempered semitone (the interval between two adjacent piano keys) spans 100 cents by definition. An octave —two notes that have a frequency ratio of 2:1—spans twelve semitones and therefore 1200 cents.
One octave is a factor of 2, so = decades per octave (decade = just major third + three octaves, 10/1 (Play ⓘ) = 5/4) To find out what frequency is a certain number of decades from the original frequency, multiply by appropriate powers of 10:
The third octave spans from 440 Hz to 880 Hz (span=440 Hz) and so on. Each successive octave spans twice the frequency range of the previous octave. The exponential nature of octaves when measured on a linear frequency scale. This diagram presents octaves as they appear in the sense of musical intervals, equally spaced.
An octave is the interval between one musical pitch and another with double or half its frequency. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1.
5-limit Tonnetz. Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as 2 −3 ·3 1 ·5 1 = 15/8.
The result is a pitch at a common subharmonic of the pitches played (one octave below the first pitch when the second is the fifth, 3:2, two octaves below when the second is the major third, 5:4). This effect is useful especially in the lowest ranks of the pipe organ where cost or space could prohibit having a rank of such low pitch.