If the first note in the series has frequency f, then 2f is an octave, 3f is a perfect 5th above 2f, 4f is an octave above 2f, 5f is a major third above 4f, 6f is a perfect 5th above 4f, 7f is a diminished 7th above 4f and 8f is an octave above 4f (as once again it is double the frequency). This tuning is very natural for string instruments, especially fret less string instruments as the notes in a scale then correspond to placing the finger on points of the string corresponding to whole number ratios of the total string length. One begins with the natural harmonic series above a given base note, these are all the notes whose frequencies are multiples of the frequency of the first note in the series. Here I will outline three tunings, equal-tempered tuning, just tuning and Pythagorean tuning - there are many more. The main divergence, and not just of opinions but also of necessity, is the relationship between the reference tone (which can be any note one chooses) and all the other notes. Two notes an octave apart are such that the higher note has a frequency precisely double that of the lower one. Due to a clear consonance in wave forms the notion of an octave is unique and also very easy to hear. Having said this, it is also true that one can usually find the best system for a particular application.Ī tuning system is a procedure for obtaining the frequencies of all notes given the reference frequency. It may come as a surprise to many but the crazy fact is that there is no perfect tuning system in which all musical notes are perfectly in accord with the others. This is usually the frequency of the musical note A4 (or la4, in the same octave as C4 or do4) and the standard value in use today is 440Hz although various alternative definitions have been used throughout the centuries some of which are still in use, for example 432Hz. There are two distinct sources of ambiguity in the frequency of a musical note: the reference frequency and the tuning system used to determine the frequency of all notes from the reference frequency. The measure of a second is universally agreed on, the correspondence between musical notes and frequencies is not. That sounds simple, but actually it is not really simple at all. As a consequence every musical note has a corresponding frequency. This fixed universal definition requires that every so often a leap second must be added to our clocks so that their 24 hour cycle remains synchronised with the rotation of the earth.Ī frequency of 1Hz means that something oscillates once per second and of course musical notes correspond to oscillations in the pressure of air. This particular atom, energy levels and number of periods was chosen as it is relatively easy to measure and was the closest one could find to the traditional definition of a second to extremely high accuracy. The current universal definition of a second is 9,192,631,770 periods of the radiation emitted when an atom of Cs133 makes a transition between two hyperfine energy levels. Given that the precision of our understanding of the world around us requires increasingly accurate measurements it was deemed necessary to find an independent and universal definition of a second, which nevertheless is as close as possible to the traditional one. Using this definition and noting that the earth's rotation is slowing down (albeit infinitesimally) at a rate of about 1.7 milliseconds per century, we see that this is not really a precise and universal definition of a second. This is easy to understand given that 24 x 60 x 60 = 86400, and it should also be clear that there is nothing terribly special about this number as it is the result of deciding to divide the day into 24 hours each consisting of 60 minutes each of which in turn is divided into 60 seconds. Originally a second was defined as 1/86400 of a day. Frequencies are measured in units of inverse seconds, and the universally accepted measure of a second is that of the SI measurement system. We will begin with the easy part, the length of one second. This post is really just a collection of facts, easy to check with basic mathematics and a little bit of physics, about the frequencies of musical notes and the misguided trend of assigning importance to the fact that some note has a particular frequency rather than a different one.
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