2 – Western Music Systems – Notes
Music authorities have determined that people with a good ear can recognize and differentiate 22 frequencies within an octave. But that is at the limit. Most average people can recognise and differentiate 12 frequencies within this range. Each of these frequencies (or small range around them) is called a “note”.
Traditionally an octave was divided into these twelve notes using a system called “just” or “pure” intonation. This division tries to make the ratios of frequencies between different notes as whole numbers. So, the frequency ratio between a particular note and the seventh note from it is 2:3. Or the ratio to the fifth note is 3:4 etc. [This whole number ratio tuning was traditionally done by the ear and since the ratios are whole numbers, interference between two notes (and their harmonics) was minimal.]
However, nowadays a tuning system called equal temperament tuning (12-TET) is the prevalent one. This divides an octave into 12 equal (logarithmic) steps. This keeps the ratio of the frequencies between any two adjacent notes the same. In practical terms this is a much easier tuning system than just tuning and approximates well to just tuning.
Since an octave is the range between one frequency and its double, and since there are twelve notes within the range, the ratio between one note and its adjacent one is the twelfth root of 2. The twelve notes in an octave are named C, C# / D♭, D, D# / E♭, E, F, F#, G, G# / A♭, A, A# / B♭, B. The next octave (again starting with C) has an identical set of notes, with each note having double the frequency of the note of the same name in this octave. So, C of one octave will have double the frequency of C of the previous octave etc. Of course, the previous octave will have notes with half the frequencies. Octaves and notes are fixed in the western system by designating that the A note of the 4th octave (A4) is 440 Hz. [So A3 is 220 Hz and A5 is 880 Hz etc.] The other notes are calculated using the knowledge that the ratio between one note and its adjacent one is the twelfth root of 2.
A logarithmic measure for the interval between two notes called the cent has long been employed. The distance between two notes is 100 cents, and the distance of an octave is 1200 cents. [The frequency distance between 220 Hz to 440 Hz, from 440 Hz to 880 Hz and from 880 Hz to 1760 Hz are all equal to 1200 cents]. We said earlier that the difference in frequencies that can be detected by a good, practised human ear is around ½ percent. This is equal to around between 8 and 9 musical cents. [You would have noticed that cent is not an equal division but a logarithmic one. The human perception of sound is to a logarithmic scale. Hence cent is an appropriate measure.]
A standard piano has 88 keys (from A0 to C8) covering slightly over seven octaves (octaves 1 to 7 – C1 to B7)]. The human vocalisation range is 125 Hz to 8000 Hz. Normal humans can vocalise songs in around three octaves. Extraordinary singers (like Freddie Mercury) are known to sing in four octaves.
Visit the following pages for notes on particular elements of music.