Audio: unison and octave (0:02)
unison and octave plays two notes in unison and then in octave on a harp. The unison and octave figure shows the score consists of the same note D4 played twice in unison followed by the notes D4 and D5 an octave apart.
Scientific pitch notation is a method for distinguishing between notes with the same name but different frequencies. It simply adds a number representing the octave to the note name. In unison and octave the notes D4 and D5 have the same name but D5 is an octave higher than D4.
An interval is a frequency ratio. The ratio is written as x:y where x and y are the frequencies of the two notes forming the interval. The ratio could be written as a fraction, x/y, but the slash symbol, /, is used for other things in music, for example, in a time signature.
Interval ratios are written as relative rather than absolute frequencies. For example, two notes with frequencies of 800Hz and 400Hz have an absolute frequency ratio of 800:400 and a relative frequency ratio of 2:1. Relative frequency ratios are shorter to write and easier to understand.
Two notes with the same pitch have a frequency ratio of 1:1. This ratio of 1:1 is the interval called unison. In unison and octave the first note is D and the second note, also D, has the same pitch. The interval D-D, is unison, and the frequency ratio is 1:1. It does not matter what the actual pitch of note D is, it happens to be 293.665Hz since you ask, the interval of unison always has the frequency ratio 1:1.
Take two identical notes, double the frequency of one of them, and a most remarkable thing happens, you get an octave.
Octave is the interval between two notes with a frequency ratio of 2:1. The frequency ratio, 2:1, defines an octave. It is the interval between one note and another which is double its frequency. For example, a note with frequency 100Hz has an octave above with frequency 200Hz, and an octave below with frequency 50Hz.
The frequency ratio of an octave, 2:1, is the simplest and most powerful ratio in music. This mathematical relationship is true of all music throughout the world and is the basis of tuning systems. It is a natural phenomenon with a scientific basis.
You may be wondering what the word octave has to do with the number 8 since the prefix, oct, means eight of something. The answer, as we will shortly find out, is that most commonly used scales contain seven notes plus the octave, making the octave the eighth note. However, the octave should really be called a twoth and not an octave to make its intrinsic twoness clear. A more cultured word would include the prefix bi, meaning two of something. Bive, for instance, to rhyme with jive.