What is an octave? It is said to be eight, but I cannot see the eight anywhere

When I searched for octave, I listened to the fact that if you take an octave band the lower cutoff is double the upper cutoff.

Where is this name octave coming from, that is, where does the figure eight show its significance in the above statement?

In the same way, if the above is clarified, I have some doubts on 1:2 and 1:3 octaves.

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It took me a while to figure out your question... You are puzzled by the fact that the latin root of "octave" implies "eight" while in signal processing terminology it refers to ratios of two, right? –  pichenettes Dec 23 '13 at 9:20
I had the similar doubt...and I thought 10 -2 =8 makes octave will do.. –  dexterdev Dec 23 '13 at 9:48
ok @pichenettes that's what really teased me octave is eight,so you mean to say it will also mean a ratio of 2 –  Shyam Dec 23 '13 at 10:19
In signal processing terminology an octave refers to a ratio of 2 or 1/2 between two frequencies. For example: A band-pass filter with a center frequency of 400 Hz is said to be "one octave above" a band-pass filter with a center frequency of 200 Hz. –  pichenettes Dec 23 '13 at 10:35
Do Re Mi Fa So La Ti Do. Eight notes: octave –  Dilip Sarwate Dec 23 '13 at 20:26

This comes from music terminology. The name "octave" comes from the fact that in the heptatonic musical scales (which are the prevalent scales in western music), the note with a 2:1 frequency ratio is the eighth note in the scale.

For example, in the C major scale (C D E F G A B C) the eighth note is one octave above / has a 2:1 frequency ratio with the tonic.

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The pitches in almost all Western music divide a 2:1 frequency ratio into 12 fairly-close to equally spaced ratios (2^(1/12) or about 1.0595), with slight variations depending on the temperament of the scale. 8 of those 12 frequency steps are whole notes in a typical major or minor scale (the other four frequency steps are sharps or flats within that scale). The 8 scale steps provides for an 8 note musical octave of scale note pitches within a DSP octave over the same 2:1 range of frequencies.

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