Question

You have invented a “septatonic” scale with 7 equally spaced notes per octave (in the same sense as the equal-temperament chromatic scale, which would be “dodecatonic” with 12 equally spaced steps). What would be the frequency ratio between adjacent notes? (in other words, what is the ratio between adjacent notes in your ‘septatonic’ scale?)

0.1428

1.1041

1.0905

1.0000

1.1225

Answer 1

The octave means doubling of frequency.

With 7 equally spaced note per octave, the frquency of each note is K (a constant factor) times the frequency of the previous note.

if note 1 has a frequency f, then the frequencies of all 7 note will be

note	frequency
1	f
2	kf
3	k2f
4	k3f
5	k4f
6	k5f
7	k6f

we see that each note is one octave higher than previous note.

the next note which is actually the first note of the scale is one octave higher than note 1 i.e,

this is the frequency ratio between consecutive notes

let f = 500 Hz which is note 1

then note 2 = kf = 1.1041 x 500 = 552.05 Hz

and note 3 = k²f = (1.1041)² x 500 = 609.518 Hz

the ratio of note 2 to note is 1.1041

and the ratio of note 3 to note 2 is 1.1041