When an octave is divided into twelve equal steps, a chromatic scale results. The ratios between sucessive notes is
constant.
IC C# D D# E F F# G G# А A# B с
261.6 277.2
293.6
329.6 349.2 370.0 392.0
1440 466.1 493.8 523.2
Determine the missing frequency for G# and D# using the ratio 1.0595. Round to the nearest tenth. What is the ratio
of frequencies between G# and D#? Would these two notes be consonant or dissonant?
4
1.338
consonant
31
a.
b.
3
1.338
41
consonant
c.
14
1.338
4
dissonant
d.
1.33
4
3
dissonant

The missing frequencies for G# and D# in the given equal temperament octave is 311.1 and 415.3 respectively. The ratios of frequencies between G# and D# is 1.33.

What is an equal temperament octave?

The equal tempered scale is the common musical scale used at present, used for the tuning of pianos and other instruments of relatively fixed scale. It divides the octave into 12 equal semitones. The ratio between successive notes is constant and it is 1.0595.

With reference to the image attached in the question,

Since we know that ratio between successive notes is 1.0595.

This implies,

[tex]\frac{C\#}{C} = \frac{277.2}{261.6} = 1.0595\\\\[/tex]

Or we can say that, C# = 1.0595C

Similarly,

D# = 1.0595D = 1.0595 * 293.6 = 311.1

G# = 1.0595G = 1.0595 * 392 = 415.3

The ratios of frequencies between G# and D# = [tex]\frac{G\#}{D\#} = \frac{415.3}{311.1} = 1.33 = \frac{4}{3}[/tex]

Learn more about equal temperament octave here

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