I'm not sure why you would not answer the below question. I only added my quiz question/answer because another question was posted with answers from a Course Hero tutor. I am looking for clarification on how to solve the below. I am Not TRYING to CHEAT!

I read your step-by-step explanation, and I still do not understand the equations. Where do numbers in the equations come from? For example, Q = 520*1.05946^{(-8 + -8)} I kind of get counting the half-steps, but why are there two -8s. Where does the second -8 come from? Please clarify.

Thank you,

Rachel Russey

This is the Step-by-step explanation from a question already posted and answered on Course Hero.

The values on the 4th column are the ratio to frequency to middle c. Or in simpler definition, how many half steps away from c.

i.e. F(fourth) is 5 half steps away from C; therefore the ratio is 1.05946⁵ = 1.334824 or 4/3

To count the half steps, simply count how many steps from the given to the required. i.e. C# to fifth = D, D#, E, F, F#, G(fifth) = 6 half steps

The same principle is applied to answer the ff. questions.

1a) Find the frequency if C# is raised by a fifth to G# is given by:

Q = Q₀ * 1.05946ⁿ¹⁺ⁿ²

where:

Q₀ = frequency of C# = 275

n₁ = no. of half steps from C# to fifth = 6

n₂ = no. of half steps from C# to G#= 7

Q =275* 1.05946^{(6 + 7)}

= 582.682578 or582.68 cps

The same steps will be applied to the rest.

1b) The frequency if this G# is lowered by a fourth to D# is given by:

Q = 413* 1.05946^{(-3 + -5)}

= 260.17977 or 260.18 cps

2a) The frequency if F is raised by a fifth to C is given by:

Q = 347*1.05946^{(2+ -5)}

= 291.7936 or291.79 cps

2b) The frequency if this C is lowered by a fourth to G is given by:

Q = 260*1.05946^{(5 + 7)}

= 519.9818 or 519.98 cps

3a) The frequency if B is raised by a third to F# is givenby:

Q = 491*1.05946^{(-7 + -5)}

= 245.5086 or 245.51 cps

3b) The frequency if this F# is lowered by an octave is given by:

Q = 368*1.05946⁽⁶⁾

= 520.4215 or 520.42 cps

4a) The frequency if the upper C (520) is raised by a third to E is given by:

Q = 520*1.05946^{(-8 + -8)}

= 206.3718 or206.37 cps

4b) The frequency if this E is lowered by an octave is given by:

Q = 328*1.05946⁽⁸⁾

= 520.6554 or 520.66 cps

I read your step-by-step explanation, and I still do not understand the equations. Where do numbers in the equations come from? For example, Q = 520*1.05946^{(-8 + -8)} I kind of get counting the half-steps, but why are there two -8s. Where does the second -8 come from? Please clarify.

Thank you,

Rachel Russey