MHB Dee Gayle's Question about Melodies in Facebook

[Sudharaka]

Dee Gayle on Facebook writes:

HELP! How many simple eight note melodies are possible using only 1 octave with no sharps/flats (8 notes)? Explain each step and show the calculation.

the answer should be in the billions..I believe the first part is simply 8^8 but I don't know what else I need to multiply to come up with the correct answer..

 

[Sudharaka]

Hi Dee, :)

Yes for the first choice you have 8 notes to choose from, for the second note you have again 8 notes to choose from and so on. So from the Rule of Product we get, \(8^8=16777216\). Here we are assuming that we are only playing one note at a time and that repetition of notes are okay.

 

[Deeva]

Hmmmm, I thought the answer would me more complicated than that, because 8 notes with 12 intervals = 78,364,164,096 (according to research online), so I assumed since there are only 4 less intervals, my answer should also be in the billions. Also, the subject is statistics. Thanks