Dee Gayle's Question about Melodies in Facebook

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SUMMARY

The discussion centers around calculating the number of possible simple eight-note melodies using one octave without sharps or flats, totaling eight notes. The initial calculation using the Rule of Product yields \(8^8 = 16,777,216\) melodies, assuming repetition is allowed. A participant suggests that considering intervals leads to a more complex calculation, resulting in 78,364,164,096 possible melodies. The conversation highlights the importance of understanding both note selection and interval variations in melody creation.

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  • Understanding of basic combinatorial principles, specifically the Rule of Product
  • Familiarity with musical notation and the concept of octaves
  • Knowledge of intervals in music theory
  • Basic statistics concepts related to permutations and combinations
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  • Research the application of the Rule of Product in combinatorial mathematics
  • Learn about musical intervals and their impact on melody construction
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Sudharaka
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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..
 
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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.
 
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
 
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