MHB Dee Gayle's Question about Melodies in Facebook

  • Thread starter Thread starter Sudharaka
  • Start date Start date
Click For Summary
The discussion centers on calculating the number of simple eight-note melodies using one octave without sharps or flats. The initial calculation suggests that with repetition allowed, the total combinations are 8^8, resulting in 16,777,216 melodies. However, a participant notes that considering intervals could lead to a much larger figure, approximately 78 billion. The conversation highlights the difference between counting notes and considering musical intervals in melody creation. The topic emphasizes the complexity of melody generation beyond simple note selection.
Sudharaka
Gold Member
MHB
Messages
1,558
Reaction score
1
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..
 
Mathematics news on Phys.org
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
 
Last edited:

Thread 'Significant figures for inherently bound values'

I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...
View full post »

Similar threads

MHB Multiplication of Fractions (Destiny C Sweet's Question on Facebook)
  • · Replies 1 ·
Replies
1
Views
2K
MHB Marie's Question from Facebook about Square Roots
  • · Replies 6 ·
Replies
6
Views
2K
MHB Jordan's Question from Facebook
  • · Replies 1 ·
Replies
1
Views
2K
MHB Approximating Trig Values using the Unit Circle
  • · Replies 11 ·
Replies
11
Views
3K
I Problem calculating Li-7 neutron - induced nuclear reaction
  • · Replies 10 ·
Replies
10
Views
2K
I Karatsuba multiplication implementation question
  • · Replies 3 ·
Replies
3
Views
2K
MHB Levels of Measurement, Basic OLS Regression Questions
  • · Replies 1 ·
Replies
1
Views
2K
Wavelength to Frequency Relationship in Musical Notes
  • · Replies 11 ·
Replies
11
Views
5K
I Find an explicit formula for this n-sum problem
  • · Replies 7 ·
Replies
7
Views
3K
Comp Sci How Comprehensive Should an Undergraduate Explanation of MPLS Be?
  • · Replies 1 ·
Replies
1
Views
1K