math and music
posted by Gray .
How would you go about listing all of the integer ratios? I would like to have the integers listed in ascending order by the product of each integer's numerator and the denominator. This is because in music, more "complex" ratios sound more dissonant.
Every list would exclude ratios that can be simplified (2/4, 3/9).
List A1 would include those ratios with values less than or equal to 1, and List B1 would include those ratios greater than or equal to 1.
Lists A2 and B2 would exclude ratios of 1/n and n/1 where n is a composite number. List A3 would exclude ratios with values less than 1/2. List B3 would exclude ratios with values less than 2/1. Lists A4 and B4 would use both exclusions.
I think this is what I'm aiming for: List A1 = {1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 2/3, 1/7, ...} List A2 = {1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 3/2, ...} and so on.
Finally, is there anyone out there who understands how these lists relate to music theory? Thanks!
Respond to this Question
Similar Questions

math
Something times something equals 97 Are you supposed to factor 97 as the product of integers? 
algebra
w10y12z _______ w6z5 Are those exponents like [(w^10)*(y^12)*z]/[(w^6)*(z^5)]? 
music
hi um could you help me i have to do a music assignment and i to talk to my class about a piece of music from my fave artist like what instruments are used the structure of the music and those kinds of things but im not good at music … 
Math
how do you reduce a fraction Dividde both the numerator and denominator by the largest common integer possible. Then cancel them out. For example, in the fraction 15/25, the largest integer that is divisible evenly into both numerator … 
math
there are 8 consecutive integers that add up to 31. Only two of the integers are equal. what is the greatest number for any one integer? 
recreational math, music
How would you go about listing all of the integer ratios, preferably in a spreadsheet? 
math and music
How would you go about listing all of the integer ratios? 
Math
Is i^2=1 for how many integers N is (N+i)^4 an integer? 
Algebra
the denominator of a fractio is an integer that is one greater than the numerator. A second fraction is the reciprocal of the integer that is one less than the numerator of the first fraction. If the product of the two fraction is … 
Math
Paulo withdraws the same amount from his bank account each week to pay for lunch. Over the past four weeks, he withdrew one hundred twenty dollars. Which rule best applies to determine the change in his account each week?