Supposedly simple statistics problem

  • Context: Undergrad 
  • Thread starter Thread starter jazzmminister
  • Start date Start date
  • Tags Tags
    Statistics
Click For Summary
SUMMARY

The discussion revolves around calculating the number of classical melodies possible using a specific notation scheme for musical notes. Each melody starts with an asterisk (*) and can be followed by three types of changes: R (repeat), U (up), and D (down). Given the constraints of the problem, it is established that there are 315 possible melodies after 15 changes, based on the defined rules of combinations and permutations.

PREREQUISITES
  • Understanding of combinations and permutations in mathematics
  • Familiarity with musical notation and terminology
  • Basic knowledge of combinatorial analysis
  • Ability to interpret and analyze mathematical problems
NEXT STEPS
  • Study combinatorial mathematics to deepen understanding of permutations and combinations
  • Explore musical theory related to melody construction and notation
  • Learn about recursive functions for calculating combinations in programming
  • Investigate advanced combinatorial problems and their applications in music theory
USEFUL FOR

Mathematicians, music theorists, educators, and students interested in the intersection of mathematics and music composition.

jazzmminister
Messages
2
Reaction score
0
I am having trouble with what seems to be a simple combinations or permutations problem as follows: Melodies for more than 14,000 songs are listed according to the following scheme" The first note of every song is represented by anasterisk * and successive notes are represented by R (for repeat of previous note), U (for a note that goes up), or D (for a note that goes down).
Classical melodies are represented through the first 16 notes. With this scheme, how many classical melodies are possible?
Any help or hints on this will be appreciated.
Thanks,
jw
 
Physics news on Phys.org
Your description sounds a bit odd, since note changes can take any number of steps. However your description seems to allow only 3 possibilities (R, U, D) at each stage. In that case there are 315 possibilities after 15 changes.
 

Similar threads

Undergrad The Actual Sleeping beauty Problem
  • · Replies 45 ·
2
Replies
45
Views
6K
Graduate Differing first-principle models for Maxwell-Boltzmann statistics?
  • · Replies 44 ·
2
Replies
44
Views
5K
Undergrad Differences between left vs right actions in some group theory questions
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Atmospheric escape parametre statistics
  • · Replies 1 ·
Replies
1
Views
2K
Graduate A new hope for ST? Hold the thought of Jonathan J. Heckman
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Determining the Number of Points in the n-Space
  • · Replies 16 ·
Replies
16
Views
2K
Testing C & Python Resources for Problems in Astrophysics for upcoming CS Exam
  • · Replies 6 ·
Replies
6
Views
2K
Stochastic mathematics in application to finance
  • · Replies 29 ·
Replies
29
Views
2K
Undergrad Which version of the Kepler Problem is correct?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Hidden phase in polarization tests of Bell's inequality?
  • · Replies 49 ·
2
Replies
49
Views
6K