Probabillity and Statistics

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Probabillity and Statistics

Postby Gongchime » Thu Jun 19, 2008 10:45 am

I have two charts. One chart has the likelihood that a musical pitch will occur in "good" western melodies. Each is weighted with a number. In the key of C Major the notes are weighted like this;

C=5, D=3.5, E=2, F=4, G=4.5, A=3.5, B=4.

I have another chart with the frequency of intervals that occur within "good" western melodies. They are weighted like this;

Unison=5 (the next note is the same as the previous note)
Minor Second=5.5
Major Second=15
Minor Third=2.5
Major Third=2
Perfect Fourth=3
Tritone=0
Perfect Fifth=1.5
Minor Sixth=.125
Major Sixth=.25
Minor Seventh=.25
Major Seventh=.25
Octave=1

I want to combine this data to find out the likelihood of all the possible combinations of motion. I'm looking for the answer to all of the questions below;

What is the likelihood that C will move to D? The answer would be expressed something like C has a 24 chances out of 123 to move to D.
What is the likelihood that C will move to the E above?
what is the likelihood that C will move to the E below?
What is the likelihood that Middle C will move to F above? to the F below? to G above? to G below? to A above? to A below? to B above, to B below? to the octave above to the octave below?

but we're not finished.

What is the likelihood that D will move to the C below?
What is the likelihood that will will move to the C above?
What is the likelihood that D will stay on D?
What is the likelihood that D will move to E above? to the E below?
to F above, to the F below? to G above, to the G below? to A above, to the A below, to B above, to B below?

still not finished.

What is the likelihood that E will move to C the below? to the C above?
What is the likelihood that E will move to D above? to D below?
What is the likelihood that E will stay on E? Move to F above? F below? G above? G below, A above? A below? B above? B below? Octave above? Octave below?

Etc...

The difficulty I'm having with the question is correctly graphing the problem. I've tried several times and each time I notice something I missed before in order to get the right answer. Especially confusing to me is the Frequency of notes graph. I thought I could put the name of the pitches on the left hand side of the page with D above at the bottom since the Major second was the most important interval then mark up lines on the graph paper the appropriate number (15).

Then at the top of that write the word Unison since that is the second most important interval continuing on up in that manner. On the right hand side of the page I wrote C on the bottom across from the first item in the other graph. Then I counted up the appropriate number of lines. then wrote the next two common pitches E and G. continuing up like that.

Then I drew a line between C the pitch to the unison interval in the other graph looking for the point in-between that would show the likelihood that the pitch would stay on the same pitch based on what pitch you're on in a melody?
Is that the right way to do it?

What I want to know is when I'm looking at the melody I'm writing and I'm in the middle of writing it and, for example, I'm on the note D, then what is the likelihood that D will move to any other note?
It has the greatest chance of going back to C since D is a less important pitch and since the motion of the Major Second is more important than the motion repeating it again. But I want to know the exact percentage of every possibility.

Tall order. I know. But it's fun and interesting.

btw I'm a musician. You can hear my Asian influenced music at www.myspace.com/gongchime. Maybe it's not so bad kuz world music artist of the year in both Korea and India sing on my tune River of Stars. I've also received awards and had music placed in music libraries.
Gongchime
 
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