I had an insight recently and (with the help of an online integrator function) solved for the function’s inverse:
x = -ln(y) + ln(sqrt(1-y^2)+1) - sqrt(1-y^2)
It’s an elegant looking broad spike.

Questions for you:
a) Any ideas on how to invert this to get y in terms of x?
b) Is there a common name or term for this function?

Thanks!

how do you figure how much to give second place and third and so on down to 10th place.

1. $15.00/hr
2. ?
3. ?
4. ?
5. ?
6. ?
7. ?
8. ?
9. ?
10. $6.00/hr

i think variance is the key but all the examples i see ask for the data set first. also i don’t know how to adjust for the $8.50/hr average.

thanks

Good luck!

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 your on in a melody? 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.