#include <iostream>
#include <iomanip>     //for setw and setprecision
#include <cstdlib>
#include <cmath>       //for pow
using namespace std;

//Set of organ pipes spanning one octave.
//Each pipe (except the first) is factor times as long as the previous one.
//
//Mathematicl note: the value that I put into the variable factor is a special
//number.  If you mutiply this number times itself 12 times, the product will
//be 2.  Thus
//factor * factor * factor * factor factor * factor * factor * factor
//* factor * factor * factor * factor is equal to 2.
//The last pipe in this set of 13 pipes should therefore be twice as long as the//first pipe, making a tone that is one octave deeper than that of the first
//pipe.

int main()
{
	double factor {pow(2.0, 1.0/12.0)};         //twelfth root of 2
						    
	cout << "Each pipe is " << fixed << setprecision(3) << factor
		<< " times as long as the previous one.\n\n";

	double length {100.0};                      //length of each pipe

	for (int pipe {0}; pipe <= 12; ++pipe) {
		cout << setw(2) << pipe
			<< "   " << fixed << setprecision(3) << length << "\n";

		length *= factor;     //means length = length * factor;
	}

	return EXIT_SUCCESS;
}