To find how many tones there are in an octave we are looking for the value of x such that ( 9 8 )x =2 then
xlog 9 8 =log2,x= log2 log9/8 =5.8849492

to 8 significant figures.

To find the number of thirds in an octave we are looking for the value of y such that ( 5 4 )y =2. Observe that:
( 5 4 )2 =1.5625, ( 5 4 )3 =1.953125, ( 5 4 )4 =2.4414063

and hence 3<y<4 and y3.1. Using logs
ylog 5 4 =log2,y= log2 log5/4 =3.1062837

to 8 significant figures.

The comparison of scales is given in the following table:
C D E F G A B C
Equal tempered scale 0 200 400 500 700 900 1100 1200
Pythagorean scale 0
1200*(log9/8)/log 2
204
1200*(log81/64)/log 2
408
498 702 906 1110 1200
Just intonation 0
1200*(log9/8)/log 2
204
1200*(log5/4)/log 2
386
498 702 884 1088 1200