#  2.  1.  2. ../robertwalker/ratios_with_factors Show tree


Find all the best ratios for a scale in cents

Scale in cents, or ratios to convert to cents first

Max quotient Precision Tolerance at which to stop calc. cents

upper lower both closest

decimal value (for 2nd cents entry if more than one)

Primes (or composite factors)

Ratios

Ratios as cents

Cents diffs

Enter a single value in cents, to see succesive approximations to it.

Alternatively, enter a scale, and then the most accurate approximation will be shown for each entry in the scale.

Alternatively, enter values as ratios, e.g. to find 7 limit approximations to 11 limit ratios etc..

Use the browser stop button if you need to halt the calculation and try again.

List all the primes you want to use as factors, or if you want to see all successive approximations, leave the primes field blank.

To set a maximum power for a prime, do it like this: "2^8 3^5" to set max powers of 2^8 and 3^5.

To exclude a prime, show it as a negative number. E.g. use -7 to search for all numbers except those divisible by 7. This can be combined with the positive primes, e.g. use 3 -9 to allow any multiple of 3, except for those that are a multiple of 9 (not sure why one would want to do it, but it comes for free!).

The entries in the factors field can also be composite.

By way of example, if you enter 6 as a value, you will find ratios with denumerator or denumerator a multiple of 6 .

 

All the best ratios for each degree of the scale (degree 0 - first note in the scale)

Ratios for degree 0

Ratios as cents

Cents diffs

Ratios for degree 1

Ratios as cents

Cents diffs

Ratios for degree 2

Ratios as cents

Cents diffs

Ratios for degree 3

Ratios as cents

Cents diffs

Ratios for degree 4

Ratios as cents

Cents diffs

Ratios for degree 5

Ratios as cents

Cents diffs

Ratios for degree 6

Ratios as cents

Cents diffs

Ratios for degree 7

Ratios as cents

Cents diffs

Ratios for degree 8

Ratios as cents

Cents diffs

Ratios for degree 9

Ratios as cents

Cents diffs

Ratios for degree 10

Ratios as cents

Cents diffs

Ratios for degree 11

Ratios as cents

Cents diffs

Ratios for degree 12

Ratios as cents

Cents diffs

Ratios for degree 13

Ratios as cents

Cents diffs

Ratios for degree 14

Ratios as cents

Cents diffs

Ratios for degree 15

Ratios as cents

Cents diffs

Ratios for degree 16

Ratios as cents

Cents diffs

Ratios for degree 17

Ratios as cents

Cents diffs

Ratios for degree 18

Ratios as cents

Cents diffs

Ratios for degree 19

Ratios as cents

Cents diffs

Ratios for degree 20

Ratios as cents

Cents diffs

Ratios for degree 21

Ratios as cents

Cents diffs

Ratios for degree 22

Ratios as cents

Cents diffs

Ratios for degree 23

Ratios as cents

Cents diffs

Ratios for degree 24

Ratios as cents

Cents diffs

Ratios for degree 25

Ratios as cents

Cents diffs

Ratios for degree 26

Ratios as cents

Cents diffs

Ratios for degree 27

Ratios as cents

Cents diffs

Ratios for degree 28

Ratios as cents

Cents diffs

Ratios for degree 29

Ratios as cents

Cents diffs

Ratios for degree 30

Ratios as cents

Cents diffs

Ratios for degree 31

Ratios as cents

Cents diffs