Cents and ratios |
Ratios with factors |
Mean tone in cents |
Under / Over |
UO, non octave & scale tree |
Quintic |
Music and virtual flowers |

Enter a single value in the
**
Scale
**
box to see successive ratio
approximations to it. Shows ratios with increasing quotients until a ratio is reached within the
specified tolerance.

You can also enter an entire scale in the
**
Scale
**
box. If there is more than one entry, only the most accurate ratio for each entry gets shown in
the
**
Ratios
**
box.
However, you can then scroll down this page to see the
successive ratio approximations for each scale degree
to see all the other
ratios found for each entry.

You can also use this applet to convert an entire scale betweenn the various notations. Enter the entire scale into
the
**
Scale
**
box as
before, then change the selection for the notation. Choose how
many
**
decimal places
**
you want to see. Values in hertz are shown with two extra decimal
places, and decimals are shown with four extra decimal places.
When converting to n-et, the tolerance is used a tenth of the
tolerance selected for the scale results. All n-ets are checked
up to 1200-et, and the best one used.

To convert to cents, just enter the scale in the selected notation and the scale in cents gets shown below.

The
**
n-et notation
**
works
like this:
**
7//17
**
means
the 7th degree of seventeen equal temperament - so this is short
for .
**
7/17 * 1200
**
cents. So - a fractional mutliple of 1200 cents.

For the
**
cents or ratios
**
use a '/' when you want to enter a ratio. All other values are understood to be in cents. So you don't need to enter the decimal point - this is just to make it quicker to enter values by hand in the applet. Note - the standard SCALA notation requires all cents values to include a decimal point.

For the ** n-et notation ** then when entering data by hand / is understood as // when n-et notation is selected. Annything else is understood as centvs.

Set the
**
tolerance
**
to the minimum difference you want between the ratio and the
cents value. Note that if you set the max quotient high, and the
tolerance low, then the calculation will be slow, - this script
isn't particularly speedy as it goes through the quotients one at
a time testing them all. Also, it is written in javascript, which
is a slow language because it is "interpreted" (each
instruction gets parsed every time it is used, rather than it all
being done at once in advance of the calculation in a separate
build step when the program gets made)..

You can show the approximations found
**
above
**
the desired value only (positive cents diffs),
**
below
**
it only,
**
both
**
(i.e. both those
sequences, interleaved - shown in order of the size of the
quotient) or the
**
closest
**
ones. The difference between both, and closest, is that with
closest the absolute values of the cents diffs keep decreasing
each time, while with both, the positive values decrease, the
negative ones do also, but sometimes a negative cents diff may be
larger than the previous positive one or vice versa.

To halt the calculation, and try again, use your browser STOP button. The calculation may well be slow if you set the tolerance low as the method used is rather inefficient. It is just one that is easy to code and works for the small ratios of most interest in scale design.

List the primes you want to appear in the ratios for the
**
Primes (or composite factors)
**
field
- e.g.
**
2 3 5 7
**
for
7-limit ratios - or if you want to see all approximations
whatever their factors, leave the primes field blank.

You can also 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. This means that three can only
be used up to the eighth power in the ratio, and three only up to
the fifth power.

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!).

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.

Entries in this field can also be composite. So for instance, if you enter 6 as a value, you will find ratios with denumerator or denumerator a multiple of 6 .

Note to programmers: You are welcome to modify this code and
copy it, and use it in your own web pages or programs - it is
free source. Use
**
View Source
**
in your browser, and cut and paste. No restrictions, and no need
to acknowledge the author anywhere including in your code - also
of course also, no warranties of fitness for any purpose.