FM: Ratios in semitones

[Exhile]

What semitones go with what ratios. Im testing rhino for fm synthesis and am struggling to get the sounds i can get with other fm synths. Rhino works in semitones whereas sytrus which im used to works in ratios.

so if rhino is on 0 i take it thats a ratio of 1? and whats 2,3,4,5,6,7,8, etc

[BertKoor]

You can calculate them. Each semitome is a factor 2 ^ (1/12).
But to make it easy for you here's a little table:

Code: Select all

Semitone  Ratio
--------  --------
 -12       0.50000
 -11       0.52973
 -10       0.56123
  -9       0.59460
  -8       0.62996
  -7       0.66742
  -6       0.70711
  -5       0.74915
  -4       0.79370
  -3       0.84090
  -2       0.89090
  -1       0.94387
   0       1.00000
   1       1.05946
   2       1.12246
   3       1.18921
   4       1.25992
   5       1.33484
   6       1.41421
   7       1.49831
   8       1.58740
   9       1.68179
  10       1.78180
  11       1.88775
  12       2.00000

For more octaves you can simply multiply or divide them by two.

[Exhile]

You can calculate them. Each semitome is a factor 2 ^ (1/12).
But to make it easy for you here's a little table:

Code: Select all

Semitone  Ratio
--------  --------
 -12       0.50000
 -11       0.52973
 -10       0.56123
  -9       0.59460
  -8       0.62996
  -7       0.66742
  -6       0.70711
  -5       0.74915
  -4       0.79370
  -3       0.84090
  -2       0.89090
  -1       0.94387
   0       1.00000
   1       1.05946
   2       1.12246
   3       1.18921
   4       1.25992
   5       1.33484
   6       1.41421
   7       1.49831
   8       1.58740
   9       1.68179
  10       1.78180
  11       1.88775
  12       2.00000

For more octaves you can simply multiply or divide them by two.

so 24 = 4.0, 48 = 8.0 ?

[Urs]

36 = 8.0

[rsmus7]

48 = 16.0

[MitchK1989]

so how do you get 3 and 5?

[Exhile]

so how do you get 3 and 5?

I think 3 would be pretty close to 19 and 5 is around 27?

[DarkStar]

3 = 2.000 x 1.49831 (approx)
=> 12 semitones + 7 semitones

5 = 2.000 x 2.000 x 1.25992 (approx)
=> 12 semitones + 12 semitones + 4 semitones

etc

[BertKoor]

so how do you get 3 and 5?

If you want it more exact:

Ratio 3 = 1 octave + 7 semitones + 1.96 cents = 19.01955 semitones
Ratio 5 = 2 octaves + 4 semitones - 13.69 cents = 27.86314 semitones

You can do the conversion from ratio to semitones and vice versa in e.g. Excel with the following formula's:

Code: Select all

Cell A1 = "Ratio <-> Semitone convertor"

Cell A3 = "Ratio"       Cell B3 = where you input ratio
Cell A4 = "Semitones"   Cell B4 = LN(B3)/LN(2^(1/12))

Cell A6 = "Semitones"   Cell B6 = where you input semitones
Cell A7 = "Ratio"       Cell B7 = (2^(1/12))^B6

[MitchK1989]

wow. This is one of the most helpful threads I have ever seen on the internet (no joke). I am going to use that code to make myself a chart... ratios 1-28 or so should be enough.

Edit... Copy/Pasted your code in and it didn't work...

[michu]

http://www.kylegann.com/Octave.html

[rsmus7]

.

Edit... Copy/Pasted your code in and it didn't work...

I tried it in openoffice and it works !

[HelgeG]

Edit... Copy/Pasted your code in and it didn't work...

Remember to prefix the formulas with an equals sign so that excel understands that they are to be calculated. the formulas work.

[MitchK1989]

Edit... Copy/Pasted your code in and it didn't work...

Remember to prefix the formulas with an equals sign so that excel understands that they are to be calculated. the formulas work.

D'OH. I'm an excel noob.

Oh well, I wound up making myself a chart of all the ratios up to 32 using a ratio to cents calculator I found.

[Exhile]

Edit... Copy/Pasted your code in and it didn't work...

Remember to prefix the formulas with an equals sign so that excel understands that they are to be calculated. the formulas work.

D'OH. I'm an excel noob.

Oh well, I wound up making myself a chart of all the ratios up to 32 using a ratio to cents calculator I found.

any chance of you sending that over to me so i dont have to go through the trouble ?