FM Ratios to Intervals

Elektron Gear Digitone/Digitone Keys
#1

Sat down with a guitar tuner and my DN today and wrote down all the corresponding musical intervals for each whole number ratio. Hope this helps you understand what harmonics you’re adding when dialing in patches. If I made any mistakes let me know and I’ll correct this post :slight_smile:

Since the ratios don’t perfectly correspond with the pitches (I think this is an equal temperament thing?) I’ve included how far off in cents some of the intervals are. Any without are within +/- 5 cents of the actual note.

1:1 = Unison
2:1 = 1st Octave
3:1 = Fifth
4:1 = 2nd Octave
5:1 = Maj 3rd (-13 cents)
6:1 = Fifth
7:1 = Min 7th (-30.4 cents)
8:1 = 3rd Octave
9:1 = Maj 2nd
10:1 = Maj 3rd (-13 cents)
11:1 = Tritone (-47.9 cents)
12:1 = Fifth
13:1 = Min 6th (+41.3 cents)
14:1 = Min 7th (-30.4 cents)
15:1 = Maj 7th (-11 cents)
16:1 = 4th Octave

Cheers!

35 Likes
#2

Time for some Ratio P-Locks :cowboy_hat_face:

Thank you!

2 Likes
#3

I’m trying to grok this but I’m not sure what it applies to. Each different operator? C to A value?

#4

It applies to any pair of operators A-C or B1-B2

Setup one of the pairs with the ratios in the list (start with fifth or octaves as it’s easy to hear).

X-Y slider all the way left or right depending on what pair you are listening to.

Then experiment with blending intervals on each pair by placing the x-y centre and choosing an appropriate algo that lets you blend/hear distinct pairs. (Algo 7 is your friend, turn down all envelope levels on syn2 so you can hear just the intervals).

3 Likes
#5

Very cool idea - going to experiment with this for some house stab chords

#6

Works a treat - especially when you apply a bit of feeeback too and experiment with the harmonic shapes - then add chord mode on top for extra thickness :+1:t3:

Turn down your levels though - it gets hot quick.

#7

@plusone are you sure about the second operators in those ratios? I thought n:1, where n=1…16, is just the overtone series, and that, for example, 3:2 is the frequency ratio corresponding to a perfect 5th and 5:4 to a major 3rd.

#8

That’s getting screenshotted, for sure. Thanks! Especially handy to know the cents needed to tune them to actual notes.

1 Like
#9

Nice! Although a Fifth is not dead on 3:1 (or 1.5) either, see this chart for interval ratios:

image
image800×453 129 KB

You could achieve a bunch of these by using the ratio offsets on Digitone. (Which didn’t exist when this thread was created)

Another way to think of it is that the ratios (as in the parameters) are really just multiplicators of the base frequency - usually the MIDI note being played. So if a ratio of 1 is C, then 1.4983 is a G - you’ve multiplied C (e.g 261.625[…] Hz for a middle C) with 1.4983

I find this stuff extremely fun - it’s actually how I came up with the concept for the Chord machine in Cycles.

22 Likes
1.333 FM Ratio