FM ratios in relation to scales?

Was playing around with FM synthesis today to kind of back up my efforts to study music theory, and I got kind of confused about the relationship between fm ratios and notes / scales.

I used a sine wave operator (ratio of 1.0000) as the root note and stacked four more sine wave operators at the 3rd (ratio 1.2599), 5th (ratio 1.4983), 7th (ratio 1.8877), and 12th intervals (ratio 2.0000). The result was fine, everything sounded clean as expected. Then I imported a midi file with a few harmonies of a guitar track I was noodling around with and tried playing it with the above FM setup and it sounded pretty bad.

The first harmony were the notes F#5 / A5, both played at the same time like a two note chord I suppose you could say. When the notes are played together using just the root operator (1.0000) they sound fine. When they are played together and the 3rd, 5th, 7th, and 12th intervals get introduced they sound dissonant. However when the notes are played in isolation with the 3, 5, 7, & 12 intervals they sound fine again.

My music theory knowledge is pretty limited and I’m trying to understand why this is? Is it because while F#5 and A5 sound good together with just the root operator, their individual harmonies on 3, 5 , 7, & 12 do not and so clash causing dissonance?

If this is right then how do you use FM synthesis to create sounds that can be played using chords without clashing harmonics? Or is FM really just for creating big thick sounds with harmonics that are played using only single notes?

Maybe space out your harmonic intervals frequencies more, as they are in the harmonic series, rather than squashed into one octave…might sound better with FM

I believe the true answer lies within Adlib Tracker II’s 'frequency data multiplier’

If you open adlibtracker2. press ctrl+E, then arrow key down a few times, you can see within adlibtracker2 FM instrument editor, the following (its how harmonics are added to FM instruments)…

FREQUENCY DATA MULTIPLIER

1octave below ( x 0 .5 )
at the voices specified frequency ( x1 )
1 octave above ( x 2 )
1 octave and a 5th above ( x 3 )
2 octaves above ( x4 )
2 octaves and a Major 3rd above ( x 5 )
2 octaves and a 5th above ( x 6 )
2 octaves and a minor 7th above ( x 7 )
3 octaves above ( x 8 )
3 octaves and a Major 2nd above ( x 9 )
3 octaves and a Major 3rd above ( x 10 )
3 octaves and a 5th above ( x 12 )
3 octaves and a Major 7th above ( x 15 )

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Without the knowledge of the mathematics behind it, is it possible that the FM being used musically is actually PM (Phase Modulation)? That being said, I can understand why the FM you’re creating is not working, and that would be due to the extra harmonics that are clashing.

Rather, they’re not clashing - it’s dissonance caused by their distance from the original note. And maybe @Garrett_Wang is onto something here - the harmonic series seem to be far above the original note - that may be why. You ask a great question @Redman, now my interest is piqued!

Yeah now that I think about it’s gotta be the relationship of the harmonics of the individual notes to one another. The intervals of F#5 don’t fit harmonically with the intervals of A5. I was basically trying to stack a scale starting at F#5 on top of another scale starting at A5 using the same ratios for both and it doesn’t fit.

Time to hit books again.

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I guess it depends if the harmonics are from within the FM wave itself or from stacking.

F#5 to A5 is 3 semitones, a minor 3rd so it should be a nice sounding harmonic interval if it is just a sine wave at F#5 and another sine wave at A5 becuase pure sine waves only contain the fundamental frequency and have no other harmonics within them.

Maybe the F#5 and the A5 are clashing because of the harmonics which are already inside your FM waveforms…but every note on pretty much any traditional instrument has the entire harmonic series within it and you can do a nice sounding minor third with those instruments, so maybe your FM waves have some inharmonic, dissonant stuff going on inside.

To create the FM waves with nice harmonics in them the adlibtracker2 frequency data multiplier ratios about will give nice results…its the harmonic series.

FM is weird because the harmonics are produced by multiplying one sine by another, by another (depends on number of operators) instead of adding sines to each other…there is a modulator sine which the carrier sine is multiplied by, or thats my understanding of it anyway…FM is some crazy shit…I think it is like ‘every point in the modulator sine’ x ‘everypoint in the carrier sine’…the resulting waveform can then be used to modulate yet another sine and so on…but the FM waves have harmonics in them already, often clangy and dissonant…thats why they are good for cymbals and hihats