Relationship between fundamental and harmonics, in semitones

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I'm trying to work out the relationship between the harmonics of a note and the number of semitones that equates to.

Eg
Fundamental = 440Hz
first harmonic = 880Hz = 12 semitones
second harmonic = 1320Hz = just higher than 19 semitones (19 semitones = 1318.51022765148Hz)
third harmonic = 1760Hz = 24 semitones
etc

Is there a calculable relationship here? Basically I want to be able to work out a semitone value that a partial x needs to be detuned to reach either the fundamental or nth harmonic. I'm working in excel so ideally want to develop a formula.

Any input very much appreciated!

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Hunter wrote:I'm trying to work out the relationship between the harmonics of a note and the number of semitones that equates to.

Eg
Fundamental = 440Hz
first harmonic = 880Hz = 12 semitones
second harmonic = 1320Hz = just higher than 19 semitones (19 semitones = 1318.51022765148Hz)
third harmonic = 1760Hz = 24 semitones
etc

Is there a calculable relationship here? Basically I want to be able to work out a semitone value that a partial x needs to be detuned to reach either the fundamental or nth harmonic. I'm working in excel so ideally want to develop a formula.

Any input very much appreciated!
The overtones do not follow rationed semitones. They get "flatter and flatter" as they ascend. So you're going to have to deal with that unless you're talking about a theoretical vibrating body which is infinitely thin.

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To calculate a pitch difference D in semitones from the frequency ratio R of a given interval, you have to calculate
D = 12*log2(R)
where log2(R) means the base-2 logarithm of R.

So for example the interval from fundamental to fifth harmonic is a ratio of R = 5.
Then D = 12*log2(5) = 27.86313714 semitones
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Thanks

PaulSC wrote:To calculate a pitch difference D in semitones from the frequency ratio R of a given interval, you have to calculate
D = 12*log2(R)
where log2(R) means the base-2 logarithm of R.

So for example the interval from fundamental to fifth harmonic is a ratio of R = 5.
Then D = 12*log2(5) = 27.86313714 semitones
I think these are the droids I'm looking for. I knew you'd have an answer Paul! Now to put it into action :)

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I'll have to necro this, just to say thanks! I am doing an additive synth, and needed these since I'm using semitone values to define each partial.

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