Relationship between fundamental and harmonics, in semitones
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- KVRAF
- Topic Starter
- 2935 posts since 14 Dec, 2003 from Edinburgh
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!
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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- KVRist
- 401 posts since 29 Mar, 2006 from The Grim North (well, Yorkshire)
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- KVRian
- 1084 posts since 12 Sep, 2008 from Your basement
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.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!
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LauraMichelJarre LauraMichelJarre https://www.kvraudio.com/forum/memberlist.php?mode=viewprofile&u=158959
- KVRist
- 437 posts since 1 Sep, 2007 from Oz
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- KVRian
- 1184 posts since 13 May, 2004 from SF Bay Area, California
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
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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- KVRAF
- Topic Starter
- 2935 posts since 14 Dec, 2003 from Edinburgh
Thanks
I think these are the droids I'm looking for. I knew you'd have an answer Paul! Now to put it into actionPaulSC 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
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- KVRian
- 1262 posts since 15 May, 2002 from Finland
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.