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Topic: Partials - harmonic, or otherwise?

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  1. #1

    Partials - harmonic, or otherwise?

    I'm a bit confused about something. We have fundamentals, overtones, and partials, and all of it is confusing me.

    A fundamental is really just a note that you start on, right? Ok, but if you're talking about an instrument - say, a C trumpet - wouldn't the 'fundamental' of this instrument be C?

    I understand that with partials, it's (at least sometimes) talking about the harmonic series. You start with the fundamental note, then the 'overtone' is one octave higher... and then the fundamentals begin. Or something like that. But my question is about if 'partials' are strictly harmonics talk, and not about regular notes.

    Another thing is how I've been reading about orchestration, and for example, they're talking about different instruments and the range they're scored for. Here are a couple quotes:

    (regarding a trumpet) Baroque composers drew on pitches up to the sisteenth partial of the harmonic series.

    (regarding a trombone) - The notes from Eb downward are weak and sound quite poor; the fundamental or pedal tones are not really feasible on this instrument. Therefor, the first playable note of each series are the second partials.

    Regarding the trumpet quote - do they mean they didn't use harmonics that were above the sixteenth 'partial' of a harmonic, or pitches all together -from the lowest note possible on the instrument-?

    Regarding the trombone - I seriously have no idea. The notes start on the 2nd partial? I dunno.


    If someone can give me a hand with this I'd appreciate it. It's been bugging me for quite a while.

  2. #2

    Re: Partials - harmonic, or otherwise?

    WELCOME TO THE FORUM

    You are starting to delve into science here and I think you might find the following WIKIPEDIA item useful as a start. You may know all this already, of course, but I believe it defines the terms to get started

    http://en.wikipedia.org/wiki/Harmonic_series_(music)#Harmonic_vs._partial

    To further understand the sound you need to come to grips with Fourier analysis. Any wave form can be broken down into a series of sine waves (which sound flute like), of different frequencies played simultaneously at different levels.

    Thus a square wave (at say 440 Hz = A3), much generated by synthesisers consists of a sine wave at 440 Hz added to a sine wave of 3 times this value (132 Hz) at 1/3rd the volume + 5 times the pitch at 1/5 the volume ad infinitum. This actually works if you take the time to do the sums. Each of the sine waves is known as a partial.

    The triangular wave is similar but includes (if I remember right) not just the odd numbered but the even numbered partials.

    The same applies to other musical instruments. A violin note includes fundamental sine wave but to this is added a lot of the 15th partial (that is 15 times the basic pitch of the note). This partial is, I believe, important to making a violin sound like a violin. There are of course many subtle effects in real musical instruments but the underlying maths are the same.

    Thats a start, its a complex subject though


    (regarding a trumpet) Baroque composers drew on pitches up to the sisteenth partial of the harmonic series.
    Many Baroque composers were writing for a valveless trumpet (like a bugle but a trumpet) and these could only play the notes of the harmonic series.
    Your sources seem to be confusing partials and harmonics, or at least in UK English

    (regarding a trombone) - The notes from Eb downward are weak and sound quite poor; the fundamental or pedal tones are not really feasible on this instrument. Therefor, the first playable note of each series are the second partials.

    The trombones lowest note is not very powerful so players start from the note an octave above - the second harmonic. I'm not a serious brass player, I can just about get a note, so I'm not entirely clear about this. I've a feeling that this rule applies to lots of brass instruments
    Derek
    Things may come and things may go but the art school dance goes on forever
    NOW WITH Cubase 5, JABB,GPO, Fender Strat, Ibanez RG, Yamaha Fretless Bass, Framus Archtop, The Trumpet and Mr T Sax, together with GREEN SEALING WAX


  3. #3

    Re: Partials - harmonic, or otherwise?

    Thanks a lot for the reply

    I used to play Trombone myself. While I do understand partials and harmonics, I was just a little confused at the way some things were worded. Since Ive taken a look at this stuff and let it set in my brain for a night or two, it started to make a bit more sense when I re-read everything.

    What was confusing me is that - well, in plain English - what was said was, "the player usually tightens their lips and plays one octave higher, because the fundamental or natural pitch of the instrument just doesn't sound as good'.

    Or in extremely plain english, "you usually play a higher note since the lower ones sound like crap"

    I've got it now though. Thanks again!

  4. #4

    Re: Partials - harmonic, or otherwise?

    Quote Originally Posted by buckshead View Post
    WELCOME TO THE FORUM

    You are starting to delve into science here and I think you might find the following WIKIPEDIA item useful as a start. You may know all this already, of course, but I believe it defines the terms to get started

    http://en.wikipedia.org/wiki/Harmonic_series_(music)#Harmonic_vs._partial

    To further understand the sound you need to come to grips with Fourier analysis. Any wave form can be broken down into a series of sine waves (which sound flute like), of different frequencies played simultaneously at different levels.

    Thus a square wave (at say 440 Hz = A3), much generated by synthesisers consists of a sine wave at 440 Hz added to a sine wave of 3 times this value (132 Hz) at 1/3rd the volume + 5 times the pitch at 1/5 the volume ad infinitum. This actually works if you take the time to do the sums. Each of the sine waves is known as a partial.

    The triangular wave is similar but includes (if I remember right) not just the odd numbered but the even numbered partials.

    The same applies to other musical instruments. A violin note includes fundamental sine wave but to this is added a lot of the 15th partial (that is 15 times the basic pitch of the note). This partial is, I believe, important to making a violin sound like a violin. There are of course many subtle effects in real musical instruments but the underlying maths are the same.
    I just wanted to point out, this is really more of an eigen value problem than a fourier analysis problem.

    An (ideal) violin has the string pinned at both ends, completely immovable, so the wave that travels along the string must go to zero at both ends. Finding sine and cosine functions that satisfy these boundary conditions is called solving for eigen values.

    Since the wave starts out at zero, the cosine coefficients are equal to zero, since cosine starts out at 1. We must also satisfy:

    sin(k*L) = 0, where L is the length of the string.
    So, k*L = n*pi/2, which means the wavelength is 2L/n, for any integer n.
    n is the number of the "partial" or "harmonic" or whatever you want to call it.

    For a wind instrument, however, a pretty good approximation is that the first derivative goes to zero at one end, and you end up with similar boundary conditions, giving k*L = (n+1/2)*pi, so the wavelength = 2L/(n+1/2)

    Of course, in reality these boundary conditions are a little bit different, a better model of a violin string has reflection/transmission coefficients at the nut and bridge, rather than a fixed string.

    But, there's really no fourier analysis involved there.

  5. #5

    Lightbulb Re: Partials - harmonic, or otherwise?

    Quote Originally Posted by Thared33 View Post
    I'm a bit confused about something. We have fundamentals, overtones, and partials, and all of it is confusing me.

    A fundamental is really just a note that you start on, right? Ok, but if you're talking about an instrument - say, a C trumpet - wouldn't the 'fundamental' of this instrument be C?

    I understand that with partials, it's (at least sometimes) talking about the harmonic series. You start with the fundamental note, then the 'overtone' is one octave higher... and then the fundamentals begin. Or something like that. But my question is about if 'partials' are strictly harmonics talk, and not about regular notes.

    Another thing is how I've been reading about orchestration, and for example, they're talking about different instruments and the range they're scored for. Here are a couple quotes:

    (regarding a trumpet) Baroque composers drew on pitches up to the sisteenth partial of the harmonic series.

    (regarding a trombone) - The notes from Eb downward are weak and sound quite poor; the fundamental or pedal tones are not really feasible on this instrument. Therefor, the first playable note of each series are the second partials.

    Regarding the trumpet quote - do they mean they didn't use harmonics that were above the sixteenth 'partial' of a harmonic, or pitches all together -from the lowest note possible on the instrument-?

    Regarding the trombone - I seriously have no idea. The notes start on the 2nd partial? I dunno.


    If someone can give me a hand with this I'd appreciate it. It's been bugging me for quite a while.
    Technically, at least as far as I recall, a harmonic is any partial except for the fundamental, but otherwise partials and harmonics are the same thing (just numbered differently). The fundamental is the nominal note, the lowest frequency wave in the sound. If you refer to the fundamental as a partial, it is the 1st partial. The second partial (aka the first harmonic) is typically (but not necessarily) an octave higher.

    In most musical sounds, the harmonics or partials follow the harmonic series. "Partial" is the more general term, because not all timbres have frequencies in the harmonic series of their fundamental. For example, gongs and tuned percussion can have partials that are "non-harmonic".

    Regarding the baroque trumpet, yes, they're talking about a note corresponding to the 16th in the harmonic series from the fundamental, rather than a component of the fundamental note. Sloppy terminology, but common usage. Since baroque trumpets did not have valves, they could only play the harmonic series. This is why they played in the clarino register: there, the notes in the harmonic series are close enough together that they could actually play scales. Same for the horn: horns play pretty high, considering that they have the same bore length as an F tuba.

    On the trombone, the only problem is that there is an entire octave between the fundamental (pedal tones) and the next note in the harmonic series, and the slide only gets you half-way there. If you start at Bb, and play chromatically down, you run out of slide at E, and (unless you have a trigger or F attachment) there is no way to get the rest of the way down to the Bb pedal. As for the quality of the notes being unusable, well, I've never known a trombone player who didn't like to play pedal tones

    Enjoy,

    Grant
    ==============================
    Grant Green ||| www.contrabass.com
    Sarrusophones and other seismic devices

  6. #6

    Re: Partials - harmonic, or otherwise?

    If you ever want to get really clear on partials/harmonics, spend some time with an additive synthesizer: it all starts to get real clear very quickly.

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