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Harmonic Pitch Question

Discussion in 'General Instruction [BG]' started by Bryan R. Tyler, Jan 14, 2005.

  1. Bryan R. Tyler

    Bryan R. Tyler TalkBass: Usurping My Practice Time Since 2002 Staff Member Administrator Gold Supporting Member

    May 3, 2002
    Just wondering if anyone could explain to me why some harmonics stay in the same pitch when played on the lower and upper octaves of the fretboard, while some others go up an octave in pitch (ex. the harmonics at the 4th and 7th frets are the same pitch as on the 16th and 19th frets, while the harmonics at the 5th and 9th frets are an octave lower in pitch than the ones at 17 and 21).
  2. Whafrodamus


    Oct 29, 2003
    Andover, MA
    Well, it all started with the invention of the bass string, by Albert Basstringenhiemer. He realized that the best way to confuse you is to make harmonics all weird, just so you could post this thread. It's like the matrix....

    Seriously though, I'd like to know a little more about this.
  3. CJK84


    Jan 22, 2004
    Maria Stein, OH

    I know only a little about this, so the following might not be accurate.

    A string has certain spots along its speaking length (the span between bridge and nut) called nodes.

    Stop a string from vibrating at a node (by touching it - not pressing it down) and a pitch that is harmonically related to the fundamental of the open string will be produced.

    At the twelfth fret there is a node - this particular node occurs at the point exactly halfway along the speaking length of the string. The harmonic whose freq is twice the fundamental will be sounded at this 12th-fret node.

    There are numerous other nodes on strings - all of which produce a different harmonic that, I think, is higher than the harmonic produced at the 12th fret.

    With nodes, avoid thinking of the concept that moving up the fretboard should produce a higher frequency. With touch-harmonics, the bridge and nut are equivalent terminal points of the string. The string is vibrating on each side of the node being touched.

    Actually, I believe it's true that, with the exception of the 12th-fret node, all touch-nodes produce two harmonics.

    One for the vibration from the node to the bridge - and another for the vibration from the node to the nut.

    I've read web sites about this before - so maybe check those out.

    Also a physics book will tell about this.

    Please keep in mind that I'm not certain about this info.

    Good luck.
  4. Alvaro Martín Gómez A.

    Alvaro Martín Gómez A. TalkBass' resident Bongo + cowbell player

    When you play an open string, you only hear one pitch, but along with it, there are lots more. The pitch you can hear is called the fundamental (the lowest possible pitch within the current length of the string), and the other (called overtones) are the harmonics. The number of harmonics determines the timbre of the instrument.

    Let's say that the fundamental is the first harmonic. The second one is found at half (1/2) the string, and it's an octave higher of the fundamental. Halfway the string equals fret # 12: Just one node, as those "sweet spots" are technically called.

    The third harmonic can be found at 1/3 of the string length. In other words: Dividing the string in three parts gives you the points (nodes) for the 3rd harmonic, and there are two: At the 7th fret and at the 19th fret. This harmonic is the fundamental plus an octave plus a perfect fifth.

    Now, here's where the situation you ask appears: The fourth harmonic (fundamental plus two octaves) can be found at 1/4 of the string length. Likewise, dividing the string in four parts gives you the nodes for the 4th harmonic, and there are three: At the 5th fret, at 12th fret and at 24th fret, but wait! We already found the second harmonic at the 12th fret! Anyway, regardless of the octave in which it's found, at frets # 5, 12 and 24 you get the same pitch. At 5 and 24 you get an octave higher than at 12, because it's already the node for the second harmonic.

    And so on: You can find the 5th harmonic (fundamental plus two octaves plus a major third) by dividing the string in 5 parts, which gives you 4 nodes (frets 4, 9, 16 and "28"). With the sixth harmonic (fundamental plus two octaves plus a perfect fifth) you get again "repeated" nodes: Dividing the string in six parts, you get 5 nodes at frets 3, 7 (which is already a node for the 3rd harmonic), halfway between frets 12 and 13 (practically unaudible because of its nearness to the second harmonic, which is stronger. You can get a glimpse of it by tapping it ala Van Halen), 19 (also for the 3rd) and "31". The higher the harmonic, the higher the pitch, the higher the number of available nodes and the harder to get.

    I tried to do my best to sound the less complicated possible. Please excuse me if it wasn't like that. Hope this helps.
  5. So, like Alvaro says, harmonics are vibrations of the string which have their nodes (places where a particular harmonic doesn't move the string) at places other than the ends of the strings.

    The fundamental is just the main vibration of the string. It has its nodes at the ends of the string: one at the nut, and the other at the bridge. Right in the middle is an antinode; the place where a harmonic moves the string the most.

    If you put your finger on that antinode, you mute the fundamental. You're holding it still right where it wants to move the most. Thing is, when you pluck the string a whole bunch of other harmonics sound as well. So you can still hear them, even without the fundamental. More precisely, you can still hear some of them. You can hear the ones with nodes at the center. Any with antinodes at the center of the string will be muted, just like the fundamental.

    Harmonics have multiple segments of vibration, unlike the findamental, which has only one. The first harmonic has two vibrating segments, and the middle of the strings stays still. So you can still hear it when you mute in the middle of the string. It wouldn't be moving there anyway, so there's no effect.
    The next harmonic divides the string into three. So it has two nodes, each 1/3 of the string's length apart. One happens to fall right over the 7th fret, and the other happens to fall over the 19th (anyone who wants to check the numbers, please do). They aren't the same pitch because they are 7 frets above the note the string is tuned to; they're the same because those are the spots you get when you divide a string into three parts.

    The next divides the string into four vibrating portions. So it has three nodes. One happens to fall over the 5th fret, another over the 12th, and another over the 24th. That's because those frets occupy positions 1/4, 2/4, and 3/4 of the way down the string, respectively. If you play these, you'll probably notice something funny. Frets 5 and 24 both produce notes two octaves above the fundamental, but fret twelve is only one octave above, just like it has always been. What's happened to the 1/4 string harmonic? It's still there (don't worry), but you can't make it out because the 1/2 string harmonic is masking it. If you want to check and make sure the 1/4 string harmonic really has a node in the middle, then you can play it with a finger at the fifth and 12th frets. If it had an antinode in either of those places, then it would be muted. It doesn't, so you can still hear it. In fact, you can touch a string at all of a harmonic's nodes, and it will still sound fine. Those points aren't moving anyway. If fact, it can sometimes be helpful to do so. I've found that touching 1/4 and 1/2 will help the two octave harmonic come out on a violin. It's bit of a stretch on the bass though.

    The progressive division of the string continues infinitely, in theory, but in real life there's a limit to the number you can actually produce.

    So, in short, harmonics aren't associated with frets by any connection other than the coincidence of being near each other. If we wanted to move all the frets around, the harmonics would stay the same. A harmonic's pitch is determined by the number of vibrating portions it divides the string into. You can touch any of its nodes and it will still sound, but you may need to touch a different node to mute all the harmonics below it, since harmonics can share nodes. All harmonics with even numbers of vibrating portions share the center-string node, for example.

    Does that help? I think I need to put up a web page explaining this sometime. Please ask for any clarification you need.
  6. Aaron Saunders

    Aaron Saunders

    Apr 27, 2002
    Anyone know what happens when you put a pickup right under a harmonic mode?
  7. For starters, that would only apply to an open string or an octave thereof. Since harmonic nodes occur at subdivisions of the *vibrating* length of the string--not the entire length of the string under tension--as soon as you fret a note, all the nodes move. SO even if the PU started out under a node, it wouldn't stay there long. In addition, if you consider all the possible node locations for all the harmonics, and then think how many places you can put your LH fingers, esp. on a fretless, then it would seem that wherever you put a PU, it's gonna be under some node or another some of the time. Furthermore, the length of string almost any PU picks up is almost certainly going to be noticeably wider than the site of the node. So some string on either side of the node will be picked up inevitably, even if the PU is parked exactly where a major node happens to be at that moment.

    So IMO the answer is, probably not much in practical terms. I've always felt that this harmonic node placement idea, which comes up a lot in connection with "sweet spot" concepts and 22 vs. 24 fret debates on guitars, is a bit of a myth.
  8. I agree. While putting the pickup under a certain node will affect the tone, it won't do it too much. The only real difference you'll hear is a greater amount of the fundamental as you get closer to its antinode.
  9. spidersbass


    Nov 29, 2004
    Downtown L.A.
  10. Bryan R. Tyler

    Bryan R. Tyler TalkBass: Usurping My Practice Time Since 2002 Staff Member Administrator Gold Supporting Member

    May 3, 2002
    Wow, I forgot to thank everyone for their helpful answers. Your responses did clear things up for me.