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Old 21st June 2012, 03:14 PM   #81
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In the formation of sounds--bells, gongs, etc., (and to a tiny degree, some piano notes that in essence have two "fundamental" frequencies--where the various formants are not mathematically related, this may be true. It's never true with a single "vibrating string" (in theory--double-, triple-, and larger-courses modify this, but, only because all strings cannot be perfectly tuned to a pitch, thus, they cannot be tuned to each other, therefore they modulate each other--which is the point of multiple courses). Since most bass guitars are single-course instruments, the 1st harmonic is always 2 * fundamental. Please check an entry level text on acoustics/physics/etc.

Now, to more pertinent information. Upon further study I have discovered two reasons why the 1st harmonic is sometimes louder (has higher amplitude, to be formal) than the fundamental: (1) electric basses (and pickups) are modeled after upright string basses (more formally, upright bass, string bass, contrabass, or bass viol in relatively increasing order of formality) which have a resonant peak around 100 Hz in their (cabinet) bodies. (2) (Probably due to (1) above and most likely derived from orchestras needing to have their bass drums cut through the bass viol sound) fundamentals below 100 Hz tend to mask bass drum (kick drum, low/floor toms, etc.) sounds because those drums often have their fundamentals around 50 Hz (thus, the 1st harmonic, sometimes called the 2nd overtone, is around 100 Hz).

There's my pedantic (not ranting, just pedantic) contribution for the day.

Did I mention that the 1st harmonic, the 2nd overtone, is always twice the fundamental in any oscillating, sound-producing, vibration mechanism (unless modulated by some outside mechanism, a tremolo bar, a second or other course of string, etc.)?

I did? Good. I'm done for the day.

Thank you.

Sincerely,

John

PS Have a nice day.

JEL
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Old 21st June 2012, 05:51 PM   #82
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I have noted that on some occasions a bass guitar string will vibrate in an orbital fashon. In other words, while it initially vibrates in the one axis, as the vibration decays the axis of vibration changes. Observing the output of a bass guitar pickup shows a shift in some harmonics along the time axis meaning they are not exactly the same pitch as the fundamental. The amount of shift taking 1 or 2 seconds to traverse one cycle. This could be cheap strings, a poorly setup instrument or some resonance within the instrument.

Fender style 4 string basses with 34 inch scales tend to have a resonance around 130Hz that kills the fundamental of notes played around the 5th fret of the G string. It doesn't affect notes of the same pitch played further up the neck. Basses with graphite necks don't do this.

Think about the geometry of a string vibrating within the magnetic field of a single magnet. When the string vibrates along the axis of the magnet and coil, the signal from the coil should pickup the fundamental vibration. But when the string vibrates side to side, the frequency would be doubled because the magnet can't distinguish which way the string is moving away from the axis of the magnet. J and P bass pickups have two magnets for each string. I'm not sure why or what effect that has.
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Old 21st June 2012, 05:53 PM   #83
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Quote:
Upon further study I have discovered two reasons why the 1st harmonic is sometimes louder (has higher amplitude, to be formal) than the fundamental:
It also has to do with where the pickup is placed. This is why the bridge pickup on a guitar has more harmonics than the neck pickup. If the pickup was placed in the center of the length of a vibrating string (12th fret on a guitar) its output would be mostly fundamental. Of course this is also determined by the charateristics of the pickup itself. A pickup with insufficient inductance will have a lower output with decreasing frequency, accentuating the harmonics.

Observe a vibrating string with a stroboscope and you can often see the different harmonic modes at play along the strings length.

Quote:
Did I mention that the 1st harmonic, the 2nd overtone, is always twice the fundamental in any oscillating,
You mentioned it, and I have seen the terms "overtone" and "harmonic" used incorrectly in several music theory texts as well. In the engineering world (electrical or mechanical) the second harmonic is twice the fundamental frequency, the third harmonic is three times the fundamental frequency, etc.....

I am writing this from inside a Motorola plant where I have worked for 40 years as an RF engineer. Some of the simulation tools we use to design RF mixer circuits will list out the harmonics and their frequencies. There is no "first harmonic" listed in the spur table it starts with the second, at 2X the fundamental frequency.
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Old 21st June 2012, 06:32 PM   #84
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Default Toh-may-toe v. Tuh-mah-tuh. (Re: 1f + 2f + . . .)

Thank you.

I'm all for reasonable discourse. When people, in effect, say: "you're wrong" without saying why, it does little to encourage reasonable discourse.

The bridge pickup will pick up more of the higher harmonics, and the neck pickup the lower harmonics. However, as long as the string vibrates at a constant frequency (and in a "string" mode and not a "rod" or some other mode, i.e. bass-register piano strings), those harmonics are integer multiples of the fundamental.

You can also change the relative percentages of the harmonics as compared to the fundamental by choosing where to pluck, pick, or bow the string: if you do so in exactly the middle (in theory, in practice there's always some variation because "exact middles", and such, are hard to find), you'll get only the fundamental: i.e. 1mv @ f for frequency (not identical, nor synonymous with pitch) at some loudness (in units of millivolts--one one-thousandths of a volt, in this instance, though it would measure similarly in units of SPL, dynes, etc).

If you pluck at 1/4 distance from the bridge to the fret/open-nut you'll get more even harmonics, i.e.: 1mv @ f + 1/2mv @ (2 * f) + 1/4mv @ (4 * f), etc. If you pluck at 1/3 the distance, you'll get more odd harmonics, i.e.: 1mv @ f + 1/3mv @ (3 * f) + 1/6 mv @ (6 * f), etc., where f is the fundamental). If you pick (causing more harmonics), or bow (causing more even harmonics due to the sawtooth like wave bowing creates), the harmonic balance will change, i.e. picking up near the bridge causes so many harmonics that it often sounds like the pitch has shifted up an octave (which indeed it may have, but, the fundamental frequency remains the same) and become metallic.

It would be nice if everyone adopted proper engineering-"language", -terms, -usage, -etc. in a consistent manner, i.e. electron current flow from negative to positive (cathode to anode), but, then one gets into holes moving the other direction, not as fast (or is it not as "mobile"? not as mobile, holes are, methinks), etc. But, we don't. We're not consistent. Conventional current flow will prevail, and be misused potentially, because it is too hard for most of us to get rid of the cultural bias we get when we're taught that positives are greater, larger, etc. than negatives instead of simply to the opposite of zero on a number line.

My purpose here--since this thread should have been allowed to die long ago, has been "jump-started" with several sets of paddles, has been hijacked or had "hijacked" "body" parts (thoughts, questions, mini-"flames", etc.) added, and has become some what "Frankenstein-ized" (and, yes, that's "St--long I sound--n" and not "Frah-kuhn-steen" . . .)--has been to: (1) provoke further thought, my own and others, and (2) to help get rid of much disinformation that exists in this thread.

While this is all fundamental to me, and what you said is fundamental to you, I'm glad we've taken the opportunities we have to potentially increase what is fundamentally non-fundamental to many other readers/writers!

Now, it's time for me to go about other things and hopefully, the next time I forget what the range of a bass guitar is, I won't "re-discover" it, think "what a long harangue that poster posted," only to discover I was the poster (see my first post way up above, if you care to), etc.




Again, thanks.

Hmm . . . that's interesting,:: (I hit some weird combination of ctrl-keys or alt-keys or ctrl/alt-keys and now the text sometimes appears backwards as I type (though, eventually, it, and the cursor get straightened back out. I''ll be curuious to see how it comes out. p[chuckle].

John

I included the "2nd overtone" because it is where a lot of the confusion comes in, "2nd overtone" versus "1st harmonic". Many people get the two confused.
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Old 22nd June 2012, 07:09 AM   #85
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There are some more things to add:

It is not just sometimes that strings don't just vibrate in one axis only - it is ALWAYS like that ! Seen from string's ends it is something like a figure of eight. And this figure even rotates (as observed by Loudthud). The latter is also responsible for the "mwaaaah" of fretless basses for instance. The fact that the string always has a two-dimensional vibration is a prerequisite that magnetic instrument pickups work at all. And now go figure how the actual three-dimensional vibration pattern of a string might look like in slow motion whith all overtones included !!!!


Regarding the integer ratios: The harmonics of a string are only integer ratios for an ideal string which doesn't exist in practice. The less the length/thickness ratio becomes the less ideal a string behaves in this respect. One way to counteract this effect is the use of longer strings for the lower notes like it is done on pianos and harps and to a lesser degree on guitars and basses with fanned frets. The overtone ratios are of course not the only reason for using the different sting lengts - tonal balance is another reason for doing this but this is not the point here. What I want to say is that even on a piano where the string lenght thing is done quite seriously it is by no means sufficient to get the harmonics right. Therefore the piano tuner stretches or compresses (I don't know the correct term since this is not my mother- tongue) the octaves of the instrument such that they are not an exact 1:2 ratio - simply to get the overtones of the lower strings in tune with the fundamentals of the higher strings.

Apart from resonances of an instrument's body there is another effect that might come into play and that I haven't seen mentioned anywhere so far. But to me it appears as being logically and physically stringent. The sensitivity of a pickup is depending on the distance of the string to the pickup. While a string vibrates it is moving between higher and lower sensitivity and therefore we have an asymmetrical nonlinearity which by itself generates even order harmonics. They might not be too strong since the output voltage is not only determined by the string position but to a great extent by the velocity of the vibration (which will also shift this harmonics by 90 degrees).

Regarding the "mud" I do agree with John. And yes - it is much more fun to have the fundamentals right but sometimes they are inconvenient to handle.

Regards

Charles

Last edited by phase_accurate; 22nd June 2012 at 07:18 AM.
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Old 22nd June 2012, 02:09 PM   #86
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Thumbs up stretched tuning

In 12-Tone Equal Temperament Tuning, the octaves are all stretched a tiny bit. In "perfect" intervals, each octave is twice the frequency of the prior. Perfect intervals would thus always be based on a multiple of the 12th root of 2 as there are 12 semi-tones in an octave. However, "perfection" is unobtainable in the real world and compromises have to be made. Rather than perfect intervals, a perfect minor third (3 half steps), a perfect major third (4 half steps), when using "stretched tuning"--most commonly 12-Tone Equal Temperament Tuning--each interval is stretched a tiny bit so that no octave is perfectly twice another in frequency. This allows us to play a conventional keyboard and have chords that are ("relatively", but not "perfectly") in tune (there are beats, that would not exist in a "perfect" tuning system, between notes in a chord).

Prior to the adoption of an equal temperament tuning system, if a composer wanted to change the key of his or her clavichord or harpsichord (precursors to the piano), they had to have it re-tuned. By adopting a stretched octave, where each of 12 semi-tones consists of 100 "cents", this constant retuning was eliminated. Each octave has 1200 cents, 100 cents per semi-tone, where each cent is slightly more--stretched--from a 1200th root of 2 ("2" from each octave being approximately twice the frequency of the prior).

If you have fairly good hearing, and if you train yourself to be able to hear this, you can take any properly tuned piano and play a two-note chord, the root and an octave higher, and you can hear the very slight beating that occurs because the octave is tuned just slightly higher than twice the root. This is because non-linearities (mostly in the ear) cause the fundamental frequency (and also the harmonics) of the root of the chord, f, to intermodulate with the fundamental of the octave, 2 * f, giving the products, f + 2 * f, 2 * f - f, etc. (see above posts). Since the octave is slightly more than 2 * f, call it g (f, 2 * f + g), you get the beat frequencies: f + 2 * f + g, 2 * f + g - f, etc.

By stretching the octave (creating g), we also obtain the ability to create chords composed of thirds, fifths, etc. that span the root (i.e. G3, C4, E4 where C4 is the "root") of the chord and remain ("relatively") in tune (though, again, here beats can be heard) over a span of octave.

Putting together thoughts from two above posts (not my posts), it is interesting to take a long piece of fairly heavy string (20-30 feet, 6-10 meters), tie it to supports at both ends, and "pluck" it at several places, the middle, 1/4 from one end, 1/3 from one end, as one can actually see the fundamental and harmonics. While using a laser to view it might be nice (it's impractical for most of us), sometimes (depending on the frequency of vibration of the string) interesting effects can be seen at night with a 60 Hz (and I imagine 50 Hz for those of you on such systems) AC light on. The next time I do that, I'll have to "pluck" in various planes to observe the effects while doing thought experiments of how those planes/plucking would affect a pickup (I'm designing one, a hum-bucker, that has . . . well, capabilities I won't talk about due to patent-application restrictions.).

Now, thanks again. This is the type of discourse I was hoping for, rather than "You're wrong." I've learned something!

Thanks.

Sincerely,

John

PS What's truly amazing about stretched tuning is that the beats themselves, when "blended" in with the rest of the chord by our ears, can become very musical.

JEL

PPS I do a bit of singing in 12-Tone Pythagorean Chromatic Tuning (you're pretty much guaranteed a closer-to-12th-root-of-integer-intervals tuning over an octave, i.e., once you've chosen a "center" pitch, say C4, you can make chords like C4, E4, and G4 and they'll have a closer to fractional/integer relationship) and 17-Tone Pythagorean Chromatic Tuning (closer to 12-th root intervals over 17 tones, then the tuning "breaks down").

J

Last edited by JohnEEADBL; 22nd June 2012 at 02:20 PM. Reason: typos, omissions
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Old 22nd June 2012, 05:36 PM   #87
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Many of the organs that have been built from the 1940's through the 1980's use 12 master oscillators to generate the top octave. Each can be tuned independently to the desired pitch of the highest octave on the keyboard. Each lower octave was generated by using an electronic frequency divider to divide the frequency by two. This ensures by design that each note was exactly half the frequency of the same note an octave higher. Just about every electronic (not pipe) organ built was made this way with the exception of the tone wheel Hammonds. They used a magnetic wheel for each note, all spinning on a common shaft to generate the tones. Hammond also built frequency divider based organs. My old Baldwin used 36 6SN7's for the dividers. The power transformer weighed about 25 pounds.

The compromises increased with the invention of the "top octave divider IC". The most popular was the Mostek MK5024, or MK50240 chip. These took a common clock in the 2 MHz region and divided it by 12 integers to closely approximate the top octave. Each lower octave was generated by frequency division.

Today virtually every keyboard generates it's tones by digital means. Digital chips have grown much faster and more powerful so that the errors in frequency are much smaller than what's obtainable from a real instrument based on a vibrating string, rod, reed or whatever.
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Old 22nd June 2012, 06:24 PM   #88
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Cool By the Bye: tube topics needed?

Quote:
Originally Posted by tubelab.com View Post
... tone wheel Hammonds. They used a magnetic wheel for each note, all spinning on a common shaft to generate the tones...
I love the sound of an old B3. Nowadays, one can get that (emulated/sampled) "sound" elsewhere, but, there's nothing like an old B3 cranked up, playing through a Leslie speaker. The last time I heard one was back in '95, as I recall: they'd built the band around the B3 player and his B3. It's been too long to recall a 15 minute conversation with the front-man/lead-guitarist, but, the B3 player had played on some gold and silver albums for a few of the top '70s/'80s recording/touring artists.

How about starting a thread, tubelab, and educate us about tubes, organs, speakers, etc.? Diodes, triodes, etc. General operation. Why tubes have to use output transformers. Why tubes, when clipping, give such a mellow sound (actually, getting to the latter is why I mentioned all the other topics, having discussed fundamentals and harmonics above). I'm sure a discussion of why tube-amps sound the way they do would be very enlightening (assuming it doesn't already exist on this forum--I'm not taking the time to search to find out--I need to figure out how to unsubscribe from this link, so I have one less thing in my junk mail . . . just scroll down a bit, John!)

It's been real. It's been fun. ... I've got other things to go do!

John

PS (edit) As I now do appear to be unsubscribed, you'll be wasting your time, some of you above-posters (I rarely pay attention to who said what), if--in the future--you want to point out something you think I said in error for my benefit! If you all continue, I hope you'll continue to enlighten each other with facts and specifics.

JEL

Last edited by JohnEEADBL; 22nd June 2012 at 06:28 PM. Reason: Added notice/Omission
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Old 23rd June 2012, 10:35 PM   #89
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I have really enjoyed this thread. It's encouraging that people are thoughtful and passionate about all this.

What is this music thing anyway, and why do we do it? There's a whole commercial industry (at least one!) built up around the demand for music, or a reasonable facsimile thereof, but music has been going on for a long time... I've found that in situations that are not acoustically confounding, the presence of low fundamentals has a most engaging effect. Hence the 28" and 32" calfskin concert bass drums, and the sinewave synth bass... I don't doubt this all creates havoc in the average commercial music venue, but there ARE other times and places to create music, as well as other reasons.

My own search for a "better" bass rig has been inspired by one simple dynamic- when things are clicking in a somewhat certain way, I'm deeply inspired to play and can step out of mundane life for a while, often hours on end, and let the music play me. Invariably this is more rewarding than me attempting to play the music!

Some figuring and headscratching as well as some fiddling about all need to take place for the equipment to serve its ultimate role in facilitating the making of music. The information and perspectives in this thread, especially coming from folks who clearly care about all this, are a significant resource. Thanks again all.
ted
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Old 24th June 2012, 09:22 PM   #90
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Back to my mentioning the psychoacoustic effects of the harmonics creating the fundamental in the brain. My basses and rig will easily produce the fundamentals of my 5 string basses, which use low impedance active pickups and/or piezo pickups. I do enjoy not only being able to enjoy the actual, deep bass fundamentals, but on occasion use a sub generator to produce an octave below what I am playing.

But I can use a passive bass through speakers rated down to 60Hz, using a power amp with a 40Hz highpass filter and get fine, usable results which are enjoyed by me, the rest of the band and the audience. Judging by the number of SVT's I still see on professional (and club) stages, I'm not the only one.

I have used very full range, decent PA quality speakers for my bass rig since the mid 70's, when I first employed folded horn cabinets and PA horns with my SVT head and later, a combination of large SS power amps and tube heads in biamped rigs...still using treble horns. Rather than just noise (scratching and string noise), I used fresh, roundwound strings, and put an active preamp into my basses and used a harmonically rich signal with plenty of low and high end, and let the guitar players swim around in their rather restricted midrange frequencies.
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