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20

Essentially all instruments produce overtones, which are frequencies other than the dominant frequency of the note. When one or more overtones is a multiple of the base (or fundamental) frequency, it's called a harmonic. Some instruments like drums do not generally have harmonic overtones. Others like guitars, violins, and flutes do have have them; more ...


19

Yes, you're right. As for why the harmonic series doesn't produce notes that work in all keys, the simple answer is that the math just doesn't add up. Let's work out the math for just intonation: Suppose you choose X Hz for the fundamental frequency and go from there. Then the octave above the fundamental should have frequency 2 X Hz. Meanwhile, the ...


17

It's a simple question with quite an involved answer. First a quick primer on wavelength, frequency and pitch. Frequency is how many times a vibration repeats in a period of time. Wavelength is the length of a single vibration, which for something like a guitar string, corresponds to the length of time it takes to repeat. You can see that if the ...


11

Harmonics occur at the whole-number ratios of the length of the string, e.g. 1/2 the length of the string, 1/3 the length of the string, 2/3 the length of the string, 1/4, 3/4, etc. The lower the numbers involved, the easier the harmonic will be to play. So for example, theoretically there's a harmonic at 6/19 the length of the string, but it will be much ...


11

There is indeed a reason! The notes you play on a trumpet with a particular fingering come from the harmonic series, which is a series of tones based on the root, or fundamental frequency. The idea is that the harmonics (also called overtones) are whole-number multiples of the fundamental frequency. If the fundamental frequency of, say, your trumpet, is ...


10

You can't actually do this - obviously you are aware that the whole pich/natural/articial harmonic bit doesn't create frequencies, it just cuts out some so the tonal quality changes. You do have technological alternatives though, if you do want to build lower frequencies related to the original root. Octave dividers are the simplest example - you can buy ...


10

WHY do harmonics happen? Well, they don't happen – not necessarily. Strings can do all kind of stuff: All these are possible ways a snapshot of a moving string could look like. Not only that, it could also move at each point with an arbitrary velocity, including the possibility of a velocity that's everywhere 0 (for an infinitesimally short ...


8

A concise way to put it is: The vibrating part of the string vibrates to accomodate for all nodes you apply to it, while keeping a constant distance between all nodes. Additionally, the string vibrates with the least number of nodes possible, since this is what takes the least energy. When you play an open string, the constraints on the string are only ...


7

You need to change your finger position on the pick so that your index finger or thumb is slightly over hanging the side of the pick. Strike the note with the pick and then brush with the flesh of your finger or thumb (depending on whether it's an up or down stroke). Notes / strings will get different harmonics at slightly different places. Use your pick ups ...


7

As leftaroundabout indicated in another answer, you could achieve subharmonics (specifically a difference tone) using two sound sources - such as two strings. See "Combination tone" on wikipedia for further specifics. Or see "Resultant tone" regarding the usage of this for organs, where sometimes two shorter organ pipes are used to sound simultaneously ...


7

When you pluck a guitar string you are always generating all of the harmonics to varying degrees. For your E2 N: 1 2 3 4 5 6 7 8 9 10 11 12 Note: E2 E3 B3 E4 G#4 B4 (D4) E5 D5 G#5 (n/a) B5 ... N; ratio of harmonic's frequency to the fundamental frequency 7th harmonic is pretty badly tuned in equal ...


6

There should be a (slightly flat) C as the 7th harmonic on the D string. You should find it at all six places where you would cut the string if you were to cut it into seven equal lenght pieces: for instance between the second and third fret, about one third from the third fret. However it might be hard to nail with a decent sound, and you will most likely ...


6

Consonants are primarily just noise—largely high, semi-random frequencies. Vowels are generally the only part of speech that have harmonic content as opposed to the inharmonic content of consonants. Bright, forward vowels like EEEEEE have way more overtones than dark, back vowels like AHHHHHH. Most consonants other than the nasals are so brief that I'd ...


5

Resonant Frequency Good guitars have the wooden top and body of the guitar carefully carved to resonate at a certain single frequency. While the luthier is carving and bracing the top of the guitar, long before the guitar is assembled and the strings are put on, he repeatedly taps the top with a knuckle, as if it were a drum, and listens to the fundamental ...


5

In my answer to How do harmonics work?, I said: [A] vibrating guitar string has components at many multiples of the base frequency (call it F). To your ear it still sounds like the fundamental, but mathematically it's more like this: a*F + b*2F + c*3F + ... The higher-frequency elements give the note it's timbre; this is how you can ...


4

From a purely theoretical point of view it has to do with two things: Excitation and non-linearity. As suggested by leftaroundabout's diagrams, WHERE you pluck on a string, eg, will affect to a large degree whether it vibrates primarily at the "fundamental" or some harmonic. This is excitation. So someone playing a stringed instrument can get a purer, ...


4

Harmonics occur on the string at points that divide the string into equal parts. Lightly touch a string right above the 12th fret bar and while doing so strum the string -- you'll notice that the string sounds an octave higher, though different from just fretting the 12th. What you're doing is dampening the fundamental frequency and "odd" harmonics (3x, ...


4

Actually, the opposite question is more relevant why doesn't a string vibrate at all the frequencies? When you hit it, you aren't providing just one vibration node, but putting in a chunk of energy. It comes down to where the nodes, or zeros are (have a look at @MatthewRead's answer over here) as with the ends of the string fixed, any wave which has an ...


4

The two existing answers are great. Here's one other way to look at things. Most things resonate; that is, when they vibrate, they prefer certain frequencies to others. Even if you hit, say, a wooden table, some frequencies will die away almost instantly; others will keep going for a short while, before it settles down into silence. Pitched musical ...


4

Any harmonic indications that are not based off of an open string are "artificial" harmonics. So, all of the harmonics in the excerpt are in fact artificial. The third harmonic is notated correctly, however, the first two are not notated correctly. When notating an octave harmonic on an open string, a harmonic symbol is used (looks like a degree symbol - ...


3

5th fret harmonics are the same note as the open string, 7th fret harmonics are the same as the 7th fret notes (low to high - b,e,a,d,f#,b). Touch and tapped harmonics are the same as the fretted note assuming you are touching, tapping one octave higher and pinch harmonics change depending on where you pick/pinch the note. For pinch harmonics if you pick ...


3

From looking at Youtube videos of him playing it: yes, it's tapped harmonics. If you listen closely you'll notice that he also struggles to make them all sing (at least I noticed on the two videos I've looked at so far), so it's clear that they're not always easy to do. I find a light touch to be important to make them sing, and it takes practice to figure ...


3

There are 'sweet spots' along the length of each string. When a string is played and is vibrating, a light tap on the sweet spot can cause a harmoinic sound. This happens because the tap slightly alters the way the string vibrates. A usual sweet spot is just above the first pickup. To hit a pinch harmonic, pick the note and almost immediately afterwards, ...


3

Here is a table that I have adapted from one in Wikipedia that illustrates how just intonation differs from 12-tone equal temperament. In modern instrument tuning, an octave is divided into 1200 cents. There are 100 cents in an equal-tempered half-step, and all half-steps are equal in their distance apart. However, in just intonation, not all half-steps ...


3

A relatively new company in Sweden, True Temperament, retrofits electric, acoustic and classical guitars with new necks or fingerboards with heavily modified fret positions that are designed to improve intonation. If I understand their intent, their "Thidell" design is for playing with something closer to pure intervals, but chiefly in the most common ...


3

Using a keyed instrument with Just Intonation creates a bunch of puzzles that need to be solved. You are either faced with observing limits on navigating from place to place, or doing "comma pumps" (equating near by intervals, or bend/vibrato between them because they are close enough). The problem isn't really Just Intonation though. It's caused by ...


3

UPDATE: Based on your comment below: "For the purpose I am interested in the tonal qualities of silver apart from shape. If you strike ANY silver resonater it makes a peculiar ring that, as I said in the question, is unmistakable. This is the tone I am interested in capturing and studying. If you strike a pure silver coin you will hear what I am talking ...


2

Pretty easily; play the note on a downstroke, make sure you catch it well, on the way out (after sounding the note) catch the string slightly with the skin of your thumb, not too much or you will kill the note, note too little or the harmonic will not sound. Practice this; and you'll have it in no time; try playing a minor pentatonic all in pinched ...


2

I'd suggest you first get handle on the sound and general position of the harmonics in this area, then use that knowledge in the context of the piece. The fourth-fret harmonic (which is also called the fourth harmonic) is played pretty much over the fourth fret and should sound two octaves above the note on the fourth fret (two octaves and a major third ...


2

Specifically, to produce the 12th fret harmonic pick the string while lightly touching it at the 12th fret. The comparison the article talks about is between that harmonic and the fretted note at the 12th fret. They should be exactly the same if the intonation is correct - see this question for more information on setting the intonation.



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