53

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 2X Hz. Meanwhile, the ...


33

It is not true in general that the higher you go on the fret board, the lower your harmonic is. Actually, if your were to play an harmonic at the 24th fret, you would hear a note sounding an octave higher than the harmonic at the 12th. Still, however, the harmonics behave differently than fretted notes. Now, let’s get physical and explain why. On perfect ...


32

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 ...


32

The tuning fork does produce overtones. The amount of overtone depends on how the tuning fork is attacked. The modes of attack also depend on the pitch of the fork. I once had a very long tuning fork for a physics demo that was 80-100Hz. You could squeeze the ends together and slide your fingers off creating a smooth fundamental tone. If you struck it ...


24

I want to make an addition to all these excellent answers. With just intonation, it's not possible to make all the chords just. Not even in a single key. Let's look at the common just major scale based on I, IV and V just major triads: C 1:1 D 9:8 E 5:4 F 4:3 G 3:2 A 5:3 B 15:8 In this scale, I, IV, V major triads (4:5:6) and iii and vi minor triads (10:...


24

It depends on the setting (what other instruments?), but generally speaking, you'd consider, in order, Sacrificing the pure fifth. As soon as any instrument plays the root, the fifth will be very present as its third overtone, so whether you actually play the fifth makes very little difference to the overall sound. Eliminating any duplicate roots. Basically ...


23

Excellent find! Trumpet, as well as the acoustically similar trombone, are very peculiar instruments when it comes to physics. They are cylindrical tubes closed at one end, so they should have a fundamental wavelength that's 4x the length of the tube, and then only generate odd overtones. Look at clarinet for an instrument that actually obeys this1. But ...


21

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 two:...


21

Is it an important thing to consider in Orchestration? You have in fact stumbled onto the very foundation (and art) of orchestration. Orchestration is about not only knowing how each instrument sounds, but how to blend those sounds together to get the effects / textures you're looking for. Composers generally don't think about blend in terms of harmonic ...


19

It's the same as on a guitar. Harmonics occur at equal divisions of the string length. Half the string is the location of the 12th fret. This produces a harmonic at twice the frequency of the open string, which is one octave higher. Dividing the string into thirds, which is at the 7th fret, produces the fifth of the 12th fret harmonic. (Halfway between the ...


18

See also this other post WHY do harmonics happen? Well, they don't happen – not necessarily. Strings can do all kinds 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. The velocity could be everywhere 0 (for an infinitesimally short moment). ...


17

A simple list of what overtones are present wouldn't tell you much. What you really want is the relative levels/intensity of each overtone. A list of the overtones with relative intensities for an instrument is called the instrument's spectrum. You might try searching for " spectrum" for the ones you are most interested in. Here's an example for a violin: ...


15

In a 12-tone, equal tempered scale, we want our frequency to double (become an octave higher) every 12 semitones, and we want our semitones to be evenly-spaced. As each fret represents a semitone, and the fundamental frequency of oscillation of an ideal string is proportionate to the reciprocal of its length, this means that every fret should be a factor ...


14

(Just in case of any confusion, this answer was originally in response to a duplicate question about pinch harmonics used by Billy Gibbons of ZZTop - thanks for the merge, Dr Mayhem!) These are probably pinch harmonics. In which case, they are not produced by a particular amp or effects setting, but are produced by the picking hand while playing (although ...


14

In the context of acoustic analysis: Overtone: any resonant frequency above the fundamental frequency. Harmonic: resonant frequency that is an integer multiple of the fundamental frequency. For almost any^* musical instrument, any time you play a sound, you get a whole series of overtones. The feature of pitched instruments that makes them pitched is ...


14

are there any inharmonic frequencies in A? Simplistically speaking, 'A' tells us the fundamental pitch of the note (or at least it would if we knew which A - e.g. A4 is often, though not always, considered to be 440Hz). However, whether or not there are any inharmonic frequencies completely depends on the timbre of the note. Looked at another way, it's (...


14

Modern harmony revolves around tonic-dominant relationships, and part of what makes a V-I or V-i sound convincing to our ears is that the leading tone goes up a half-step to the tonic. In the common-practice era, this is why we see so many examples in minor that seem to be well described by the idea of a melodic minor scale. On the way up, we want to hear ...


14

Other answers so far make good points -- matching timbres (and sound spectra) is actually essential to orchestration, and composers have been noticing these patterns (and using them in orchestration) even before analysis of harmonic spectra was possible. I would add one other related issue to answering the title question about "differences in harmonic ...


13

You might be actually playing A 110, two octaves below A 440. The open A string on a standard tuned guitar is actually two octaves below the A that is normally tuned to 440. To play the A that should be at 440 Hz, you have to play the 5th fret on the high E string, or the 10th on the B string, or the 14th on the G string, etc. Why? The 440 A is the A above ...


12

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 ...


12

The difference is quite simple, and we might be over-complicating it in other answers. Overtone: any resonant frequency above the fundamental frequency. Harmonic: resonant frequency that is an integer multiple of the fundamental frequency. A harmonic is a type of overtone. All resonant frequencies above the fundamental are overtones, but only the ones that ...


12

I 've read that all periodic sound waves have a fundamental frequency That's true - if a wave is periodic, it has a fundamental frequency. (Oddly, just because a wave has a fundamental frequency, it doesn't necessarily mean that there's any energy at that frequency though - it may be that all the energy is in the harmonics!) I was wondering if all ...


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 ...


11

We first need to categorize each interval, assign it a "consonance amount". That's the first problem we find. In the case of the fourth, for example, some consider it perfect consonance, and others consider it a dissonance, depending context (and who you ask). For simplicity, let's define ours based on Wikipedia's: 1: Perfect consonances: unison, octave, ...


11

I believe that this is referring to where you would place your finger to get the desired harmonics. The harmonic that generates the major third is right before the 4th fret, which would be 3.85. 3.2 would be a harmonic near just beyond the 3rd fret, which should give you a D on the G string. This picture outlines the placement of the harmonics and the ...


11

Can the harmonic series explain the origin of the major scale? Emphatically yes, but that doesn't mean the major scale is literally contained in the harmonic series. We seem to be dealing basically with a black-and-white fallacy here: there aren't just two options “the entire major scale is contained in a single harmonic series” and “the harmonic series can'...


11

When we say that the pitch ratio between notes is 2:3, that ratio only expresses the ratio of the fundamental frequencies. However, there will of course be lots of other ratios between the harmonics of those notes which may be relevant to the perceived consonance. Let's consider two notes each with 3 partials: One note has a fundamental at 100Hz, and ...


11

Does the difference in harmonic series between instruments have a significant effect on the consonance of the sound? Absolutely - and not only between instruments. Different ranges of the same instrument have different harmonic structures - a commonly-given example is the 'muddy' sound at the bottom end of the piano, caused partly by relatively weak lower ...


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