31

That's true not only for pianos, but for every (stringed) instrument, and the reason is basic physics. When you hammer a string with a piano key, or pick it with your finger, or with a pick, etc. you impart a certain amount of energy to it, depending on how hard you hit it -- the harder you hit it, the more energy you give it. Next, you should know that ...


20

There is a lot of half answers provided and frankly some of the information is ambiguous, possibly false. The question itself is not complete enough to elicit an answer. The best I can do is provide a bunch of information that I think is relevant to the discussion and hope that it helps. Using the simple ideal model for a vibrating string, vibrating ...


14

It is a coincidence, because there is no simple relation between the wavelength of sound in air, and the wavelength in the structure of the instrument (either in the wood or the strings). The fact which is critical to the sound of a violin is the lowest vibration frequency of the air inside the body, which is about an octave higher than the lowest note. ...


14

This is a really interesting and complicated question in the physical simulation of string dynamics. Actually, it’s not entirely true that high pitch notes run shorter. There is a tendency for higher order partials (inharmonic overtones) to decay faster (run shorter). But due to the complexities of piano tuning and string coupling, it is not true that if you ...


14

This answer can hopefully be useful as an additional perspective on top of the existing ones. Note that the spectrograph is a plot of (the log of) power output vs frequency (power being energy per unit time). It appears that the fundamental harmonic has been "washed out" into the broad background at low frequency, and perhaps broadened (it's hard ...


12

If you multiply both sides of the ratio by the same factor, the ratio doesn't change, so 2:3 is the same as 4:6 (just takes twice as long). So, in the time it takes the root to oscillate 4 times, the Major third oscillates 5 times and the perfect fifth oscillates 6 times, giving us a combined ratio of 4:5:6. More generally, we just need to put it in the ...


12

It's probably impossible to give a definite answer by just looking at the spectrum, but here are a few thoughts: [EDIT: the first point below has become irrelevant since the OP edited the title of the question.] first of all, the strongest harmonic is the third one, not the seventh, if you start counting from the fundamental, i.e., the strongest harmonic ...


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 ...


10

I refer you to Wikipedia. The motion of sound can be hard to understand because we can't see its propagation. We can sometimes understand it more easily by analogy to waves we can see, for example waves on the surface of water, or light waves from a light bulb. Although they are different kinds of waves (sound waves are longitudinal whereas water and ...


10

The higher the string, the shorter and thinner. The lower the string, the longer and thicker. The lower strings have more mass and do not let go of the vibrations as quickly as the higher strings. Additionally, the lower strings have more harmonics and more opportunity to resonate with other strings in the piano, which adds to the sustain. If you need more ...


9

where are these additional ratios within the chord ratio equation? They're right there, almost in plain sight - all you have to do is simplify the numbers: Major 3rd - C - E - (4:5) = 8:10:12:15 Perfect 5th - C - G - (2:3) = 8:10:12:15 Major 7th - C - B - (8:15) = 8:10:12:15 Minor 3rd - E - G - (5:6) = 8:10:12:15 Perfect 5th - E - B (2:3) = 8:10:12:15 ...


9

Destructive interference would effect what you hear, but that doesn't change the composition. You could do other things to make a performance or playback inaudible, like move very far away or put a jackhammer next to the listener. Interfere however you like, that won't change the composition, because the composition is purely conceptual.


8

You can do this. All you need to do is invert the signal, i.e. generate a waveform that is the exact negative of the input waveform and add it to the input so there is no signal left. This is how noise-cancelling headphones work. Then you add in your own signal. Why anybody would go to the trouble of doing this, is a completely different question.


7

Where did these small number ratios "come from"? People have tried to come up with small and nice numbers for frequency ratios, and that was the smallest and nicest they could get. Wikipedia tells the history https://en.wikipedia.org/wiki/Just_intonation A:B:C is a condensed way of listing the relationships of the frequencies of a three-note chord. All ...


7

There is no historical evidence that the ancient Greeks ever measured the frequencies of sounds. They developed their theories of intervals using the relative lengths of strings or pipes, which are an equivalent way to relate intervals to geometrical ratios of lengths. There is no obvious reason why the Greeks could not have invented the siren (see below), ...


7

1) The quantity of sound waves produced in air depends on the intensity or amplitude. If you pull your guitar string back a very short distance from its normal resting position, then the oscillations in air particles will be small, and they won't bang against your ear drum as hard. This produces a quieter-sounding noise. The frequency 440 Hz is how many ...


6

I don't think the potted plants will make much difference. The curtains might, but material thick enough to make any difference won't be cheap. Personally, unless I was an experienced acoustical engineer I'd run a mile from this one. You're in danger of not only failing to improve the sound but even making it worse. You might soak up a lot of the high ...


6

Simplistically speaking (and ignoring lots of important detail about intonation and temperament), the major third has a frequency ratio of 5:4 compared to the root, and the perfect fifth 3:2. Let's imagine that we have a root at frequency 100 Hz, and pick out the first few partials of each note of a major chord. Root: 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, ...


5

This can be a rather complex process. If you want to infer something about the geometry and materials of the bracings and the quality of the tone produced you had better make sure you have all the guitars in the exact same set up in the lab and that the microphone or other device is mounted at the same location relative to the guitar. The acoustic field ...


5

Yes, it's coincidence, mostly. Consider that 200 years ago A was maybe 415 Hz, not 440 or 444 Hz. It is "mostly" true that there's no real value to a resonant chamber more than 1/4 wave of the lowest tone desired, but there's also a lot of art bordering on black magic to create a body which produces a "pleasant" resonant strength at all wavelengths (...


4

The "test" described is being used incorrectly to support a potentially false claim. In linear system you will NEVER excite an undertone. This is simply not possible. It could be done by some non-linear coupling that cause sub harmonics to be generated. In Tim's experiment there is a false conclusion being drawn from the fact that plucking the high e ...


4

You have some good answers already but here's a test that I just performed on my upright acoustic piano. I pressed A3 (A below middle C) gently so that the damper was lifted but no sound was made. If you cannot manage this then play as softly as you can and wait for the note to end. Assuming that my piano is tuned well, the fundamental of this string is ...


4

Historically the ratios that define intervals come from the natural harmonics of a linear vibrating system. The harmonic frequencies are related to the fundamental tone by the relation fn = n*f1 (f1 = the fundamental frequency) We get the following sequence f1 2*f1 = octave 3*f1 = Defines the 5th, actually this is an octave and a 5th above f1, you can ...


4

It is fundamentals only. Apart from the mathematical problem (how to reduce a long series of overtone coefficients into a simple ratio) just the fundamental is accessible to normal tuning. The harmonics are called tone color since they are specific to an instrument. Even for piano a different octave will exhibit different overtones.


4

In general, older (like pre 1000AD theorists) counted only intervals from the bass. Thus, a major chord has the ration 4:5:6. This is enough to calculate other ratios though. The musical reason is that intervals against the bass supposedly (I think so too) show up stronger than against other voices. (Thus the dissonance of the fourth against the bass as ...


4

In other words, if i pluck an A string on a guitar with the A being 440hz, that means that single pluck has ejected 440 sound waves into the space which are now reflecting off surfaces? No. The string will start generating sound waves at a rate of 440/second. How many waves it will generate, depends on how long you allow the string to vibrate. If you don't ...


4

From the comments you seem to be asking not about the frequency spectrum, but about the stereo field. Yes, this is probably done by adding pseudo-stereo information using a 'stereo reverb' plugin. It conceivably COULD have been achieved by recording the (marimba?) sound in a very reverberant room with stereo microphones, but I suspect it's a dry sample ...


4

Being EXACTLY 1/5 is a coincidence (see Carl Witthoft answer). But the musical instrument size (or generally everything made to produce sound) is pretty much related to the wavelength of the sounds it produces. The laws of physics dictate that you cannot efficiently radiate sound (or any other waves, say, electromagnetic waves) using something much less than ...


4

Midi files are such a thing -- they describe, with flat numbers, the basics of what's going on in the music. Typically they are not read by humans and I'm unaware of any robust tools for doing so, though there does seem to be a few homebrew ones available by searching for "midi visualization". The other thing that comes to mind is the music animation ...


4

Having thought about this some more, I've decided to rewrite my answer... Your doubts about the acoustic properties of the harp are understandable. When heard in an orchestral setting, the harp is relatively quiet, requiring careful orchestration if one wants it be heard within a multi-instrument texture. However, a concert pedal-harp is in fact capable of ...


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