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 ...


11

is the crest of a sound wave equaled to high amplitude/ high volume and if so, does that mean the trough is low amplitude/ low volume? Not exactly. A sound wave is something that is perceived when sound pressure is changing at a rapid frequency - oscillating up and down at 20 cycles per second or more. If we say that the crests are high pressure and the ...


11

You certainly need to make the complete instrument before you try to scale it, as another answer said. Unless the design is an accurate copy of the Yamaha recorder, the pitch of the head joint on its own could be anything. In particular, it will depend on the design of the joint between the head and the rest of the instrument. To scale an instrument "...


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 ...


9

I went down a similar road. There is an entire branch of physics related to sound that is called acoustics. Starting to look for books and more information on "acoustics" will help you find more and better materials as you move forward. The subject of acoustics is pretty broad - there are many aspects of acoustics that are not directly applicable to ...


9

"in a vacuum" will not make sound, but yes your thoughts are on the right track. All vibrating bodies, strings, plates, beams, etc, have a natural set of harmonics (or overtones as described by some). These are usually determined by the boundary conditions on the vibrating object and a related to the fundamental tone by a simple relationship. For the ideal ...


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 ...


8

For a pipe without any holes, the fundamental pitch of a pipe is determined by f = v/2L, where v is the speed of sound and L is the length of the pipe. But when you start putting holes in, you get a mix of pipe lengths. It gets messy (mathematically) in a big hurry. Placing a hole in the pipe shortens its length, but the new length - the effective length - ...


8

This has been done, at least as an experiment. There's a paper Artificial buzzing lips and brass instruments: Experimental results (pdf download link) in the Journal of the Acoustical Society of America describing how they did this for a trombone mouthpiece. Mechanical saxophone embouchures have been done before as well. Here's one playing John Coltrane's ...


8

Actually music notes are not discrete. The guitar, like the piano, is designed to have equal tempered tuning rather than just tuning. In that tuning system notes are discrete, half step = 12th root of 2. Even in just tuning we only have 7 notes in the diatonic scale but we are free to make slight deviations and some cultures do use quarter steps (a half ...


7

The main problem is that it's an oversimplified assumption to consider an open hole as a perfect open boundary condition for the air column. In fact such a hole still has a significant impedance. On the other side, the mouthpiece is not a perfect closed (reeds) or open (flutes) boundary condition, and also a closed hole still affects the column somewhat. A ...


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

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

To make an electronic organ sound like a conventional pipe organ, the most important component is the sound reproduction itself. Even on your tiny one-manual ten-stop instrument, a full 8-note chord can sound 80 pipes simultaneously. On a larger instrument, there may be several hundred individual pipes sounding together. In contrast to this, an electronic ...


6

The answer to this actually depends on the instrument. There are three essentially different reasons why an instrument's overtones might be (more or less) harmonic, and at least two of them might be in play for stringed instruments. The vibrating element resonates at a harmonic set of frequencies (as a string does), as described in the other answers. An ...


6

The answer lies in a mixture of engineering and "pure" physics. And a lot of Fourier Transforms :-) . As we all know, the strongest resonances happen when the second string's pitch is an integral multiple of the first string. To see why, let's start with just the sound wave in air reaching the second string. The first crest excites the string, and just as ...


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

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), ...


5

What you observe is a physical property of many resonators / oscillators. In the case of vibration every resonator has different modes of vibration. In the case of a drum head or a cymbal these modes are not harmonic, in the case of strings or air columns the modes of vibration wich are noticeable are harmonic. Think of a string: It is fixed at both ends if ...


5

Have a look at the picture at https://www.moeck.com/en/service/faq/the-recorder-family.html. The instruments are indeed (roughly, at least) scaled proportionally in all three dimensions. I would do that, especially since you're talking about a small change of scale rather than printing an alto or tenor recorder from plans for a soprano. I would try to ...


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 ...


4

Looks like you're asking two things: 1) the equation of the curve for the bent section at the end, 2) the variation in sound, if any, due to spacing between the 'out' and 'in' sections of the slide. In any case, the answer is that there's next to no effect from the curve selection or the spacing. The most likely effect might come from the choice of location ...


4

A crest and a trough both cause the eardrum to move away from its normal, undisturbed, resting position. Hence, the crest and the trough both embody a loud sound. When there is no sound, the ear drum is still; it is resting in a central position. When sound waves strike the eardrum, it moves the eardrum inward (crest) and outward (trough). The ear converts ...


4

Why and how? How Frets are designed in such a way? If you actually have a guitar in your hands, it's very obvious how frets work. The fret is raised above the fingerboard, so if you place your finger behind a fret, the string will become 'stopped' at that fret such that the 'speaking length' of the string is the length between the bridge and the fret. Here'...


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 ...


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