60

Note: For the physics and neurophysiology covered in this answer I am going to be oversimplifying for brevity. They are not the "same" but they have the same pitch class. Notes that sound similar are said to have the same pitch chroma and the collection of all these notes are said to be in a pitch class. The octave, however, does differ in pitch height ...


50

The linked answer is a bit of a mess, and it's a common mess for people to make. When we talk about the exact frequencies of each pitch class, we have to know the temperament, and a reference pitch. For example, 12-tone equal temperament (12TET) with A4=440Hz is a standard in modern music. From those two parameters, we can extrapolate the exact frequency of ...


46

By definition this is not possible. Just intonation ratios are rational numbers, N/M where N, M are integers. Equal temperament is based on defining the smallest ratio as the n-th root of 2, 2^(1/n). For 12TET n = 12. What you are basically asking is if an irrational number can be made to exactly match a ratio of integers. This will never be possible....


33

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 ...


29

The short answer is that for 12-tone equal temperament (12TET), the de facto tuning system for western music, Db and C# are exactly the same sounding note. Exactly what frequency that note sounds like for a given octave also depends on the pitch reference, which is typically A4=440Hz. According to 12TET, we break the octave into 12 equal ratios. Since an ...


26

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 ...


24

They're not the same sound, and depending on how specific you're being, they're not the same note (though they're both 'A', 440Hz is A4, 880 is A5). In most contexts, they'll be the same degree of the scale, which means they'll function similarly (but not the same) as part of chords and harmonies. You may be able to hear that two different A notes, played ...


23

It's because the way the ear actually hears pitch differences (for most people) is based on frequency ratios, rather than absolute frequency differences. If I played you "Twinkle Twinkle Little Star" starting at on a note of 400 Hz, and then played it again with another 300 Hz added to the frequency of each note, it wouldn't sound like the same tune. ...


23

Are there any All-Pass filter plugins(AU, VST, AAX)? The standard EQ plugin of Reaper (ReaEQ, you can also get this as a separate VST plugin) has different modes for the filters (a parametric EQ is nothing but a cascade of tweakable filters), including allpass. What does changes the phase relationship among various frequencies mean and what is its musical ...


22

440 Hz is the standard that has been adopted. Before it was, an instrument tuned in one country or even city was out of tune in another; confusion reigned. The short version of it is that countries got together in a conference and agreed on using 440 Hz as a standard. Bach tuned at 415 Hz, which was the standard in those days and is still ...


21

The other answers approach this from dividing the octave and showing that equal divisions must be irrational. Another way of looking at this is to consider whether we can compose an octave by successive multiplications with a rational number. The result is of course the same: we can't. Start with the Fundamental Theorem of Arithmetic: every integer ...


20

There is no one way to use an EQ, but there are a few common techniques that people use to EQ, and they can be applied on most sources. First a few general tips: Make small changes. EQs are not magic, and they will not instantly improve your recording. They are best for making small tweaks. Be careful with boosting. It's oftentimes better to attenuate ...


19

Because of dynamics called room modes. Room modes are the collection of resonances that exist in a room when the room is excited by an acoustic source such as a loudspeaker. (...) each frequency being related to one or more of the room's dimension's or a divisor thereof. To keep things simple, we will assume the room has 6 parallel walls (right prism or ...


17

In general, smaller intervals do not sound as pleasing in a bass register as they do in a treble register. This is a general effect that occurs regardless of whether you play a consonance or a dissonance, although it is more noticeable with dissonances. What happens is that the overtones of the bass notes end up having more noticeable clashes between them, ...


16

The "Jazz Bass Mid Scoop" is absolutely real! When the Jazz bass is played with both pickups at the same volume, the sound will be mid-scooped. The term "mid-scooped" means that the mid frequencies, somewhere between bass and treble, will be reduced in volume. When the pickups are set to different volumes, the scoop goes away and the ...


15

They are both the same note, if note means letter name. They're both A, but 880 is an octave higher than 440. The 440 A has harmonics on most instruments, one of which being the second harmonic exactly an octave higher. In fact, on some instruments, this note is almost as loud as the fundamental, so the two can sound nearly the same. Most of us would hear ...


15

Too long for a comment. The existing answer does a good job of explaining that it's because of equal temperament, but as to why we use equal temperament, an equal temperament fifth is 1.4983... which sounds almost exactly like 1.5 but it's cleverer. 1.49830708...^12 = 128 exactly. 2^7=128 i.e. if you stack 12 tempered fifths on top of each other, you will ...


15

I don't understand what you mean by 'pitched at'. Most instruments will use A=440Hz as a reference point, and that's how each and every orchestral instrument gets to be in tune with the rest. A flute is a concert pitch instrument, thus will play a C or whatever and it'll sound like a concert C. You may be confused by transposing instruments, like trumpet, ...


15

As I understand the question, this is pure mathematics: No it is impossible. No matter, how many divisions you have, say n, the step width will always be nth root of two and therefore an irrational number. The just relations are rational numbers, so there will always be approximations, but the more you choose, i. e. the higher n is, the closer you will be ...


15

For the purposes of this question, lets consider three broad categories of musical sounds: Unpitched sounds - examples include cymbals, bullroarer Semi-pitched sounds - examples include tom-tom drums, wood blocks Pitched sounds - examples include woodwinds, strings, brass, xylophone, glockenspiel, most non-percussion instruments Maybe instead of categories ...


14

Well first, the amount of power inherent in the average festival rig or even an installed club system will dwarf what you can get out of any four speakers on the planet. That chest-thumping kick drum that's a mainstay of EDM is produced by moving a lot of air very quickly, creating a shockwave you can feel. That requires a lot of big cones, in turn requiring ...


14

I'm just going to answer the question "What about tangent, or other functions", since the rest seems to have been fairly well handled. All sounds that we hear as having a definite pitch or note can be represented by a periodic function. As I wrote in my comment, any repeated shape represents a periodic function. Most periodic functions, both in the real ...


14

I think that your attempt at "understanding how the pitch affects the note" needs an answer with a deeper root than has been given. This is slightly mathematical, but rather necessary. First, let's establish common simplified terminology: A frequency is a physical characteristic of the sound and it is absolute (does not depend on the instrument, tuning ...


14

Essentially, it's because we humans perceive pitch on a logarithmic/exponential scale. We hear an octave when the frequency is doubled or halved, not when it has a certain amount added or subtracted to it. Since musicians (well, the western ones, anyway) divide the octave into 12 equal parts, we had to take the 12th root of two as our factor to represent a ...


13

The ratio between the frequencies of successive half-tones in a 12-tone equally tempered scale is 21/12. So to lower the frequencies by a half tone, you need to stretch the file so it is 21/12 ≈ 1.05946309 times as long.


13

There is one observation with respect to primes. No prime power (except 0) is a power of any other prime. Thus no number of stacked fifths will be equal to any number of stacked octaves. (Taking a fifth to be a ratio of 3:2). Thus, any useful music over more than a few notes will need tempering. "Pythagorean" tuning uses only ratios using 2 or 3. "Just" ...


12

It is significant when you are trying to tune an instrument by ear, using the purity of intervals as your guide. You (and the pages you link) refer to jumping up 7 octaves vs. 12 fifths, but don't forget that any notes you reach that way can also be brought down by one or more octaves as well. To illustrate this, let's bring all the notes down into the same ...


12

If you mean this curve: probably because it was only calculated using the first 6 harmonics. Plomp & Levelt 1965: In this way, the curves ... were computed for complex tones consisting of 6 harmonics. ... shows how the consonance of some intervals, given by simple frequency ratios, depends on frequency. And this one: was also only calculated with ...


11

Yes, some frequencies are easier to hear. We tend to be specially sensitive to frequencies around 2000 and 5000 hertz. The resonance of the ear canal and the transfer function of the ossicles of the middle ear cause of this phenomenon. We see this measured in equal-loudness contour charts, a study first performed by Harvey Fletcher and Wilden A. Munson, ...


11

The figure in the Wikipedia article tells you what you are asking, if you're willing to tabulate the deviations by reading the green line. The vertical axis is the number of cents that the key is tuned away from equal temperament, e.g. the C two octaves above A440 (C7) is about 10 cents sharp, i.e. the frequency is a factor of 210/1200 sharp, or the actual ...


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