Its not intuitive to me how we first determined a note was 440Hz in the first place.
Also, when was this first done…AND…is there any ‘non-subjective’ reason why we have decided that particular frequencies are ‘better’ than others? they seem arbitrary.
Example: why is middle C selected at 261.62Hz? why can’t we select a particular pleasing note at 282Hz or 875Hz etc?
It’s as simple as 1Hz is one cycle per second. I’m not sure what the first tuning technique was, but the meaning of the frequency measurement is well defined.
There shouldn’t be an expectation that the notes that an instrument is tuned to matches up to integer number of cycles per second. There is a long history behind tuning A to 440Hz, and then to finding the other notes. For a start look at “equal temperament”.
It’s even worse than you think. The frequency (440 Hz) is based on the second which is itself arbitrarily defined. Those fractional Hertz are that way because we shoehorned a weird time period in for counting pulse wiggles.
I know nothing about music theory but I won’t let that stop me.
The first frequency measurement was a 60Hz wave by Edouard-Leon Scott with his phonoautogram.
As for what is a pleasing sound, that has fluctuated quite a bit. Concert A is now 440Hz but some claim the previous standard of 432Hz is better. Middle C is not “selected” to be anything. Because we now use equal temperament i.e. successive notes are in an equal ratio, to get the number of cycles for the next note you multiply by the twelfth root of 2 which is approximately 1.06. So Middle C is 220 (middle A) x 1.06 (A#) x 1.06 (middle B) x 1.06 = 262 (rounded). If you use the unrounded root rather than 1.06 you get the correct number.
Also, what is A has changed over time. In the mid 1800s, A435 was a standard. Even today some orchestras tune as high as A444. Baroque pitch seems to have standardized around A415 from what I read, but I could swear I’ve read period organs have varied wildly from A being in the high 300s to the high 400s. It’s just a somewhat arbitrary standard.
Huh? The tuning fork was invented in the early 18th century, for starters, if we are talking about precisely reproducible audio frequency standards.
That is common today for various historical reasons, but there has been and still is a range of tunings in use, and a performer has to be ready to deal with that. The differences among contemporary orchestras today are on the order of a few hertz, though, it’s not that wild.
Because 282 Hz is halfway between C sharp and D, not a C 
Note, in music it is possible to transpose a melody to a different key. The notes will sound the same relative to each other, but the whole thing will be higher or lower in pitch.
There is going to be some audible effect of “pitch inflation” (or deflation) on the timbre of a given instrument.
Just to slightly restate what’s already been said: ONE pitch is arbitrary. You can take A above middle C to be 440 Hz, or 432 Hz or 415 Hz, or whatever you want, really. But if you’re using an equal temperament scale, that fixes the pitch of all other notes. Once you’ve chosen your A to be 440 Hz, you can’t arbitrarily choose C to be anything other than 261.6 Hz because 261.6 = 440 / 2^{9/12}
432 was never really a standard. The first standardization was to 435. There was some movement to standardize middle C to 256 because it was mathematically appealing, but it never really caught on.
C at 256 only gives you A440 if you use Pythagorean tuning (which doesn’t really work with chromatic music). Equal temperament give you an A of 430.54.
Was this the first device that was able to show some particular note was the result of a measurable vibrations per second?
This was my first question…which I think got lost in the discussion. How did we first know (prior to oscilloscopes and the like) that something giving off a single note was vibrating at a known and defined Hz. Even 60 Hz is too fast to count vibrations per second.
It’s much easier to measure wavelengths of sound. I suspect that the first determination of frequencies derived from the known wavelengths and a measurement of the speed of sound.
We didn’t. Pitch wasn’t standardized to any degree until the 19th century. There were tuning forks, which could be used for calibration, but different tuning forks had different frequencies. They could be anywhere from about 400Hz to 460Hz. Orchestras, organs, whatever would be in wildly different pitches in different cities.
well…at some time…somewhere we were able to measure the number of vibrations of a tuning fork; or the number of pressure waves per second…or something.
When did we first measure the number of vibrations per second a sound was, and how was it measured?
You mention 440Hz or 460Hz…How were those numbers measured and determined?
As mentioned above, the phonoautograph could directly measure the frequency of a sound. It was patented in 1857. Perhaps that was the first time such a direct measurement was possible. Much earlier than that, instruments could be tuned using tuning forks, pitch pipes, or just by directly comparing to another instrument, without actually knowing the numerical value of the produced notes in cycles per second.
Sorry. I realize we keep getting distracted by discussion of historical pitch standards.
The numbers 460, 440, 409, 422, whatever weren’t determined until later. The tuning forks would be used to calibrate locally, but until the invention of measuring equipment like the phonautograph they wouldn’t have had a number to go with it.
As Chronos points out, once you have measured the speed of sound a measurement of frequency is reasonably easy and gets you frequency for free.
What is required is an understanding of tone and acoustics to join the dots. Even Pythagoras is believed to have joined most of the dots. But until a useful measure of time existed a quantitative answer won’t have been possible.
The big dog in the history of acoustics is Helmholtz. He pretty much single handidly brought about a modern understanding of acoustics and understanding of musical tone, harmony and timbre. He built a polyphonic siren, a device that generated known frequencies ab-initio and could demonstrate beat frequencies. This was about 1850. A simple siren is a great way of demonstrating frequency and tone. Hard to argue with such a simple device.
Just on the subject of scales and temperament. These are a case of you can’t get there from here. The unique prime factorisation theorem sees to that. Equal temperament allows arbitrary modulation of key, and is beloved by jazz artists but it is in some ways an exercise in levelling out the grief making most intervals equally lousy. Remarkably few instruments are actually tuned to equal temperament. They just approximate it in different ways. Bach’s Well Tempered Cavier is not written for equal temperament. It is written for instruments that provides a good temperament for the keys each piece is written in. Even a modern piano isn’t tuned to equal temperament. And may even not even attempt to approximate it depending upon its use case. A skilled piano tuner only needs a single tuning fork and a selection of wedges to selectively damp harmonics to create a good sounding temperament.
I’m not sure why jazz artists are specified here. Equal temperament well predates jazz. And jazz artists love experimenting outside 12tone ET. Calling it “beloved” seems to be an overstatement to me.
Yeah, I don’t know anyone who actually likes equal temperament. It’s like democracy: terrible, but better than everything else.
Depends on your jazz artist and era. Sure ET and modulation in general predates jazz, but there seems to be a particular love of the harmonic theory and modulation in general provided by ET in much jazz theory. Every book or course on improvisation seems to springboard from an assumption of ET. Typically the first chapter introduces the circle of fifths as the basis for discourse. No ET, no closed circle of fifths.
Once you get to a higher understanding of harmony and melody it breaks down, but ET tends to remain as a fundamental underpinning of some of the freedoms.
I still don’t quite understand. The theory of the circle of fifths goes back to the 1600s, well before ET. You don’t need ET to have circle of fifths theory. (Although you do I suppose to get back to the same starting note—perhaps that’s what is meant by “closed.”) But jazz music is very much based on playing in between the notes if you’re playing an instrument that is not fixed pitch. One of the bases of jazz started with ”blue” notes that are outside traditional Western harmony and temperaments. I don’t find most jazz sticks rigidly within ET, which is why I don’t understand the “love” comment.
Ok. Maybe I get it. With the chromaticism and upper chord extensions of harmonies, ET does make that stuff easier to deal with. I’m not sure I’d call it a specific love this genre has for it, but I’m just quibbling at this point.