Physics of Music: Why Are Musical Notes Standard Frequencies?

[jobyts]

Is there a specific reason why the music notes are of the well-known frequencies? Or, the frequencies just became the de facto standard from some historical musical instrument?

http://www.techlib.com/reference/musical_note_frequencies.htm

I was wondering if sound processing is similar to our brain tuned to the specific light frequencies (colors).
What's the science behind 7 notes? (I've heard chinese music has only 5 notes) Western and Indian classical music has 7 notes, even though both are not directly related or borrowed. Is it just a random coincidence, or there is science behind it?

 

[chroot]

The notes were chosen so that they produce pleasing sounds when overlapped. For example, a major third interval corresponds to a frequency ratio of 5:4. All pleasing chords are based on these integer frequency ratios. (The octave is a ratio of 2:1, the perfect fifth is a ratio of 3:2, etc.)

The simplest tuning systems, like those of Pythagoras, made use of the 3:2 ratio. As it turns out, a stack of twelve 3:2 steps is almost exactly equal to a stack of seven 2:1 steps. There is a slight difference, however, and it created some very real problems. A wide variety of solutions blossomed, each a trade-off in some way. Western music eventually settled upon the equal temperament system, which fudges the ratios a bit to make everything fit mathematically, while rarely subjecting the listener to noticeable dissonances.

The point of reference for the entire system, the A above middle C at 440 Hz, is a historical choice.

- Warren

 

[junglebeast]

"All pleasing chords are based on these integer frequency ratios."

That's very interesting..but I don't believe that it's impossible to make music that someoen might like that uses a different frequency ratio

 

[chroot]

That's very interesting..but I don't believe that it's impossible to make music that someoen might like that uses a different frequency ratio

Well, that's true -- beauty is in the eye of the beholder.

Most people, however, prefer the "consonance" of integer pitch ratios, because the waves overlap in a periodic fashion. (Three wavelengths of one note exactly correspond to two wavelengths of another, in the case of a [Pythagorean] perfect fifth interval.) When the waves overlap this way, no beat frequencies are produced.

Beat frequencies, or "dissonances," are regarded by most listeners as unpleasant. The "most unpleasant" pitch ratio is the tritone, (or augmented fouth, or diminished fifth, or "Devil's interval"), which has a pitch ratio of sqrt(2):1 in equal temperament

- Warren

 

[junglebeast]

Well, that's true -- beauty is in the eye of the beholder.

Most people, however, prefer the "consonance" of integer pitch ratios, because the waves overlap in a periodic fashion. (Three wavelengths of one note exactly correspond to two wavelengths of another, in the case of a [Pythagorean] perfect fifth interval.) When the waves overlap this way, no beat frequencies are produced.

Beat frequencies, or "dissonances," are regarded by most listeners as unpleasant. The "most unpleasant" pitch ratio is the tritone, (or augmented fouth, or diminished fifth, or "Devil's interval"), which has a pitch ratio of sqrt(2):1 in equal temperament

- Warren

Thanks for enlightening us. That does make sense. There's probably also a large aspect of social / cultural influences that shape our opinion of what is aesthetically pleasing

 

[chroot]

Thanks for enlightening us. That does make sense. There's probably also a large aspect of social / cultural influences that shape our opinion of what is aesthetically pleasing

I don't know the answer to that question, and it's perhaps impossible to sort out. On the other hand, we understand some of the neurological underpinnings of the experience of beauty (see https://www.amazon.com/dp/0131872788/?tag=pfamazon01-20 for enjoyable insight). We also know that all cultures, even aboriginals, have similar tastes. For example, all cultures appear to agree on a specific female waist-to-hip ratio as being the most beautiful. It appears that many (but certainly not all) of our feelings on beauty are hard-wired into us.

- Warren

 

[mgiddy911]

That unpleasant tritone is a staple in some types of music however. Examine some songs from 'Metal' music.

There are plenty of songs that make use of dissonance in a good way but again it is up to the listener to decide what they think sounds good yet at the same time the author is open to make what ever type of music whey want and it they think it sounds good then so be it.

The accepted western scale uses the equal temperament scale but as mentioned earlier that doesn't mean it is the end all be all when it comes to music composition. For any guitar players out there if you have ever examined internet sites that show you scale charts they generally have the common scales like major, the various minors (natural, harmonic etc), the pentatonics, but they also tend to list loads of "exotic scales" Indian, Spanish, Gypsie, Hungarian... etc. at first glance (or first listen) a lot of those scales sound strange or dissonant but that's only in comparison to the well know major and minor scales. That doesn't make them any less valid or useful in composition of music.

I think its worth taking a course in Physics of Music, I really enjoyed the course I took. Its a good way for physics students (or even non science/math oriented people) to experience something new that applies to their everyday lives

 

[f95toli]

Thanks for enlightening us. That does make sense. There's probably also a large aspect of social / cultural influences that shape our opinion of what is aesthetically pleasing

Perfect intervals (I, IV, V and VIII) are sometimes referred to as natural and are found in music from all over the world meaning just about all humans will find them pleasing, major intervals are "cultural" and are mostly found in western music.
Nowadays scales from e.g. Indian music are pretty common even in pop-music which shows that we can quite easily get used to new sounds.

Also, the A at 440 Hz is -as Chroot has already pointed out- just there for historical reasons. It is also to some extent a modern phenomena (due to the availability of electronic tuners); throughout most of history musicians just tuned their instruments so that they were in tune with the rest of the orchestra and the intervals were correct.
Many musicians still tune their instruments to other frequencies either on purpose or because they simply tune by ear using an "incorrect" starting frequency; Hendrix is a famous example, his "A" was usually around 410-420 Hz.

 

[junglebeast]

We also know that all cultures, even aboriginals, have similar tastes. For example, all cultures appear to agree on a specific female waist-to-hip ratio as being the most beautiful.

I think white people tend to find other white people more attractive, and I think black people tend to find other black people more attractive. They have different characteristics...larger lips, wider nostrils, larger butts (heard, "I like big butts, and I cannot lie?"), etc. Every culture looks different and has different proportions and the people from that culture tend to like the look of their own culture. I've also heard that fatness and long fingernails used to be considered attractive back in the days when they were synonymous with wealth. Plump women were considered attractive not too long ago...and now it's all about skinny women. So...while I'm sure that there are some basic fundamental qualities to attraction...I think the evidence shows that there isn't an "ideal" ratio for certain body part sizes that makes a person attractive to anyone.

 

[chroot]

I think the evidence shows that there isn't an "ideal" ratio for certain body part sizes that makes a person attractive to anyone.

No, as I said, the evidence clearly indicates that there is a ideal ratio. I'm not just making this stuff up!

In the studies referenced above, only frontal WHR preferences differed significantly among racial and cultural groups. When actual (circumferential) measurements were made, the preferred WHR tended toward the expected value of 0.7 universally.

http://en.wikipedia.org/wiki/Waist-hip_ratio

- Warren

 

[junglebeast]

No, as I said, the evidence clearly indicates that there is a ideal ratio. I'm not just making this stuff up!
http://en.wikipedia.org/wiki/Waist-hip_ratio

- Warren

I could argue with you, but I immediately want to tap that ***...

 

[signerror]

Beat frequencies, or "dissonances," are regarded by most listeners as unpleasant. The "most unpleasant" pitch ratio is the tritone, (or augmented fouth, or diminished fifth, or "Devil's interval"), which has a pitch ratio of sqrt(2):1 in equal temperament

This is rubbish. What joker says dissonant intervals are unpleasant? Dissonance is tense, unstable, a strong drive towards resolution - but tension is hardly unpleasant, neither in music nor Shakespearean drama nor stretching. This must be some sort of historical mistranslation, but it amazes me it's still be being perpetuated.

I particularly disagree with the characterization of the tritone as "most unpleasant".

Right there, in measure one! And there's other tastelessly dissonant notes too, 2nds and 7ths.

Oh no, the guy hit a wrong note. And look, he hits it again!

And here he just assaults your ears with a nonstop barrage of unpleasantness:

 

[signerror]

Is there a specific reason why the music notes are of the well-known frequencies? Or, the frequencies just became the de facto standard from some historical musical instrument?

There isn't, and as evidence I point out that over the last few centuries the whole spectrum has shifted by more than a semitone.

http://en.wikipedia.org/wiki/Pitch_(music)#History_of_pitch_standards_in_Western_music

However, individual humans can remember pitch/frequency for a long time (I'm not sure through what physical mechanism), so there's considerable inertia on shorter time scales.

 

[Loren Booda]

How do we know that the Western music scale is based on an original 440 Hz? I suppose Pythagoras could have used a standard string (copper of a particular gauge, say) tensed by a 1 kg weight, say, with two frets separated by one meter, say. He might have created notes comparable within perhaps a few Hz, or 1% error.

In Latin class we were told that ancient language pronunciation has changed considerably over the centuries. Written music dates from somewhere around the ninth century AD, I believe.

 

[slider142]

How do we know that the Western music scale is based on an original 440 Hz? I suppose Pythagoras could have used a standard string (copper of a particular gauge, say) tensed by a 1 kg weight, say, with two frets separated by one meter, say. He might have created notes comparable within perhaps a few Hz, or 1% error.

In Latin class we were told that ancient language pronunciation has changed considerably over the centuries. Written music dates from somewhere around the ninth century AD, I believe.

440Hz is quite new; it was only recently denoted concert A in 1925 by the US and 1939 by an international conference in London. The standard for tuning instruments has drifted all over the map before these periods. Ie., Mozart used 422 Hz (next time you play Mozart, tune your instruments a semitone + a microtone flat :D), while it was common in other periods for extremely different pitches to be used in the same country, ie., secular vocal pitch vs. church music pitch. Ie., 17th century North German church pitch was around 560 Hz!

 

[chroot]

Right there, in measure one! And there's other tastelessly dissonant notes too, 2nds and 7ths.

Bravo!

- Warren

 

[Coin]

"All pleasing chords are based on these integer frequency ratios."

That's very interesting..but I don't believe that it's impossible to make music that someoen might like that uses a different frequency ratio

There have been attempts at this, not just spicing up a traditional piece with dissonance but actually rejecting the idea that the standard simple-ratio relations are desirable at all. Look up "twelve-tone music" or "atonal music" (the former is much easier to find)

It has produced some fascinating works but not been a good path to commercial success

 

[jobyts]

They have applied golden ratio in music too.

http://en.wikipedia.org/wiki/Golden_ratio

 

[Ivan Seeking]

The Music Instinct
Science and Song
http://www.pbs.org/wnet/musicinstinct/

 

[physics girl phd]

There was a PBS special on this (http://www.pbs.org/wnet/musicinstinct/" ) just last night. While I've heard quite a lot of this thing before, there were some interesting things. Apparently young babies tend to cry varying their tones with set intervals, like a third or a fifth. They also tend to have preference for tonal music versus dissonant music... even if they were not likely exposed to this in the womb (say if they are born from deaf parents, would would not have had music playing regularly in the household.

I did, however, think it pretty hilarious that they had Brain Greene (string theorist) on explaining resonance on a string. A lot of other things were PBS-predictable too. Bobby McFarrin.. Yo Yo Ma... augh. I certainly didn't stay up til 11PM when it was finishing up.

edited to add: augh -- Ivan beat me to it! 3 min! I take too long to type!

 

[BoomBoom]

I did, however, think it pretty hilarious that they had Brain Greene (string theorist) on explaining resonance on a string.

Me too...I thought that show was fairly well done until the last 5 minutes or so when they throw in string theory, straight out of left field! What was that all about?

 

[Ivan Seeking]

Me too...I thought that show was fairly well done until the last 5 minutes or so when they throw in string theory, straight out of left field! What was that all about?

I think the point was that music is just one representation of a mathematical structure found throughout nature.

 

[Ivan Seeking]

edited to add: augh -- Ivan beat me to it! 3 min! I take too long to type!

I could tell you were about to post so I jumped on it.