How does that work?

[DJpullchord]

Yo.

Just had a look because I’m bored and noticed the relationship between frequency and note is not linear? Does that mean our brain is doing something weird?

[Earbrass]

Ever noticed that the frets get closer together the further you go up the neck? There's a clue there.

[DJpullchord]

Yeh but it’s still a semi tone.

[Stylon Pilson]

Indeed, it's not linear. Going up an octave corresponds to a doubling in frequency. Most guitars are tuned using twelve tone equal temperament, which means each semitone corresponds to multiplying the frequency by the 12th root of 2 - approximately 1.05946.

S.P.

Edited October 22, 2018 by Stylon Pilson

[fretmeister]

Exactly how bored are you?

[Owen]

G in a chord of C is not the same as G in a chord of Eb - in the classical world.

[paddy109]

35 minutes ago, Stylon Pilson said:

Indeed, it's not linear. Going up an octave corresponds to a doubling in frequency. Most guitars are tuned using twelve tone equal temperament, which means each semitone corresponds to multiplying the frequency by the 12th root of 2 - approximately 1.05946.

S.P.

[DJpullchord]

4 hours ago, Stylon Pilson said:

Indeed, it's not linear. Going up an octave corresponds to a doubling in frequency. Most guitars are tuned using twelve tone equal temperament, which means each semitone corresponds to multiplying the frequency by the 12th root of 2 - approximately 1.05946.

S.P.

Fantastic.

If sounds were divided up into a different amount and used culturally for centuries,  would it be accepted as the norm? 

Are we just conditioned to hear and use this division of the octave because it’s the only thing we’ve heard in western music?

[tonyquipment]

5 hours ago, Stylon Pilson said:

Indeed, it's not linear. Going up an octave corresponds to a doubling in frequency. Most guitars are tuned using twelve tone equal temperament, which means each semitone corresponds to multiplying the frequency by the 12th root of 2 - approximately 1.05946.

S.P.

 

[BassTractor]

11 hours ago, owen said:

G in a chord of C is not the same as G in a chord of Eb - in the classical world.

...and there's a daily pet peeve annoyance for me right there: the proverbial sopranos not fathoming that aspect, and using the wrong intonation, therethrough denying the very harmonic development they were supposed to express. Aaaarrgh!

... aaaand lower my shoulders...

OK, I'm fine again.

[Mykesbass]

4 hours ago, BassTractor said:

...and there's a daily pet peeve annoyance for me right there: the proverbial sopranos not fathoming that aspect, and using the wrong intonation, therethrough denying the very harmonic development they were supposed to express. Aaaarrgh!

... aaaand lower my shoulders...

OK, I'm fine again.

And today's award for finest usage of archaic language on the internet goes to @BassTractor

[BassTractor]

6 minutes ago, Mykesbass said:

And today's award for finest usage of archaic language on the internet goes to @BassTractor

Ha! 😃 What was archaic? Was it "therethrough" maybe? 

Hm. Probably everything was... I'm getting old; my back hurts and I can't ride my dinosaur anymore. 😥

[Jus Lukin]

-

Edited February 27, 2022 by Jus Lukin

[Stylon Pilson]

13 hours ago, DJpullchord said:

If sounds were divided up into a different amount and used culturally for centuries,  would it be accepted as the norm? 

Are we just conditioned to hear and use this division of the octave because it’s the only thing we’ve heard in western music?

Well, the octave sounding pleasant is universal - it's a basic consequence of physics. If you have two waves, one of which is exactly twice the frequency of the other, then they sit on top of each other nicely. See this image, for example:

You'll notice that wherever the waveform crosses the y-axis, those points stay in the same place moving down the image.

However, our subdivision of the octave into 12 semitones is definitely a western cultural thing. Other cultures divide into different amounts (see here) and that's even before we start moving away from equal temperament and into other tunings.

S.P.

[Bridgehouse]

I suspect some of our familiarity with harmonics and our own comfort with certain frequencies relates to the human voice as well:

(taken from Wikipedia article on harmonics)

Many acoustic oscillators, such as the human voice or a bowed violin string, produce complex tones that are more or less periodic, and thus are composed of partials that are near matches to integer multiples of the fundamental frequency and therefore resemble the ideal harmonics and are called "harmonic partials" or simply "harmonics" for convenience

[TrevorR]

It's an unashamedly populist explanation and I'm sure that academic types could poke many holes in the details of the explanation but as a layman's guide to how scales and temperament work this is a good watch. The whole of the Howard Goodall's Big Bangs series was hugely informative, watchable and entertaining.

 

 

[missis sumner]

Never mind the original question 😄, how do speakers manage to produce all those different sounds all at once?

[Stylon Pilson]

11 minutes ago, missis sumner said:

How do speakers manage to produce all those different sounds all at once?

Easy, they just add waveforms together.

The real question is, how does our brain manage to pull them back apart into their components? So far, the best answer that we've got is "magic".

S.P.

Edited October 24, 2018 by Stylon Pilson

[Owen]

1 hour ago, missis sumner said:

Never mind the original question 😄, how do speakers manage to produce all those different sounds all at once?

That's nothing. A needle on grooved plastic and sound comes out? THAT is bonkers. 

[Norris]

2 hours ago, owen said:

That's nothing. A needle on grooved plastic and sound comes out? THAT is bonkers. 

Or indeed a rapid series of on/off switches as used in digitised sound

[Count Bassy]

On 23/10/2018 at 09:42, Stylon Pilson said:

Well, the octave sounding pleasant is universal - it's a basic consequence of physics. If you have two waves, one of which is exactly twice the frequency of the other, then they sit on top of each other nicely. See this image, for example:

You'll notice that wherever the waveform crosses the y-axis, those points stay in the same place moving down the image.

However, our subdivision of the octave into 12 semitones is definitely a western cultural thing. Other cultures divide into different amounts (see here) and that's even before we start moving away from equal temperament and into other tunings.

S.P.

There are also other 'fundamental' intervals that work very nicely, but these get modified in equal temperament so that they but work equally well in all keys - but are less than perfect in any key.

[TrevorR]

8 hours ago, Stylon Pilson said:

Easy, they just add waveforms together.

The real question is, how does our brain manage to pull them back apart into their components? So far, the best answer that we've got is "magic".

S.P.

Easy answer... immense levels of processing power that would make the guys at Cray feel ashamed. All crammed into a compact mobile housing with a range of hugely sensitive sensors built in.

Amazing thing the brain.

Edited October 24, 2018 by TrevorR