Semitones, Octaves and Note Frequency

Can someone validate this for me please - trying to get something straight in my mind:

 

- Note = Semitone

- 12 Semitones in an Octave

- One Octave Higher than a Semitone is a note that has twice the frequency

- One Octave Lower than a Semitone is a note that has half the frequency

 

So, if I had a note at 20Khz (Higher end of audible frequency range) then 1 octave below would be 10Khz, an octave below that 5Khz, then 2.5Khz, 1.25Khz and so on. Since there are 12 semitones in an octave this would suggest that the higher the octave, they greater the frequency between semitones?

 

Am I off base with these assumptions?

 

Many Thanks,

 

Andy

That's it pretty much

That's it pretty much

 

Thanks triplets!

A note is a note,another note a semtone higher is a different note...a semitone higher!

A note an octave higher than any given note is indeed double the frequency.

 

In the tempered system usually considered universal,a semitone higher is 1.059463094... times the frequency of the reference note.(That being the 12th root of 2,so multiplying any number by that amount 12 times will double the original number...ie an octave or 12 semtones).

 

A tone is thus the 6th root of 2 higher,a minor 3rd the 4th root of 2,a major 3rd the3rd root,and a tritone the square root.

 

 

So whereas E would be 3x440Hz/2=660Hz in a perfect theoretical harmonic,a tempered one is 659.25511382573871Hz...

 

You dig?

A cent is thus the 1200th root of 2 higher...

A cent is thus the 1200th root of 2 higher...

Hey thanks! it's good to know what a cent is...

 

let me see if I got this right, 100 cents = $1

 

8) yeah, I'm just kidding... but really it's neat to know the relative value of a cent; I always assumed it was 100th (of a half step)

 

or is that the same as 1200th root of 2

Yeah,it's the same. The rate needed to double the frequency in 1,200 steps.

(1.000577789506555).

A cent is thus the 1200th root of 2 higher...

 

No need to count quite that high. It's the 12th root of 2.

 

Don't you feel better now??

 

12th is a semitone,1,200th a cent.

Do the maths!

See me after class.

My bad Mr. Moth. I didn't read "cents".

 

Note to self: don't try to figure out math (or maths) before the first cup of coffee of the day.

Note = Semitone

No.

 

- A note has a fundamental, and its frequency determines the perceived pitch of the note.

- A semitone is the interval between two notes next to each other in the chromatic scale (12 note scale).

 

- One Octave Higher than a Semitone is a note that has twice the frequency

- One Octave Lower than a Semitone is a note that has half the frequency

Worth noting that this is only true in theory. In practice, one octave higher is a little over twice the frequency. That make an octave lower a little under half the frequency.

 

then 1 octave below would be 10Khz, an octave below that 5Khz, then 2.5Khz, 1.25Khz and so on. Since there are 12 semitones in an octave this would suggest that the higher the octave, they greater the frequency between semitones?

Yes, musical intervals follow a logarithmic frequency scale. Here are the theoretical frequencies of the notes on a piano keyboard. In practice, piano tuners typically "stretch" the tuning, meaning higher notes are actually higher, lower notes are actually lower, so that an octave higher is a little over twice the frequency.

 

http://www.vibrationdata.com/Resources/piano_keys.jpg

In practice, piano tuners typically "stretch" the tuning, meaning higher notes are actually higher, lower notes are actually lower, so that an octave higher is a little over twice the frequency.

 

Why David?

In practice, piano tuners typically "stretch" the tuning, meaning higher notes are actually higher, lower notes are actually lower, so that an octave higher is a little over twice the frequency.

 

Why David?

 

Because we typically don't perceive octaves as 2x the frequency, but a little over 2x.

Because we typically don't perceive octaves as 2x the frequency, but a little over 2x.

 

But isn't that just because that's the way they're tuning the instrument and we've gotten used to it? Or is there some other reason that we perceive octaves a little over 2x?

Why David?

This is a bit more detailed: http://en.wikipedia.org/wiki/Piano_tuning#Stretched_octaves Remember, equal temperament, which we pretty much all use today in western music, is nothing but a compromise.

Wow! Thanks for the info guys...

 

Very interesting!

12th root of 2

 

So is the 12th root In the same notation as a square root, cube root etc? Sorry I can't represent this mathematically - iPad limitation.

 

You dig?

 

Like a Navvy

So is the 12th root In the same notation as a square root, cube root etc? Sorry I can't represent this mathematically

 

http://upload.wikimedia.org/math/7/0/b/70b8b8fc763c20423a65bd934e378085.png

So is the 12th root In the same notation as a square root, cube root etc? Sorry I can't represent this mathematically

 

http://upload.wikimedia.org/math/7/0/b/70b8b8fc763c20423a65bd934e378085.png

 

Ok...just as I thought..

This is a bit more detailed: http://en.wikipedia.org/wiki/Piano_tuning#Stretched_octaves Remember, equal temperament, which we pretty much all use today in western music, is nothing but a compromise.

 

Thanks David!

 

That link was helpful. Now I get it.

A good piano tuner will offer the client a choice of how much they'd like the top and bottom stretched. I mention this to make the point that there really aren't any "absolute" frequencies for the notes subject to stretch tuning, as it's a matter of personal choice, or in some cases, need.

I knew about piano tuning, but the link at the bottom of the Wikipedia link David gave increased my understanding: http://en.wikipedia.org/wiki/Pseudo-octave

A good piano tuner will offer the client a choice of how much they'd like the top and bottom stretched. I mention this to make the point that there really aren't any "absolute" frequencies for the notes subject to stretch tuning, as it's a matter of personal choice, or in some cases, need.

 

Yeah, a piano with no beating or harmonic "inconsistencies" would sound dead.

 

Perfection sucks.

Isn't this stuff what Logic Pro's "Software Instrument Scale Settings" section is all about...

http://documentation.apple.com/en/logicpro/usermanual/index.html#chapter=43%26section=6

Isn't this stuff what Logic Pro's "Software Instrument Scale Settings" section is all about...

http://documentation.apple.com/en/logicpro/usermanual/index.html#chapter=43%26section=6

 

No. That allows you to adjust the intervals within an octave, we're discussing stretching the octave itself - which Logic itself doesn't allow you to do. Some instruments, however, such as the EVP88, do allow you to do it.

Because we typically don't perceive octaves as 2x the frequency, but a little over 2x.

 

I don't believe that's true, and even on that Wiki page if you listen to the midi examples, the perfect 2:1 octave sounds far more consonant.

 

Pianos are tuned that way to make them "sing", and as Ski pointed out, this is not a fixed formula but up to pesonal preference. It also doesn't hold for other types of Western instruments, each class of which have their own tuning peculiarities according to their inherent structure.

 

It is strange that higher pitches sound better sharp than flat, and lower pitches sound better flat than sharp. But we do generally perceive a perfect 2:1 octave as the most consonant.

 

EDIT: Until you get to about 9000Hz, then bigger octaves come into play, which makes sense in terms of elasticity of membranes.

Because we typically don't perceive octaves as 2x the frequency, but a little over 2x.

 

I don't believe that's true

 

Little exercise for you: listen to that sample, and tell me if this sounds in tune to you? If not, can you tell if a particular note strikes you as being flat or sharp?

 

I'm honestly curious to hear what you (and anyone else interested in doing the test) think.

 

http://logicprohelp.com/tuning.aif

What's that G doing in there? Oh, and the top C sounds a tiny bit flat.

 

(disclaimer: this is before having my coffee today...)

The top note sounds maybe slightly flat, but the notes are not held for long enough really.

 

I tested the Mel scale with pitch oscillators in Logic, and I found (at great expense to my ears) that from 1000Hz, 2000Hz sounded like an octave, 4000Hz again sounded like an octave, but 8000Hz had to be sharpened to around 9100Hz to sound like an octave.

 

I've not read the full paper that the Mel scale is based on, but from the abstract I see that it was based on the opinion of a mere five people.

High note flat & possibly the second highest as well but to a lesser degree