Tone Generator Inaccuracies?

[sonusmagus]

I need to create very accurate tones @ 96K

I tried to create a 830.61Hz sine wave @ 96K

To get a perfect loop I should be able to multiply 830.61 X 9600 = 7973856 (or 83.061 seconds)

Then simply set start of loop at zero and end of loop at 7973856 and it SHOULD be 100% accurate

When I generate the tone and look at what has been calculated, something is wrong

This has always worked for me with Sound Forge

Any ideas on this?

Thanks

TINLEY

[steve]

A frequency of 830.61 Hz has a period of 1/830.61 seconds.
At 96000 Hz sample rate, to convert seconds to samples, multiply seconds by 96000.
So a single cycle at 830.61 Hz would be 96000/830.61 = 115.57770795 sample periods.

68991 cycles of 830.61 Hz at 96000 Hz sample rate would be:
1 cycle period = 96000/830.61 samples
68991 cycles = (68991 * 96000)/ 830.61 = 7973821.64914942
So 7973822 samples will be very nearly perfect.

[sonusmagus]

I had the first calculation, thanks

But where does 68991 come from?

What would make it perfect?

Can I do this:

83061 cycles of 830.61 Hz at 96000 Hz sample rate would be:
1 cycle period = 96000/830.61 samples
83061 cycles = (83061 * 96000)/ 830.61 = 9600000
So 96000.00 samples will be perfect

I was trying to account for the two decimal places and over complicating it

Now makes perfect sense to me

Thanks

TINLEY

[steve]

But where does 68991 come from?

I looked for the closest number of complete cycles to your figure of 7973856 samples.

To do that:
We know that 1 cycle is: "(sample rate)/frequency" samples.
How many cycles in 7973856 samples = (number of samples)/(samples per cycle)
Which gives us:
7973856/(96000/830.61)
= 68991.29721 cycles
Rounding to the closest number of cycles = 68991 cycles.

What would make it perfect?

Any whole number of samples that is an exact multiple of 96000/830.61
Try 100 seconds

[steve]

Any whole number of samples that is an exact multiple of 96000/830.61
Try 100 seconds

or 3,200,000 samples (33.333 seconds)

[Robert J. H.]

Any whole number of samples that is an exact multiple of 96000/830.61
Try 100 seconds

or 3,200,000 samples (33.333 seconds)

that's a pretty nasty frequency, isn't it?
The exact value (to 50 places) would be:
830.60939515989027704488357786743025088666010693809 Hz

The question is now how much accuracy one wants.
Steve's 33.3... seconds are perfect for 830.61 Hz
For 830.609 Hz it would be:
1,000 s / GCD(96,000,000 , 830,609) = 1,000 / 1 = 1,000 seconds
and for 830.6094 Hz:
10,000 s / GCD(960,000,000 , 8,306,094) = 10,000 / 6 = 1,666.667 seconds

That's the problem with such irrational, transcendental numbers...

Robert

[steve]

The exact value (to 50 places) would be:
830.60939515989027704488357786743025088666010693809 Hz

Is that for G#5/Ab5 at A440?

[Robert J. H.]

The exact value (to 50 places) would be:
830.60939515989027704488357786743025088666010693809 Hz

Is that for G#5/Ab5 at A440?

Exactly, for equal temperament to be precise.

[Robert J. H.]

Here's the Octave formula for the frequency value:
>> vpa(sym(440)*2**(11/sym(12)))

It works only with the Symbolic package installed.

[Gale Andrews]

I guess this is of most interest in the "Audio Processing" board so I moved it there.


Gale