Need the frequencies of 20 logarithmically distributed non harmonically related sines

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#4
just guessing at a manual way of doing it.

Start at 17kHz and list the first 10 harmonics.
Guess at the next lower frequency ~half an octave below. say 17k/1.4 ~12kHz.
list all the harmonics up to your first limit of 187kHz. Do any coincide? Adjust the 12k till you have sufficient gap between all the individual harmonics.
Proceed to the next F, again about half an octave below. Repeat non coincidence test.
Repeat a further 17 times.

Now stop when you get bored.

Put all that into the spreadsheet mentioned and adopt a fixed ratio between the fundamentals. Make no adjustment to the new frequency, just use the spreadsheet to identify frequencies that are closer than your tolerance to be able to separate them. use an adjustable frequency factor. Step that frequency factor.

You may discover that the best spacing of all the frequencies occurs when the factor is 1.39825 ( or any other number that pops out of the investigation.)

Keep in mind that the frequencies do not need to be integers.
But whatever comes out must be able to be converted to a digital software implementation.
 
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#6
Perhaps an evenly tempered scale, with a non-transcendental number of tones
per octave? You would obviously want to avoid interger tone counts like 12, 19,
and 31 tones per octave. Also 13 steps per tritave, these logarithmic scales are
purposefully rich in near-harmonics. How to make it so that you have the least
harmony in such a system? That nightmare I would just let a computer monte-
carlo and sucessively aproximate possibilities until a best (worst) fit is found.

Do we want the worst overall average, or the least harmonic best single case?
 
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#7
Those 20 fundamentals will give ~20000 harmonics by the time the window has reached 187kHz.

Can one reasonably expect a sampler to be able to differentiate between all those frequencies to be able to measure them separately?
 
#8
janneman said:
This is what AP uses in there FastTest procedures. Nonharmonic, so that HD products in the FFT fall in empty bins. I guess that's why you want them?

jan
Click to expand...

Hello

Yes, that's what I need.

It look like a logarithmically distributed progression of the frequencies.

I want to do a multitone IM THD test, a test who will be closer to musical signal. Nelson Pass did a sim of a 7 signal multitone IM THD test and it was very revealing.

My Pc can generate simultaneous sines at a -110 db noise floor, it's more easy than doing it with an analog sines generators.

Thank you

Bye

Gaetan
 
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#9
gaetan8888 said:
Hello

Yes, that's what I need.

It look like a logarithmically distributed progression of the frequencies.

Thank you

Bye

Gaetan
Click to expand...

Actually, there's a program called makewave.exe from AP, used to be free, where you can specify how many freqs, what band, crest factor, phase relations etc and it calculates the table for you.
It might still be at ap.com under legacy downloads.

jan
 
#10
Samuel Groner said:
The factor a between two frequencies is simply:

a = (fend / fstart)^(1/(n - 1))

Where here fend = 17 kHz, fstart = 30 Hz and n = 20. So a = 1.39609, and the resulting frequenices are 30 Hz, 41.88 Hz, 58.47 Hz etc.

Samuel
Click to expand...
I agree. This gives a progression like notes on a piano. Bach well tempered keyboard.
But I am not sure this is the wanted answer.
What is the defintion of "frequencies logarithmically distributed".
 
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#11
mchambin said:
What is the defintion of "frequencies logarithmically distributed".
Click to expand...
f👎/f(n-1) == f(n-1)/f(n-2), for any n
--> log(f👎) - log(f(n-1)) == const, for any n

Samuel's formula does NOT guarantee that the frequencies and harmonics will never collide. Choose the wrong params and they do collide.

Years ago I wrote a small C program that calculated FFT bin numbers which do the job, basically a simple brute-force sieving algorithm. Can't seem to find the sources nor the executable, though.
 
#13
I see, it is much more involved than I thought.
Re reading the posts, I see the requirement is more about "non harmonic tones".

The frequencies in the file ( ISO non harmonic tones ) attached to post #3 are not exacly logarythmicaly spaced.

20 frequencies from 30Hz to 17KHz with f👎/f(n-1) =(17000/30)^(1/19) spacing don't give frequencies or harmonics collision.
But I see, it is required, not only to avoid collision, but to stay far from it. I understand, this is the reason, for a non exact spacing.
This becomes, as said in post #6: A nightmare.
 
#14
Do it manually for just two frequencies. Stop when you reach the 10th harmonic of your upper frequency limit, i.e 187kHz.
Try 10kHz and 17kHz as your first two.
Are any of their harmonics coincident?
Are any of the harmonics close enough to each other that the sampler cannot separate them?
How far do you need to move the 10kHz fundamental such that all the harmonics are separated by a gap that your sampler can differentiate?
 
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#15
Spectral Contamination

I think what you are looking for is similar to this. The challenge is a set of numbers that have both HD and IM products that don't overlap. I have used these a lot and they very effective for both electronic and acoustic stuff. Not much fun to listen to. Ultrasonic tones may not give much useful into but you could scale from these I suppose. The AES paper would give more details. The latest generation of DAC and ADC chips have no troubles with these to really low numbers (-100 dB or better). You do need a good FFT and capture system for this to be useful. I usually use at least 128K point FFT. For really good stuff I'll use 500K or 1M point FFT's. That can take a while. For transducers the ESI Juli@ internal DAC and ADC are more than good enough. For state of the art electronics either the TI PCM4222EVM or the AKD5394A w/ an external clock work great.
 

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#17
Hello

I've use the SGOne sine generator software to generated the frequencies suggested by janneman but using only 20 of them.

The software will generate all the 20 frequencies but at a quite low level, the more frequency it generate the lower are the level.

Anybody know a better software to generate 20 multitone sine ?

Thank

Bye

Gaetan
 
#18
This is to be expected. Ultimately all the signals sum in amplitude thus the more tones you have, the lower they all have to be so their sum stays below full-scale. The amplitude of each of the "n" signals would need to be "1/n * full-scale".
 
#19
1audio said:
I think what you are looking for is similar to this. The challenge is a set of numbers that have both HD and IM products that don't overlap. I have used these a lot and they very effective for both electronic and acoustic stuff. Not much fun to listen to. Ultrasonic tones may not give much useful into but you could scale from these I suppose. The AES paper would give more details. The latest generation of DAC and ADC chips have no troubles with these to really low numbers (-100 dB or better). You do need a good FFT and capture system for this to be useful. I usually use at least 128K point FFT. For really good stuff I'll use 500K or 1M point FFT's. That can take a while. For transducers the ESI Juli@ internal DAC and ADC are more than good enough. For state of the art electronics either the TI PCM4222EVM or the AKD5394A w/ an external clock work great.
Click to expand...

Hello

I've try all my soundcards with the multitone signal and none are clean from a bit high of IM THD.

I don't have the PCM4222 but I may use my PCM4202 with a PCM2707 usb/I2s
to made an external soundcard for the FFT test, but the PCM2707 are limited to 16 bit.

Thank

Bye

Gaetan
 
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