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Play any sound, i.e: piano type sound, at any desired frequency?

Posted 7 years ago

Hi all, Please kindly let me explain further on this: All the software I have seen in the web for playing sounds seems to be always restricted to the musical ratios (musical notes) defined by any of the existing musical scales. However, I need to make a chord with any number of string-type sounds, so that I could assign any arbitrary frequency to each of them, frequencies choosen at will (not related to any existing musical scale).

Could someone tell me if there are any mathematica commands I could use, or any other way to do so.

enter image description here

Many thanks in advance for your help, indeed Best regards,

28 Replies
Posted 2 years ago

Thanks a lot for your reply and information.

POSTED BY: k Lu

Yes I included an attachment in the 6th post above. However, so much time has passed since I posted this, by this time, I found FLStudio and Harmor which allows me to use any music scale, you can see that at:
https://www.youtube.com/watch?v=f2CoqkRNdgo
and the theoretical basis for my scale at:
https://www.youtube.com/watch?v=gbK_V_7ivDA

Posted 2 years ago
POSTED BY: k Lu

In this synthesizer the harmonics for simulating musical-instrument timbre are calculated using interpolating functions and the avalilabe harmonics-data of current musical notes. The manipulate routine could be improved using AudioGenerator

We do agree, calculating the harmonics this way for the guitar timbre is a crude approximation, however, if you have in mind experimenting with some particular frequencies, then you should find the real harmonics by using a real musical instrument and a spectrum analyzer.

I made the database of up to 21 harmonics for all the equal-temperament notes, however, I thought it was far enough to use 12 harmonics in this synthesizer.

I think, at this point, I must made the following remark: Even considering those delays in the Mathematica Play command, no other software allows you to do things like this, I think all this a great.

Mathematica is a truly powerful tool of liberation.

It would be great if mathematica could improve the time response for the PLAY command when using functions.

I know that by previously using the table command the time response is reduced, however I didn't find the way to use that in this dynamic case, I just have to directly use large piecewise functions within the play command.

I am attaching again the SYNTHESIZER code with some minor changes, just copy the contents, paste and run.

Attachments:

No, it is just that I was trying to paste the code directly into the screen (I didn't notice there is a button for uploading files but just for images), so I previously converted it to a .txt file. Later I realized the button was there.

By the way, the number of sound buttons of this app could be increased and they could be arranged as piano keys icons, or guitar string icons. I hope to see people contributing to this open project, mainly on improving the time response of the PLAY command.

This is great! Is there a reason you did not attach the notebook itself but a .TXT file?

POSTED BY: Sam Carrettie

As promised, I am attaching an image of the console (Manipulate output) and the source code (.txt file) of the new project: 'FREE MUSIC, FREE SOUNDS' SYNTHESIZER

Just copy an paste the code of the .txt file into mathematica, and run.

Please also kindly read the text included at the top of the code and share any ideas, harmonics database, and comments on this project. Remember, this is a new open project.!

Best regards, https://domingogomezmorin.wordpress.com

enter image description here

Attachments:

In the mean time, if you are willing to check the code and make some suggestions to improve this project, please kindly let me know your email address and I will send to you the whole code.

enter image description here

My webpage is: https://domingogomezmorin.wordpress.com

Ok, I'll try to send it to wolfram demonstrations project.

Could you please share the code?

POSTED BY: Vitaliy Kaurov

Excelent suggestion. Many thanks for your help,

I suggest that you send Wolfram a suggestion that AudioGenerator should accept instrument names ("Piano") as well as standard waveforms ("Sawtooth"). I'm pretty sure that this is possible -- hard for us, but perhaps not so much for the developers.

If they can do this, then Wolfram Language would have a shot at replacing General MIDI as a more flexible and general music generator.

The more people who suggest this, the more likely it will happen.

Well, many thanks to all of you for your comments. I'll try to find function by myself, it is a hard task, but it seems there is no other way.

Best Regards

According to the documentation, you can use any ratio. There are ways of adjusting the pitch by multiples of semitones, but you don't need to do this.

This 'technique' is a bit of a hack. What we really want to do is to use AudioGenerator with a suitable envelope (model). The documentation lists several models that are built-in. One promising one is to use a Time Series. You could create a function that would duplicate the harmonics and decays of any arbitrary sound. This is non-trivial, of course.

As I said, this is on my list of things to do.

at this point, another important question emerges:

The shift factor used in the audiopitchshift is an arbitrarily chosen numerical factor, or is it a restrictive musical ratio (semitone units)?.

If the later then this shifting is definitely not an option to follow. The chords need to be totally free from any pre-established ratios.

It seems, you need to previously convert the sound into an audio file, that's the meaning of the command AudioPitchShift

this is getting quite interesting...

Posted 7 years ago

Thinking about this some more. For a continuous note, such as made by a violin or trumpet, it may be sufficient to know the harmonics and their amplitudes relative to the fundamental. That would not include non-continuous components, for example the sound of the trumpet note being initiated. However, for struck or plucked instruments, such as guitar or piano, we would want in addition to know a decay rate for the fundamental and each harmonic. Then a sampled sound list could be constructed from the fundamental.

I tried to do this for the midi sound for a guitar as produced by Mathematica by first analyzing the sound for the harmonics. But I found that many of the tools would not work. I saw no way to just get a simple list of sample amplitudes. I tried to use Periodogram, but it was not clear that the partition option could be used to get the spectral component values at a set of time-delayed windows, for fitting to exponential decays. Of course this is just about getting the characteristic -- I could record a guitar and analyze the result.

So I tried George's suggestion. I could indeed shift the frequencies of a 5 sec guitar note (E2). But when I compare the result of shifting E2 by 2x (1 octave) and E3, they are not the same pitch. I insert an image, since I am sure the boxes would be a mess as code:

enter image description here

POSTED BY: David Keith

Many thanks George, interesting, I'll try this one. I am desperately looking to achieve this, because it also deals with a math research I am working on. It seems to be a choice, let's see...

p.d. By the way, pretty nice your wolfram demonstration on linear equations system

SoundNote[] uses standard MIDI. By default, the pitches are Equal temperament, A = 440 hz. The MIDI standard allows you to alter the pitch, but I have found no (easy) way to do this.

MIDI should be an obsolete standard, mostly because it defaults to Western, equal tempered scales, which is really appropriate for Western (Eutorpean) music since 1760 or so. (Bach's Well-Tempered Clavier was written to exhibit the utility of a well-tempered scale, not equal temperament.) Indian, Chinese, and older Western Music (e.g. Baroque and Renaissance and before) use different scales.

Looking at the new audio functionality is on my list of things to do. I haven't checked this out, but you might be able to create an audio entity using SoundNote[], specifying the instrument, and then manipulate the pitch using AudioPitchShift[]. If that works, then you could wrote a function that would wrap up the code and have as an input one of the various MIDI instruments.

I suspect that you'll have to add the harmonics yourself to reproduce a given sound, if you want it at any frequency.

POSTED BY: Frank Kampas

The Mathematica Command SoundNote uses internal functions to develope those complex sounds, however, to my disgrace mathematica does not show those special functions and the command only uses the frequencies of known musical notes. Besides, the point is that I am not making a research on how to construct those string-type sounds but on analysing chords of string-sounds at any chosen frequency, so I guess somewhere I could finally find those functions instead of trying to contruct them by myself which no doubt would be a so hard task.

Posted 7 years ago

Often these complex instrument sounds consist of the fundamental and a set of harmonics at amplitudes related to that of the fundamental. So one approach to simulating such sounds is to determine these additional components, either through available writings or by Fourier analysis of examples. Then you could write a function which accepts a fundamental frequency and outputs a sum of notes representing the full set of components. The fundamental could then be any frequency, not just those of standard notes.

POSTED BY: David Keith
Play[Sin[256*2 \[Pi] t] + Sin[1.25*256*2 \[Pi] t] + 
  Sin[1.5*256*2 \[Pi] t] + Sin[2*256*2 \[Pi] t], {t, 0, 1}]
POSTED BY: Frank Kampas
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