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

GROUPS:
 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.Many thanks in advance for your help, indeed Best regards,
1 year ago
25 Replies
 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}] 
1 year ago
 Hi Frank, It seems I didnĀ“t explain my point as I should. I didnĀ“t ask for sine-type waves.I am looking for arbitrary chords using string-type sounds (piano, violin, guitar) at any frequency. That is, chords that do not follow the ratios of the musical notes of any existing musical scale. The frequencies of the sounds must be choosen at will directly using Herzt units (not musical notes).So to do so, I would need either the wave equation for simulating the string-type sound along with the Play Command, or any existing mathematica program code (or commands). Got it? Many thanks in advanced for any help on this matter. I have been struggling on this for some time and I am frankly frustrated, I am not quite sure if mathematica has any synthesizer code that could help, or if there is any other synthesizers out there that could do the job.The mathematica command SoundNote does not do the job, it only works with the frequencies of musical notes, not with any frequencies chosen at will
1 year 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.
1 year ago
 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.
1 year ago
 I suspect that you'll have to add the harmonics yourself to reproduce a given sound, if you want it at any frequency.
1 year ago
 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.
1 year ago
 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
1 year ago
 David Keith 1 Vote 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:
1 year ago
 this is getting quite interesting...
1 year ago
 It seems, you need to previously convert the sound into an audio file, that's the meaning of the command AudioPitchShift
1 year ago
 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.
1 year ago
 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.
1 year ago
 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
1 year ago
 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.
1 year ago
 Excelent suggestion. Many thanks for your help,
1 year ago
1 year ago
 Could you please share the code?
1 year ago
 Ok, I'll try to send it to wolfram demonstrations project.
1 year ago
 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. My webpage is: https://domingogomezmorin.wordpress.com
1 year ago
 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' SYNTHESIZERJust 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 Attachments:
1 year ago
 This is great! Is there a reason you did not attach the notebook itself but a .TXT file?
1 year ago
 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.