[music-dsp] Calculating the gains for an XY-pad mixer
Hi Everyone, This may be a fairly idiosyncratic issue, but I think someone here might be able to comment on the correctness of what I've done. I am implementing a mixer in which the gains of four sounds are controlled using a single XY-pad. There is one sound associated with each corner of the XY-pad and placing the cursor at a corner sets gain of the corresponding sound to 1 and all others to 0; whereas placing it in the middle mixes all four sounds equally; and placing it on an edge mixes the sounds at the two nearest corners only. I have two schemes for calculating the four gains from the cursor position, one for correlated sounds and the other for uncorrelated sounds. I'm hoping that someone might flag any problems--theoretical or otherwise--with either of them (though they seem to me to sound ok) For correlated sounds (such as four waveforms in a subtractive synthesiser), I understand that a linear crossfade is appropriate and the four gains should sum to 1. The scheme I came up with for doing this is to divide the XY-pad rectangle into four smaller rectangles by drawing a horizontal line and a vertical line through the cursor position, and then to use the areas of the rectangles as the gains. The gain for a given corner is the area of the 'opposite' rectangle, e.g. the gain for the sound associated with the bottom left corner is given by the area of the top right rectangle, etc.; I can supply a figure if necessary. Of course the areas need to be normalised so that they sum to 1. Now for uncorrelated sounds, I understand that the squares of the gains should sum to 1. My solution is to use the previous scheme but with the gain being given by the square root of the area of the corresponding rectangle. This somehow seems a bit too simple, but maybe it's correct. Do these seem like reasonable ways to get the gains for the two cases? Thanks, Aengus. www.am-process.org -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Calculating the gains for an XY-pad mixer
What you are trying to calculate is called barycentric coordinates, you might give them a google (: As far as them all adding to one (which barycentric coordinates do), I'm not sure if that's appropriate or not, because you have to remember that volume is linear, but the perception of that linear scale is not linear. Normally when you are trying to work with the perception of volume (in this case, trying to keep it the same loudness), you work in decibels, which are a non linear scale, but are linear to the ear. Hope this helps. Someone will surely chime in if i've misled you on the second part :P On Thu, Jan 17, 2013 at 8:59 PM, Aengus Martin aen...@am-process.org wrote: Hi Everyone, This may be a fairly idiosyncratic issue, but I think someone here might be able to comment on the correctness of what I've done. I am implementing a mixer in which the gains of four sounds are controlled using a single XY-pad. There is one sound associated with each corner of the XY-pad and placing the cursor at a corner sets gain of the corresponding sound to 1 and all others to 0; whereas placing it in the middle mixes all four sounds equally; and placing it on an edge mixes the sounds at the two nearest corners only. I have two schemes for calculating the four gains from the cursor position, one for correlated sounds and the other for uncorrelated sounds. I'm hoping that someone might flag any problems--theoretical or otherwise--with either of them (though they seem to me to sound ok) For correlated sounds (such as four waveforms in a subtractive synthesiser), I understand that a linear crossfade is appropriate and the four gains should sum to 1. The scheme I came up with for doing this is to divide the XY-pad rectangle into four smaller rectangles by drawing a horizontal line and a vertical line through the cursor position, and then to use the areas of the rectangles as the gains. The gain for a given corner is the area of the 'opposite' rectangle, e.g. the gain for the sound associated with the bottom left corner is given by the area of the top right rectangle, etc.; I can supply a figure if necessary. Of course the areas need to be normalised so that they sum to 1. Now for uncorrelated sounds, I understand that the squares of the gains should sum to 1. My solution is to use the previous scheme but with the gain being given by the square root of the area of the corresponding rectangle. This somehow seems a bit too simple, but maybe it's correct. Do these seem like reasonable ways to get the gains for the two cases? Thanks, Aengus. www.am-process.org -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Calculating the gains for an XY-pad mixer
Thanks--it's good to have that term. It looks like I am calculating the barycentric coordinates of the cursor in the XY-pad square. As regards the perception issue, standard way of crossfading between two correlated sounds (I think) is just linear in amplitude, and for uncorrelated ones, it's linear in the square of the amplitude. That's basically what I'm trying to extend to four sounds, and I suppose that's my question: does this seem appropriate? On Fri, Jan 18, 2013 at 4:06 PM, Alan Wolfe alan.wo...@gmail.com wrote: What you are trying to calculate is called barycentric coordinates, you might give them a google (: As far as them all adding to one (which barycentric coordinates do), I'm not sure if that's appropriate or not, because you have to remember that volume is linear, but the perception of that linear scale is not linear. Normally when you are trying to work with the perception of volume (in this case, trying to keep it the same loudness), you work in decibels, which are a non linear scale, but are linear to the ear. Hope this helps. Someone will surely chime in if i've misled you on the second part :P On Thu, Jan 17, 2013 at 8:59 PM, Aengus Martin aen...@am-process.org wrote: Hi Everyone, This may be a fairly idiosyncratic issue, but I think someone here might be able to comment on the correctness of what I've done. I am implementing a mixer in which the gains of four sounds are controlled using a single XY-pad. There is one sound associated with each corner of the XY-pad and placing the cursor at a corner sets gain of the corresponding sound to 1 and all others to 0; whereas placing it in the middle mixes all four sounds equally; and placing it on an edge mixes the sounds at the two nearest corners only. I have two schemes for calculating the four gains from the cursor position, one for correlated sounds and the other for uncorrelated sounds. I'm hoping that someone might flag any problems--theoretical or otherwise--with either of them (though they seem to me to sound ok) For correlated sounds (such as four waveforms in a subtractive synthesiser), I understand that a linear crossfade is appropriate and the four gains should sum to 1. The scheme I came up with for doing this is to divide the XY-pad rectangle into four smaller rectangles by drawing a horizontal line and a vertical line through the cursor position, and then to use the areas of the rectangles as the gains. The gain for a given corner is the area of the 'opposite' rectangle, e.g. the gain for the sound associated with the bottom left corner is given by the area of the top right rectangle, etc.; I can supply a figure if necessary. Of course the areas need to be normalised so that they sum to 1. Now for uncorrelated sounds, I understand that the squares of the gains should sum to 1. My solution is to use the previous scheme but with the gain being given by the square root of the area of the corresponding rectangle. This somehow seems a bit too simple, but maybe it's correct. Do these seem like reasonable ways to get the gains for the two cases? Thanks, Aengus. www.am-process.org -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp -- www.am-process.org -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Calculating the gains for an XY-pad mixer
Barycentric coordinates don't just apply to triangles. Trust me, I'm a (video game) engineer (tm) hehe In geometry, the barycentric coordinate system is a coordinate system in which the location of a point is specified as the center of mass, or barycenter, of masses placed at the vertices of a simplex(a triangle, tetrahedron, etc.) - from wikipedia On Thu, Jan 17, 2013 at 9:22 PM, Ross Bencina rossb-li...@audiomulch.com wrote: On 18/01/2013 4:06 PM, Alan Wolfe wrote: What you are trying to calculate is called barycentric coordinates, Actually I don't think so. Barycentric coordinates apply to triangles (or simplices), not squares (XY). http://en.wikipedia.org/wiki/Barycentric_coordinate_system_(mathematics) http://en.wikipedia.org/wiki/Simplex Aengus wrote: Do these seem like reasonable ways to get the gains for the two cases? They seem reasonable to me. Do you have a reason for doubting? Ross -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Calculating the gains for an XY-pad mixer
On 1/17/13 11:59 PM, Aengus Martin wrote: This may be a fairly idiosyncratic issue, but I think someone here might be able to comment on the correctness of what I've done. I am implementing a mixer in which the gains of four sounds are controlled using a single XY-pad. There is one sound associated with each corner of the XY-pad and placing the cursor at a corner sets gain of the corresponding sound to 1 and all others to 0; whereas placing it in the middle mixes all four sounds equally; and placing it on an edge mixes the sounds at the two nearest corners only. sounds like the Prophet VS. a nice old implementation of wavetable synthesis. their square was turned 45 degrees into a baseball diamond position. I have two schemes for calculating the four gains from the cursor position, one for correlated sounds and the other for uncorrelated sounds. I'm hoping that someone might flag any problems--theoretical or otherwise--with either of them (though they seem to me to sound ok) For correlated sounds (such as four waveforms in a subtractive synthesiser), I understand that a linear crossfade well, it doesn't *have* to be linear (in the sense of straight-line mapping), but it should be *complementary*. is appropriate and the four gains should sum to 1. that's what we mean by complementary in a voltage sense. The scheme I came up with for doing this is to divide the XY-pad rectangle into four smaller rectangles by drawing a horizontal line and a vertical line through the cursor position, and then to use the areas of the rectangles as the gains. The gain for a given corner is the area of the 'opposite' rectangle, e.g. the gain for the sound associated with the bottom left corner is given by the area of the top right rectangle, etc.; I can supply a figure if necessary. Of course the areas need to be normalised so that they sum to 1. that's a clever way to look at it. it's straight-line linear and it's complementary. Now for uncorrelated sounds, I understand that the squares of the gains should sum to 1. My solution is to use the previous scheme but with the gain being given by the square root of the area of the corresponding rectangle. This somehow seems a bit too simple, but maybe it's correct. it is for *totally* uncorrelated sounds. not partially correlated or negatively correlated. Do these seem like reasonable ways to get the gains for the two cases i don't think this has anything to do with barycentric coordinates, but i thought it might deal with your mixing gain issue: http://music.columbia.edu/pipermail/music-dsp/2010-December/069419.html for me, the issue was splicing more than mixing, but i think this issue of the linear values adding to 1 vs. the squares of the linear values adding to 1 is addressed. take a look at the whole thread in the archive and tell us if this speaks to your issue at all. splicing is the same as 1-dimensional mixing as you move your crossfade fader from one end to the other. one thing you probably want to do is align your different sounds so that the have the best cross-correlation. you should always be able to avoid a negative crosscorrelation. if one sound is pure white noise, the cross-correlation will be pretty much zero and that would be the fully uncorrelated case. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
