Grant Muller

Processing HarmonicTable: Part 2

Since the last post I’ve had to make far more changes than I expected. If you looked at the previous examples, there was using a loop to create the hex buttons, making translations to relative to other translations on the screen. In the process I completely lost track of the absolute position of the button, which basically made it impossible to detect the location of the mouse on the screen in order to tell which button I was pressing. As a result I had to create a separate class to represent the Hex Button, and store the absolute starting point of each hex button and the length of one side. This is all the information I needed to create and detect a hexagon anywhere on the screen. From there I just created an array of these buttons in the setup() block, and drew them all over the screen:

hexButtons = new ArrayList</p>
<HexButton></p>
<p>&lt;</p>
<p>p>();</p>
<p>for (int j=2; j &lt;20; j++){
resetNoteNumber(rowNumber);
for (int i=0; i&lt;12; i++){
hexButtons.add(new HexButton(this, space+(i<em>xOffset), parseInt(height-(j</em>b)), length,    noteNumber));
noteNumber++;
}</p>
<p>j++;
rowNumber++;
resetNoteNumber(rowNumber);</p>
<p>for (int i=0; i&lt;12; i++){
hexButtons.add(new HexButton(this, space+parseInt(a+c)+(i<em>xOffset), parseInt(height-(j</em>b)), length, noteNumber));
noteNumber++;
}</p>
<p>rowNumber++;
}

As you can see I’m still making relative translations to locations on the screen, but I’m storing them in the class to be accessed later. This way I can still change the proportions and space variable at the top and not have to change a bit of code anywhere else to resize and reposition items. This greatly simplifies my draw() block:

public void draw(){
background(255);
for (int i = 0; i &lt; hexButtons.size(); i++){
HexButton button = (HexButton) hexButtons.get(i);
button.drawHex(false);
}
}

Now detecting the position of the mouse is simple:

public void mousePressed(){
for (int i = 0; i &lt; hexButtons.size(); i++){
HexButton button = (HexButton) hexButtons.get(i);
if (mouseX >= button.startX+a &amp;amp;amp;&amp;amp;amp; mouseX &lt;= button.startX+a+c &amp;amp;amp;&amp;amp;amp; mouseY >= button.startY &amp;amp;amp;&amp;amp;amp; mouseY &lt;= button.startY+(2*b)){
println(button.note);
activeNotes.add(button.thisNoteNumber);
midiOutput.sendNoteOn(0, button.thisNoteNumber, 100);
}
}
}

Notice I only bother performing this function when the mouse it pressed, this saves me some cycle since I have no intention of sending a midi note on unless the mouse is pressed (or dragged, which is using the same function as above). Also notice the activeNotes array. I’m storing notes that have already been pressed, so that I don’t retrigger a note unless the mouse is pressed again, which is necessary for mouse drags. After the mouse is released, I just send a note off to all notes in the acttiveNotes array.

I also revised the array to create the rows of notes across the screen. Previously it was hard coded, but with the following bit of code:

public void resetNoteNumber(int rowNumber){
if (rowNumber == 0){
noteNumber = noteNameMap.get(startingNote);
previousNote = noteNumber;
} else if (rowNumber % 2 == 0){
noteNumber = previousNote + 3;
previousNote = noteNumber;
} else {
noteNumber = previousNote + 4;
previousNote = noteNumber;
}
}

I can just change the starting note field in the class to be whatever I want, and it will always move up by rows in 5ths and 3rds. So I can make my starting note A2 instead of C2, and everything lines up without a hitch and without any code changes:

harmonictablea2

I tested it out with some seriously 80’s sounding FM pad, dragging across intervals, drawing random chord shapes in honeycomb patterns, etc. Here is a short output:

Audio clip: Adobe Flash Player (version 9 or above) is required to play this audio clip. Download the latest version here. You also need to have JavaScript enabled in your browser.

As usual here are the updated files:

HarmonicTable HexButton NoteReference

Its a lot of fun, even though I can only play it with the mouse. Last step is to get a touch screen. Anyone want to donate one?

Processing HarmonicTable: Part 1

Earlier this year while reading Harmonic Experience by W. A. Mathieu, I was introduced to the concept of lattices to represent tones, chords and keys. These lattices can be used to represent the basics of music composition in a visual way that makes more sense than standard scales on staffs. Here is an example:

ChordLattice

The lattice is effectively several staffs of music stacked on top of each other, so that the note can be displayed horizontally and vertically. Starting from any note in the lattice, moving horizontally (diagonally right or left), jumps by a 5th (for example C to G, or G to D). Moving vertically jumps by thirds (C to E, or G to B). Since nearly all music is the construction of 5ths in 3rds, this system makes it easy to create patterns visually for chords, cadences, scales etc, that will always look the same no matter where you start on the lattice. In the example above, you can see that Major chords are always point up triangles, Minor chords are the opposite, point down. Until recently this system didn’t translate directly to an instrument. Any chord on a keyboard will have similar but different fingerings and patterns depending on the starting note, so one still has to memorize a ton of different patterns for one scale, chord, or modulation.

A few weeks into reading Harmonic Experience, providence saw fit to lead me to the C-Thru AXiS controller. The AXiS is a Harmonic Table based midi controller that creates a table much like the lattice in Harmonic Experience, separating notes not in semi-tones like a keyboad, but by 5ths and 3rds (and of course many other inter-relationships based on this). Here is the layout of the AXiS: natural_keyboard If you look the relationships between the keys become clear. They are reversed from Mathieu’s lattice, 3rds are horizontal (diagonally), and 5ths are always straight up. To play a Major triad on the AXiS, just play that triangle pattern using starting at any key. C Major will have the same pattern as Bb Major, etc. There are of course drawbacks to this system (playing inversions, etc), but for the most part it accomplishes the goal of simplifying the muscle memory aspects of playing music so the user can concentrate on composition and performance. you learn the pattern for a scale, chord or mode only once, then you may modulate it anywhere without the need to retrain your fingers.

The problem with AXiS is the price tag. Its around $1700 for one from what I can tell, which is a pretty steep entrance fee for a device I may not be able to get used to. They are in the process of creating a cheaper smaller version, but I want to try it now. The solution was to build one in processing. I’ve only just started, but combining the midi reference classes I’ve been working on along with (eventually) a touch screen, I think I should be able to pull something off that works well enough for me to test this thing out. I started by looking for ways to draw regular hexagons, and came across this site. With a some basic trigonometry and a lot of cut-and-try with the vertex functions, I came up with this function:
int length=30;
float a = length/2;
float b = sin(radians(60))*length;
float c = length;
public void drawHex(){
beginShape();
vertex(0,b);
vertex(a,0);
vertex(a+c,0);
vertex(2*c,b);
vertex(a+c,2*b);
vertex(a+c,2*b);
vertex(a,2*b);
vertex(0,b);
endShape();
}
This will construct a regular hexagon based on the length of one side. After that I used a series of translation matrices to draw them all over the screen: public void draw(){ rowNumber=0; setNoteNumber(rowNumber); for (int j=2; j<20; j++){ pushMatrix(); translate(0+space, (height-(j*(b+space/2)+1))); drawHex(getNextNote()); for (int i=1; i <12; i++){ translate(space+(2*a)+(2*c), 0); drawHex(getNextNote()); } popMatrix(); j++; rowNumber++; setNoteNumber(rowNumber); pushMatrix(); translate(a+c+1.5f*space, (height-(j*(b+space/2)))); drawHex(getNextNote()); for (int i=1; i <12; i++){ translate(space+(2*a)+(2*c), 0); drawHex(getNextNote()); } popMatrix(); rowNumber++; setNoteNumber(rowNumber); } } [/sourcecode] I predefined the number of horizontal hexagons to 12 for each row, this means that STRAIGHT horizontally across a row I will have a perfect chromatic scale. The number of vertical keys I simply copied from the AXiS.After predefining the number of columns and rows, it meant that I could construct the size of the screen based on the length of one side of the hexagon. I also included a variable that allows me to declare an amount of fixed space in between the keys (in case my fingers are too big for the key's surface). One variable, named length, can be changed to create a bigger surface with larger keys. After implementing some simple code to write the note name into the key as well, I was finished with the layout. Here is a snapshot of it directly out of processing: Virtual Harmonic Table Its of course much bigger. With the key surface complete now all I have to do is map the key locations to the midi note they’re associated with, and use some on press functions to trigger them. After that I just need to get access to a touch screen, anyone want to donate one? Here is the preliminary code to draw the hexagons, as well as the code required to map midi notes: HarmonicTable NoteReference In┬áPart 2 I’ll have have midi functionality implemented and some testing done. In Part 3 I’ll have it implemented with a touchscreen, most likely a laptop, at that point I’ll make the rest of the code available.

Java Midi Reference Class

Lately I have been doing some work with Processing to create visuals from music. One of the concepts I’m working with is live visuals based on video feeds from cameras that are tracking the show, or band, or whatever. This alone would be enormously boring, so to heighten the experience, I thought of using the audio output of the show to control features of the video feeds, like playback speed, positions, color and hue, etc. This turned out to be way too processor intensive, and given the properties of sound, would be impossible to synchronize with a live show.

The solution was to use MIDI to trigger these events, rather than having to perform audio analysis first. Using rwmidi and Processing, I started an experiment to see what I can do to video, using MIDI messages as triggers, NoteOn’s as ellipses with alpha masks, or Pitch Bend controllers tracking hue logarithmically. So far these experiments have been successful, but I found myself referring to a MIDI reference constantly.

The problem is most musicians don’t think in MIDI numbers. Even though the messages I’m using have no musical information, they’re derived from the world of music. So Note names like C4 (The note C in the 4th position) have a MIDI number (60). When I’m creating a drum beat in Ableton for instance, I don’t look for note number 60, I look for C4. This means that every time I wanted to map this information to an event in Processing, I had to first look up the note number. After a while you memorize them, but that’s lame, and if I leave the project for a while and come back, I’ll have to go back to looking them up again.

I couldn’t find any solution for this in code, so I created a simple Java class to handle MIDI Reference Data:

MidiReference

Which you can download from the link above. Right now it only handle Notes and their associated midi numbers. The crux of the code consists of two loops:

//Loop through all of the note numbers
for (int noteNumber=0; noteNumber&lt;127;){
    //loop through the ranges (-1 through 9)
    for (Integer range=-1; range&lt;10; range++){
        //loop through all of the note names
        for (String nextNote : noteNames){
            //if  the note name contains a "flat" then it has the identical note number
            //as the previous flat, decrement the total note number count and insert into
            //the map so that note numbers can be translated from either sharps or flats
            if (nextNote.contains("b")) noteNumber--;
                noteNameMap.put(nextNote + range.toString(), noteNumber);
            noteNumber++;
        }
    }
}

and

//Loop through all of the note numbers
for (int noteNumber=0; noteNumber&lt;128;){
    //loop through the ranges (-1 through 9)
    for (Integer range=-1; range&lt;10; range++){
        //loop through all of the note names
        for (String nextNote : noteNames){
            String noteName;
            //if  the note name contains a "flat" then it has the identical note number
            //as the previous flat, decrement the total note number count and insert into
            //the array a string made up of both the previous notes name and the current one
            if (nextNote.contains("b")){
                noteNumber--;
                String previous = noteNumberArray[noteNumber];
                noteName = previous + "/" + nextNote + range.toString();
            } else {
                noteName = nextNote + range.toString();
            }
                noteNumberArray[noteNumber] = noteName;
                noteNumber++;
        }
    }
}

The first loop rolls through all of the potential note names and maps them to a number, in order from 0-127 (all of the MIDI notes). The second does the opposite, so that you can quickly refer to the note name by number (which is something that Processing will find easier to do).

If you find this kind of thing useful, feel free to use it. I will expand it from time to time as I add new reference data for myself.