the concept formally known as intermals

A simple protocol for describing chord voicings as a signal.

decimal + interval = decival

A decival (or intermal) is a way of encoding a chord voicing and relative root pitch as a floating point value.

  • The number to the left of the decimal defines the root in semitones.
  • The numbers to the right of the floating point defines rising semitone steps for each subsequent voice.
   -12.074   <---- Signal    
     / \ 
    /   |> Three additional 
   /    |> voices 0, 7,
  /     |> and 11 semitones 
 /      |> above the root.
|< Root twelve semitones below 
|< whatever reference pitch.

It might be useful for shooting harmonic information around as signals in rnbo. You can do weird chord maths maybe. The possible chord voicings are simultaneously limited and limitless.

Example decivals/intermals

Relative to C:

0.43 //root, major 3rd, minor 3rd

0.434 //root, major 3rd, minor 3rd, major 3rd

0.34 //root, minor 3rd, major 3rd

2.34 //root, minor 3rd, major 3rd

F stacked 5ths
5.777 // f c d a  

B half-diminished
11.334 //root, minor 3rd, minor 3rd, major 3rd

-1.43  //root, major3rd, minor3rd