Another multi-dimensional abstraction for music that's at a bit higher level is a musical lattice. The number of dimensions is limited by the largest prime you accept in the ratios you use. (Typical western music approximated by 12-tone equal temperament uses primes of 2, 3, and 5. Powers of 2 are often ignored because notes an octave apart are perceived to be sort of equivalent for harmonic purposes.)
Spectrogram is 2D (plot of amplitude given time and frequency).
Its interesting to think about it for a spectrogram because "similarity" is different in each dimension (freq vs. time).
Frequency is also perceived logarithmically, so you would probably want to convert to e.g. Mel scale before applying this algorithm (a 2000-2100Hz change is much subtler than a 200-300Hz change).
Isn't that 3 dimensions (amplitude, time, and frequency)? The plot of course fills 2 spatial dimensions and uses color to represent the 3rd dimension. But I don't know very much about this.
You can also view digital images as 1-dimensional arrays of bits. (This is roughly how fax machines work.) That doesn't mean they can't also be 2-dimensional images, or representations of 3-dimensional images, or indeed an encoding of a 3D scene directly.
Similarly, you can unpack a linear sequence of sound samples into a two-dimensional plot of frequency and amplitude with a fourier transform.
You're describing audio, not music. Music as data isn't quantified in the same way as audio (see the various forms of musical notation that exist), and in fact music displayed in a sequencer or tracker looks pretty similar to the 2D bitmaps in the article.
There are three-dimensional views of music, e.g. time-frequency-amplitude. See https://en.wikipedia.org/wiki/Spectrogram
Another multi-dimensional abstraction for music that's at a bit higher level is a musical lattice. The number of dimensions is limited by the largest prime you accept in the ratios you use. (Typical western music approximated by 12-tone equal temperament uses primes of 2, 3, and 5. Powers of 2 are often ignored because notes an octave apart are perceived to be sort of equivalent for harmonic purposes.)
https://en.wikipedia.org/wiki/Lattice_(music)
Spectrogram is 2D (plot of amplitude given time and frequency).
Its interesting to think about it for a spectrogram because "similarity" is different in each dimension (freq vs. time). Frequency is also perceived logarithmically, so you would probably want to convert to e.g. Mel scale before applying this algorithm (a 2000-2100Hz change is much subtler than a 200-300Hz change).
Isn't that 3 dimensions (amplitude, time, and frequency)? The plot of course fills 2 spatial dimensions and uses color to represent the 3rd dimension. But I don't know very much about this.
1 reply →
How is music 1-dimensional?
A microphone records amplitude of sound waves over time, i.e. the air pressure -- that's the dimension.
You can also view digital images as 1-dimensional arrays of bits. (This is roughly how fax machines work.) That doesn't mean they can't also be 2-dimensional images, or representations of 3-dimensional images, or indeed an encoding of a 3D scene directly.
Similarly, you can unpack a linear sequence of sound samples into a two-dimensional plot of frequency and amplitude with a fourier transform.
5 replies →
You're describing audio, not music. Music as data isn't quantified in the same way as audio (see the various forms of musical notation that exist), and in fact music displayed in a sequencer or tracker looks pretty similar to the 2D bitmaps in the article.