Does any one know of a better specification when generalizing the basic concepts of pitch and time in music? If one would map the time to an X axis and pitch to Y axis for instance. I am mostly concerned about finding most fitting words for these basic musical concepts.

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    Pitch and time are the correct terms. Is that what you're asking? Jan 22 '20 at 9:09
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    @Richard I am looking for something which describes best these two fundamental aspects of music, i.e. the height (frequency, pitch, etc.) and the time (including duration). But i wasn't sure whether pitch and time could describe these meanings at best! May be they do!
    – Student
    Jan 22 '20 at 9:45
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    X and Y axes seem about as good as it gets. My problem would be that a point on the graph would only show the pitch of a note (good) and where it started (not so good). Duration?
    – Tim
    Jan 22 '20 at 11:06
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    @Tim In that case the X distance between the points on the graph would indicate the durations.
    – Student
    Jan 22 '20 at 12:06
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    And what depicts rests - music isn't all notes?
    – Tim
    Jan 22 '20 at 12:37

Sheet music is pitch vs. time. In fact, it's a highly customized representation of the Fourier transform of the waveform. The waveform is amplitude vs. time; strictly speaking its Fourier transform shows the frequency spectral amplitudes of a "snapshot" in time.

If you look up 'sonogram' you'll find graphs showing a time-sequence of Fourier transforms, usually with amplitude (of frequency) as the third or heat-map axis.

  • The fourier transform of a single note in sheet music would usually show many different frequencies, due to the harmonics and other components of the notes. "it's a highly customized representation of the Fourier transform of the waveform" becomes truer the closer our instrument's timbre is to a sine wave.
    – topo morto
    Jan 23 '20 at 4:50
  • @topoReinstateMonica I believe for simplicity we are assuming pitch in OP's axis is FFT's fundamental frequency of said pitches, and the point is that OP already has the abstraction down, giving some uses (sheet music, FFT). Jan 23 '20 at 4:52
  • Sure - it is just worth being clear what a big simplification that (usually) is. "The waveform" that sheet music looks like a fourier transform of would generally sound very different to the music as normally heard.
    – topo morto
    Jan 23 '20 at 5:59

Now that you are thinking about abstractions of music, you can put many different frameworks over the abstractions. I don't think there's a "better" abstraction, point of view, or generalization; but there are different ones that vary in usefulness depending on the study or observation you are performing. They are tools without an intrinsic value.

One way of thinking about those axis without considering the whole piece (perhaps only small sections) is chords vs scales. Both can be abstracted as a collection of intervals, the difference being that the former extends vertically, and the later horizontally. Of course we'd need to use very loose definitions of chord (any set of notes) and scale (any sequence of notes), but that's just part of the abstraction.

Another way of thinking about those axis considering the whole piece (or perhaps big chunks of it) is harmony vs rhythm. Considering context, the vertical axis tells us the harmonic movement of the piece, and the horizontal axis tells us in which rhythms the pitches are being played.

You could even go chords vs rhythm, or harmony vs melody. Or anything else you can think of. For musical usefulness, I believe you already are on the lowest level of abstraction at pitch vs time. But those horizontal and vertical relationships tell much more than pitch and time, so you can superimpose other frameworks to further analyze them.

In short, the most fitting words that match those axis (or potential conversions) depend on what you are analyzing and what you are trying to achieve, so there's no "better specification". Pitch and time could be MIDI note and time specification, or OSC specification. Maybe vertically you want to normalize into a specific scale, or harmony. Maybe horizontally you want to normalize to seconds, beats, eight notes, MIDI Baud rate, etc.

Are you doing this out of curiosity or do you want to implement something in particular? For more specific implementations, you are basically describing every music / audio notation ever. Piano rolls, FFT, modern sheet music, gregorian notation, tablature (3D!), etc.

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