# What is a note?

That simple. What is a note in digital signal processing? Is it a single value of y[n] in a system with a difference equation e.g. y[n] = a1 * x[n] + ... or a combination of samples?

I've seen DSP programs that output single values to e.g. a sound card and others that output blocks at a time with anywhere from 64-1024 frames per block... both referring to their output as a series of notes.

Is a "note" what is heard at a given time, i.e. composed of a single sample in the former case and of many in the latter? Or just the latest chunk whose samples have a single frequency?

the etymology of the word "note" as it applies to music is simply the notation, the note that a composer would make to paper to represent a particular action taken by the musician performing the music. like "taking notes".

normally in audio-to-MIDI conversion, a musical note is something that can be represented with a pair of MIDI Note-On and Note-Off messages. it has a beginning and an end, in time, and likely has other properties like pitch and loudness/intensity, which are also part of the MIDI Note-On message.

• So it's fair to say that in a DSP program a note might be represented by an integer number of samples? (Obviously some longer than others) – aralar Oct 10 '15 at 20:54
• in a DSP program, ultimately everything (or anything) is represented by an integer number of samples. if your sample rate is way too low, perhaps it would be meaningful to describe the length of a note with fractional precision, but i don't see why that would happen. notes that are longer need more samples than notes that are shorter. – robert bristow-johnson Oct 10 '15 at 21:07

A 'note' is what you hear when you push down and hold a single key on a piano. It is a sound with a given 'pitch' that is applied for a specific 'duration' in time.

When a single key is pressed upon a piano, what we hear is not just one frequency of sound vibration, but a composite of multiple sound vibrations occurring at different mathematically related frequencies. The elements of this composite of vibrations at differing frequencies are referred to as harmonics or partials. For instance, if we press the Middle C key on the piano, the individual frequencies of the composite's harmonics will start at 261.6 Hz as the fundamental frequency, 523 Hz would be the 2nd Harmonic, 785 Hz would be the 3rd Harmonic, 1046 Hz would be the 4th Harmonic, etc. The later harmonics are integer multiples of the fundamental frequency, 261.6 Hz ( ex: 2 x 261.6 = 523, 3 x 261.6 = 785, 4 x 261.6 = 1046 ).

Below is a logarithmic sonogram (created by my C++ software) for 3 seconds of a guitar solo on a mp3 recording. It shows how the harmonics appear for individual notes on a guitar, while playing a solo. You can even see how the guitarist is bending a note upward in frequency, just before the start of Note A.

You could read the linked Wikipedia article on Pitch Detection to get a more elaborate definition of a 'note' in musical terms.

A link for the C++ source code of my Pitch Detection software, which made the sonogram, is also below.

https://en.wikipedia.org/wiki/Transcription_(music)#Pitch_detection

https://github.com/CreativeDetectors/PitchScope_Player