# Proper terms for comparing notes

I am trying to find a way to properly name different ways of comparing notes, Let's say we have two notes, let's name them NoteA and NoteB, let NoteA be C3 and NoteB C4. NoteA = C3 NoteB = C4 The fist way of comparing NoteA and NoteB would be compare them by the position these notes would represent in a Piano Roll style way, in which NoteB would be higher than NoteA.

``````NoteA < NoteB
``````

On the other part comparing them by Pitch Class would result on a totally different output for the comparing process, as NoteA and NoteB are both built with the Pitch letter C and the accidental Natural

``````NoteA == NoteB
``````

I'll repeat both compares with different notes to further illustrate the process

``````NoteC = C3
NoteD = Dbb3 (D double flat 3)
``````

CompareMode1:

``````NoteC == NoteD
``````

CompareMode2:

``````NoteC < NoteD
``````

My question in here would be which would be the proper terms to name each type of comparison, for example:

``````Compare Mode 1 -> Compare by Pitch
Compare Mode 2 -> Compare by Pitch Class
``````

Mode 1 name sounds sloppy to me.

First, the term pitch class already has a well-defined meaning in music theory, and this isn't it. Basically, pitch class refers to the set of pitches under an octave equivalence relation, generally represented by the integers modulo 12. Typically all enharmonic notations for the same pitch class are regarded as mathematically equivalent, as the general assumption (unless stated otherwise) is 12-tone equal temperament. (And that seems to be the assumption in the question too.)

There's no meaningful sense in which a standard pitch class is greater than another, as the "counter" resets to zero with every octave (unless you want to make some arbitrary definition for a "central" pitch class: C=0 is sometimes used for that purpose).

Anyhow, as to the two "modes" mentioned in the question, Mode 1 is just comparison by pitch (sometimes called pitch height or tone height in psychoacoustics). Aside from the chroma/octave representation in the question (e.g., C4), pitch is sometimes represented mathematically in other ways, such as in the MIDI standard where C0 is simply 0 and each note is given an integer.

As for Mode 2, I'm not quite certain what exactly it is trying to accomplish through mathematical representation. There's no real musical or acoustical sense in which C4 < D♭♭4 in 12-TET. And it's even more confusing to state (as I assume Mode 2 would) that C♯4 < D♭♭4.

The only thing the letter names do in 12-TET is designate the staff position, so Mode 1 and Mode 2 are reflecting completely different elements, one psychoacoustic and the other notational. Why the "less than" relation should even be used in the latter is a little unclear, unless you're writing music notation software and decide to represent staff position numerically. (And I can't think of a common term off the top of my head for such a relation.)

There are musical situations where it makes sense to perhaps compare scale steps in a tonal scale, so even if C♯ and D♭ are played at the same pitch height, they have different tonal function. But in that case, we're usually talking about pitch class (or chroma) where, as mentioned above, we end up in a circular arithmetic space, perhaps modulo 7 when working within a diatonic scale.

I hope this clears some things up, but I'm not aware of a standard term for what you're trying to accomplish with Mode 2 other than informal terms like "letter" or "note letter" or something like that. If all you're trying to do is track staff position or staff height, why not call it that?

You are trying to establish an order in the mathematical sense on notes, which is of questionable benefit.

There is already a well-established concept called interval so one would say, it is a Wikipedia: diminished second between your example notes and that covers all information of both of your modes (misunderstable, since mode is already a musical term).

Also note, that the assumption that double-flatted d equals to c only holds in 12tet tuning.

• I differ on your opinion about the benefit from math systems in music, but this is not the topic on this question, this types of comparison are for sorting and re arranging notes inside the system, indeed I know what an interval is, but I think there should be two ways to name this comparisons modes. I can tell you that both are equally used, and both are equally functional, they are just for different things. Jun 16, 2020 at 21:30

“Mode 1” is comparison by sound (where Dbb4 == C4, they are enharmonic equivalent), “Mode 2” is comparison by notation (where they are two different things).

• I like your idea, maybe Mode 1 could be Absolute Pitch, and Mode 2 could be by Notation.. Thanks Jun 16, 2020 at 21:32