# Eight numerals vs. twelve half-steps

I see a lot to piano tutorials (like Laura Palmer's Theme) that use roman numerals to indicate chord progression.

In Laura Palmer's Theme, it's:

i - I - III - iv - I - vi - IV - i

In the key of C this progression is:

Cm - C - E - Fm - C - Am - G - Cm

However, due to the different halfsteps on the piano, and that there's only half-step between E and F, D and C, this seems complicated to transpose to new keys.

So isn't 12 half-steps being used, eg:

1m - 1 - 5 - 6m - 1 - 10m - 6 - 1m

Or are these actually different things, and there's something I'm missing here?

Thanks!

The answer is essentially that the major and minor scales are central to our thinking around harmony. The notes diatonic to those scales are much more important than non-diatonic notes in terms of the functional harmony. So we label those but not the chromatic notes between degrees.

And yes they are slightly different things. Your concern seems to just be locating and/or notating a particular note or degree within the chromatic scale from a given starting point. But Roman numeral analysis is also about the functions of these various degrees. The diatonic degrees which get labels typically have a function while the others usually don't (though they can still be represented through b and # prefixes).

So the point is to give a label to only the bits of information that are going to be of use. You could use digits 1-12 and give the same meaning to 8 as you would V. But such a system doesn't make any distinction that 2,4,7,9, and 11 are less important and used less frequently. Using more precision than you actually need just means there's more data to wade through to get to the important bits.

Here's a pop quiz: how many months old are you? I bet you had to base it on years and do the math. We could say you have to be 216 months old to vote but it's much easier to use and remember the number in years.

The Roman numerals cut directly to the precision that we need for working with harmony—the scale degrees.

• Right, it's starting to clear up now... So V could also be noted as 8, and III could be noted as 5, but it's not done for good reasons. In that case, the III is always five half-tones up from any root, and it's no problem keeping track. – knutole Oct 11 '17 at 9:23

It's awkward working like this. instead, ignoring the odd semitones between E and F and B and C.

Using Roman numerals instead, the sequence becomes i I III iv I vi V i.

This uses small Rn for minors, caps for majors, assuming the key is C either major (I) or minor (i). That works for me, possibly not politically correct, but reflecting NNS, in a bastardised way. served me well for many a year, without complications.

Then it's transferrable to any of the other keys.

Yes, you are missing something in here. The Roman numerals refer to the degrees of a (major) scale (while you're thinking of the chromatic scale). So, in C major, a I would refer to C, II to D,... VII to B. The lowercase numerals mean a minor triad, the uppercase a major triad.

For instance, the fourth degree of a C major scale is F. So IV would refer to F major triad, iv to F minor triad. If you have a look at your example, it matches exactly.

As you can probably see now, it's completely invariant to transposes. If you would like to transpose it to, say, E major, you would substitute E for I, F# for II, G# for III, A for IV, B for V, C# for VI and D# for VII, but the numerals themselves remain unchanged. In this case, your i - I - III - iv - I - vi - IV - i would be played as e - E - G# - a - E - c# - A - e.

By the way, the notation is not very consistent beyond these basics, and for various 7th or even more complicated chords, you can encounter a wild variety of symbols. (Actually I hope I didn't mess up with it even now. Someone please warn me if I did.)