Student’s question:
In the IFR chord column drawings, I notice that sometimes you use flat symbols and sometimes you use sharp symbols. I get that #5 is the same note as b6, but is there a rule about when I should use one symbol or the other?
Some ideas to think about:
Yes, in most situations there will be an advantage to using one symbol or the other. But the most important point is the one that you stated right off the bat. In the equal-tempered system of modern Western music, enharmonic notes refer to the exact same pitch. So in terms of the absolute note names, C# and Db are the exact same note. And in terms of our harmonic analysis, #5 and b6 are also the exact same note.
But in most harmonic situations, one of these choices will result in a more elegant vision of the complete scale. Let’s look at a couple of examples. First let’s consider the 3D harmonic environment that we study in Mixed Harmony Essentials. As you know, the 3D chord includes the note #5. The complete scale of the 3D harmonic environment is as follows:
1 2 3 4 #5 6 7
Now let’s look at these exact same notes if we use a different name for #5. If we instead call this note b6, we get the following notes:
1 2 3 4 b6 6 7
Notice how awkward this scale is to think about mentally. Now there’s no scale degree with a number 5, but we have two variants of the 6. This is a much more convoluted way of describing the notes of the harmonic environment, so we naturally prefer the first set of notes above.
In other words, the choice of how we name the altered notes is actually determined by the other notes in the scale. It’s the presence of natural 6 in the scale above that causes us to prefer the name #5 for the altered note. This way each tonal number is represented exactly once in the resulting scale.
Let’s look at another example, also taken from Mixed Harmony Essentials. This time we’ll look at the scale of the 1D harmonic environment:
1 2 3 4 5 6 b7
Now let’s look at these exact same notes if we use a different name for b7. If we call this note #6, we get the following notes:
1 2 3 4 5 6 #6
Notice the same problem here again. Now there’s no scale degree with a number 7, and again we have two variants of the 6. I think you can appreciate that this spelling of the scale is more cluttered and cumbersome.
But remember that they are still enharmonics
Remember that in modern music, both the chord and the overall harmonic environment can change quickly. One moment you might find yourself in the 3D chord where it makes perfect sense to call the altered note #5. But then just a moment later, you could find yourself in a different chord that includes the note b6. While this is literally the exact same pitch as #5, it might make sense to label the note differently when the chord changes, for the reasons described above.
Key takeaway: Whenever you’re wondering whether it’s better to use a sharp or a flat symbol with an altered note, just look at the remaining notes of the harmonic environment. Wherever possible, make the choice that preserves the presence of all seven tonal numbers in the resulting scale, and that doesn’t repeat any tonal numbers.
Also be aware that there are some harmonic situations in which this principle doesn’t lead to any clear choice. Especially with more artificial constructs like the whole tone scale (just to cite one example), there will be times when both sharp and flat symbols can be equally valid choices. But with most traditional harmonic environments, you’ll find that one of the two options gives you a scale that is much more elegant and nicer to think about.
