# Interval quality in key signatures

I have plotted all m2, M7, M2, m7, m3, M6, M3, m6, aug4, dim5 intervals in all key signatures, and it seems that the notes don't move vertically or change accidentals (barring for accidentals in the key signature) if you go to a flattened/sharpened variant of the key signature such as (Cb, C, C#), (Eb, E), (Gb, G), (Bb, B), (Db, D), (F, F#), (Ab, A) (i.e., using the key signature's name as root note). Is this correct or did I mess up when transposing?

• I wonder if I misunderstood your question. As a clarification, let's say you start with the C major key signature. Does your interval plot include notes outside the key signature, such as the M2 from B to C#? My answer is only correct if you're plotting intervals between notes that stay within the key. Chromatic tones will not work as desscribed. Commented Jan 6, 2022 at 15:19
• I don't know, I am still learning.
– Emil
Commented Jan 6, 2022 at 16:17
• When you were figuring out the intervals, did you add any accidentals not already in the key signature? Commented Jan 6, 2022 at 17:17

NOTE: This answer is given in terms of major keys, but the same holds true for (natural) minor. It also is only true for notes within the given key; it does not hold true for chromatic pitches outside the given key.

This is correct. As long as the letter-name (and mode) of the key doesn't change, the key signature change is no different than transposing every single note in the key up or down a half step.

When moving from X to X♭, the lines and spaces of the scale stay exactly the same, but with each pitch lowered a half step.

When moving from X to X♯, then lines and spaces again stay exactly the same, but with each pitch raised a half step.

Since every line/space is transposed by exactly the same amount, the intervals between each line/space stay the same.

However, when the letter name of the key changes, the intervals between lines and spaces (can) change. The B line and C space are always a half-step apart in all of the "keys of C" (C♭, C♮, C♯) or G, but they're a whole step apart in the key(s) of D, E, F, A, and B.

This is almost correct, but accidentals not in the key signature will burn you. The most common example of those are leading tones of minor keys. For example, when transposing music from F minor to F sharp minor, you need to transpose all E naturals in the F minor version to E sharps in the F sharp minor version.

Chromatic scales and/or portions thereof may need to be handled deftly when transposed. A B♭-B-C-C♯-D passage in E flat major will naively get transposed to B-B♯-C♯-C double sharp-D♯ when transposing to E major, while B-C-C♯-D-D♯ may be a lot more readable and stick to other conventions depending on where you put the barlines.

• I don't require the pitches to remain the same, I recreate all intervals in each key and then compare the results, not sure if that matters for your answer. I uploaded it here if you could check how your point applies ?
– Emil
Commented Jan 6, 2022 at 7:39
• @Emil - You're lucky enough to have picked only intervals that appear in the major scale. (I checked your PDF and found this.) If you picked any interval that didn't appear in the respective major scale, such as E-G# for major 3rds with a C major/A minor/no-accidentals key signature, you'll quickly find that you do need to change accidentals on notes in order to keep the same interval when transposing (e.g. to Eb-G natural in Cb major/Ab minor/7-flat key signature for another major 3rd). Commented Jan 6, 2022 at 13:53
• Allright, one needs to keep the delta to the key signature the same, I see what you are going for.
– Emil
Commented Jan 6, 2022 at 14:21
• I probably need to revisit how flats/naturals/sharps work in other sigs, but I think a natural just reverts to key sig so I think it should not matter that much if I don't think relative to C major.
– Emil
Commented Jan 6, 2022 at 14:31
• @Emil, I added an answer to get into that question about accidentals in context of key signatures. Commented Jan 6, 2022 at 19:54

I have plotted all m2, M7, M2, m7, m3, M6, M3, m6, aug4, dim5 intervals in all key signatures, and it seems that the notes don't move vertically or change accidentals...

When you word it specifically as "don't...change accidental" then, yes, your point is true of all the diatonic intervals in any key.

But you might be overlooking an important point. If you don't think literally of accidentals, but think in terms of "alteration applied" as raised or lowered tones, the idea applies to chromatic intervals as well. Consider an augmented fourth (`A4`) that involves a chromatic tone, like an `A4` built on the second major scale degree, solfege `RE`...

The lines and spaces don't change.

And while the specific accidentals change, the alterations applied do not. The diatonic fourth above the second scale degree in major is always a perfect fourth. To augment it we always raise the upper tone. Whether a `♯` or `♮` is used to signify raising the tone is just a matter of the key signature is sharps or flats.

I think the reason this matters, that it's worth pointing out, is because the reading approach is to look for tones raised/lowered from their diatonic position and applying some general principles about intervals. For example, any time you see a third, and there is some kind of accidental to raise it, you are probably dealing with a "bigger" third, a major third...

I think the reading strategy is something like, for example with `M3` in `C#` major, don't read each and every letter and sharp/flat, but first get anchored on the diatonic `LA` (the `A#`) and then, rather than thinking literally `C` double-sharp, just play a `M3` above `LA`.

And the deeper insight is that this kind of chromatically raised major third will probably be functioning as a secondary dominant. That raised tone above the `LA` is actually an alteration of the tonic, likely making it a temporary leading tone that will ascend to the next scale degree up, up to `RE`.

You can have weirdness like this...

...where the raised tone actually forms an augmented third, but such a case is probably either very chromatic music, or just bad enharmonic notation. If the music is truly very chromatic then these kinds of rule-of-thumb strategies won't be of much help.

• You mean a sharp accidental does not always mean "+1 semitone" to whatever is in the key signature? This is so confusing, perhaps I have never encountered one of them in a song yet, hmm.
– Emil
Commented Jan 6, 2022 at 20:37
• @Emil, that is correct. It can become confusing in certain situations. But keep in mind in my example of that - `C#` in a key signature of `C` flat, which is +2 semitones - I gave it as an example of a bad enharmonic spelling, which is bad because it's confusing. Commented Jan 6, 2022 at 20:58
• What kind of music are you concerned with reading? Don't go too far "down the rabbit hole" if you don't need to. Commented Jan 6, 2022 at 21:00
• I like to play folk music, jazz and classical music. I will probably need to watch out for these.
– Emil
Commented Jan 6, 2022 at 22:29
• My thought is music like Bach's WTC, late 19th century piano music, 20th century atonal, that's the kind of stuff that gets very chromatic, and uses key signatures with lots of sharps/flats. Hard to read. Folk and earlier classical will be easier to read, chromatic elements will be there, but generally less of it, and the key signatures tend to be simpler. Commented Jan 6, 2022 at 23:35