# Why does spelling change the consonance/dissonance of the exact same interval?

The interval of F# to A is a minor third, an imperfect consonance. But if we spell the F# as a Gb, suddenly we have created an augmented 2nd, a dissonance. Sonically, these two situations are the exact same thing. Their frequency ratios are exactly the same, the only difference is that they are spelled differently. However, this sonically nonexistent difference somehow changes a consonance to an interval that is considered dissonant. This is not limited to this one situation; the augmented fifth, diminished 7th, and diminished fourth all have consonant equivalents, and yet are somehow considered dissonant. How does spelling change an interval's consonance?

• This question assumes 12tet - or does it..? And be careful with terminology - those two are not the same interval - they're the same distance apart, in semitones.
– Tim
Feb 25 at 9:24
• @Tim Yes, this assumes 12tet, though playing the same two tones wouldn't create a different sound in any temperament. Feb 25 at 9:31
• I know this answer was about dissonance but I don't remember the details of the video. Not sure if it was about chords or chord progressions though. music.stackexchange.com/a/75189/60885
– Emil
Feb 25 at 9:35
• Does this answer your question? Why is a minor 3rd consonant but an augmented 2nd dissonant? Feb 25 at 19:22

The spelling doesn't make it dissonant or consonant; the consonance or dissonance determines the spelling.

Rather than spell the notes, assign them numbers: C = 0, C# = 1, D = 2, ..., B = 11.

Now consider the C minor scale. The first three pitches are 0, 2, 3.

The E harmonic minor scale also contains 0 and 3: `4 6 7 9 11 0 3 4`.

However, if one plays the two scales, the 0-3 in the C minor scale has a very different character than the 0-3 in the E harmonic minor scale.

In order to reflect this contextual different in sound, the otherwise enharmonically equivalent pitches are given different spellings: `C D Eb` for the C minor context, and `C D# E` for the E harmonic minor context.

Also, historically, before equal temperament was standardized, `C#` and `Db`, for example, were not necessarily the same pitch. Even today, instruments with "continuous" tuning ability, like violin or voice, will adjust notes sharp or flat —that equal temperament would otherwise deem equivalent — to create better intonation of intervals in specific contexts. For example, the minor third or a chord might be adjusted very slightly higher, or the major third very slightly lower, bringing them closer to their just-intoned equivalents.

• Also most wind instruments can adjust notes sharp or flat. Feb 25 at 15:57
• For the most part, D sharp will be lower than E flat, not the other way around, unless the goal is Pythagorean tuning. Feb 25 at 19:38
• @phoog But don't musicians (in 12-TET) tend to lower minor thirds and raise augmented seconds? Feb 25 at 20:38
• @Aaron if they're lowering or raising anything then it's not equal temperament, is it? Feb 25 at 22:42
• @phoog Recordings, no. I was just thinking of ensembles in which the director asked whomever had the third of a chord to raise or lower it compared to its equal-tempered basis. Feb 26 at 0:01