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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?

OprenStein
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  • [This](https://music.stackexchange.com/questions/21910/why-is-a-minor-3rd-consonant-but-an-augmented-2nd-dissonant) should answer your question. – Peder Feb 25 '23 at 08:24
  • 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 '23 at 09:24
  • @Tim Yes, this assumes 12tet, though playing the same two tones wouldn't create a different sound in any temperament. – OprenStein Feb 25 '23 at 09:31
  • 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. https://music.stackexchange.com/a/75189/60885 – Emil Feb 25 '23 at 09:35
  • @OprenStein - as Aaron states, it actually would - depending upon the key the different temperament was tuned to. Or if the 'intervals were played on violin, trombone or even sung. – Tim Feb 25 '23 at 09:42
  • If you search for e.g. xenharmonic wiki you will also find a lot of information regarding different variants of the intervals (there are an infinite amount of intervals that can be called a minor third) – Emil Feb 25 '23 at 09:50
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    Does this answer your question? [Why is a minor 3rd consonant but an augmented 2nd dissonant?](https://music.stackexchange.com/questions/21910/why-is-a-minor-3rd-consonant-but-an-augmented-2nd-dissonant) – phoog Feb 25 '23 at 19:22
  • @Tim playing the same two tones cannot produce a different sound. In some tuning systems, F sharp and G flat aren't the same tone, but in any 12-tone temperament, whether equal or unequal (and in many tuning systems with more than 12 tones per octave), they are the same tone, and playing that tone with an A will yield the same acoustical result. – phoog Feb 25 '23 at 19:34

1 Answers1

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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.

Aaron
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    Also most wind instruments can adjust notes sharp or flat. – Lars Peter Schultz Feb 25 '23 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. – phoog Feb 25 '23 at 19:38
  • @phoog But don't musicians (in 12-TET) tend to lower minor thirds and raise augmented seconds? – Aaron Feb 25 '23 at 20:38
  • @Aaron if they're lowering or raising anything then it's not equal temperament, is it? – phoog Feb 25 '23 at 22:42
  • @phoog I’m speaking on-the-fly adjustments during performance, not the initial tuning system. – Aaron Feb 25 '23 at 22:56
  • @Aaron well in that case, those adjustments are typically in favor of 5-limit just intonation (sometimes 7-limit), where a minor third is 316 cents and an augmented second could be any of several sizes, but the distance between the 8:5 minor sixth and the 15:8 major seventh is a mere 275 cents. The Pythagorean sizes are 294 cents and 318 cents. Do you have any recordings in mind? – phoog Feb 25 '23 at 23:18
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    @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. – Aaron Feb 26 '23 at 00:01
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/143183/discussion-between-phoog-and-aaron). – phoog Feb 26 '23 at 06:37