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I'm reading a book where the augmented 3 interval(two note) is considered a dissonant. However being that its enharmonic equivalent is a perfect fourth, I can't see how this can be so.

I've done a little digging and some say that it has to do with the context of the music. So I'm presuming that if perhaps a composer for example drifted into a different mode/scale he may spell the perfect fourth interval as a Aug 3rd (and therefor a dissonant) in this new context. Depending of course on the scale.

So for example this interval would be written in as a Aug 3 if the composer was writing in c lydian; the e sharp clashing with the f sharp of the lydian mode.

Am I right in this thinking

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    As a clarification, you are referring to the interval (two notes) of an augmented third? (As opposed to and augmented triad (e.g., C E G#).) – Aaron Jul 22 at 0:47
  • Yeah, so C E# . Sorry I should have made that clearer – Cameron Brown Jul 22 at 0:49
  • Thanks. Then your understanding is correct. It depends on the context. In addition to the Lydian example you give, it could also theoretically come up during some sort of modulation. I don't know of an example in practice. – Aaron Jul 22 at 1:29
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    Depending on the "language" (in the sense of style and other details), even the perfect fourth is considered dissonant if it's "alone", with no other voice to put in a context. Many examples of two-voice counterpoint that produce a perfect forth are considered like this. When a third voice comes into play, things change for the perfect fourth, and also put in different "situations" the resulting voice-conducting for the augmented third. Also, if you consider it as a melodic interval (in a harmonic context), it's usually difficult to sing. – Pipetus Jul 22 at 1:32
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    Actually many people hear the P4 as dissonant. So it is not clear that your question makes sense in this context. Perhaps a little more reading on this topic would help. – ggcg Jul 22 at 15:28
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All augmented and diminished intervals are considered dissonant. The interval C-E# is only equivalent to C-F in a tempered scale (particularly the equal-temperament that most keyboards now use.) On stringed and wind instruments as well as with voices, C-E# is different from C-F.

Augmented intervals generally expand and diminished intervals contract. Perfect, major, and minor intervals have their own voice-leading procedures.

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    "On stringed and wind instruments as well as with voices, C-E# is different from C-F": this is hardly universal truth. Most musicians I know would have no clue about how or why they should treat them differently, and consequently would not treat them differently. – phoog Jul 22 at 4:48
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    phoog's comment is right, but still +1 because C-E♯ is conceptually not a 3:4 fourth. If the score says C-E♯ but the musicians intuitively intonate it as a fourth and the listener hears that as well, it's probably the composer's fault for not clearly bringing out the true intend in the context. – leftaroundabout Jul 22 at 10:26
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    @leftaroundabout you assume that the composer intends there to be a difference, but what if the composer is one of those musicians who isn't aware of the difference? What if the composer's intent is that the E sharp be tuned as a 16:15 half step higher than E and that E is a 5:4 major third above C? What if the composer's intent is that the piece be performed in some 12-tone temperament? You should not draw conclusions about a composer's intent solely from the composer's choice of a particular enharmonic spelling option. – phoog Jul 22 at 10:45
  • @phoog I didn't draw any conclusions about what the composers intend is, but I stand by it that the intend isn't an audibly consonant fourth. That doesn't mean the actual frequency ratio can't be very close to 4:3, as it is for the 12-edo augm3, but then the context should divert attention away from that. If none of that applies, then I would indeed claim that it's a mistake by the composer. Either make the augmented third really dissonant to the listener, or just write a perfect fourth instead. – leftaroundabout Jul 22 at 11:01
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At first sight some augmented intervals could be transformed in consonant intervals considering the semitones. So it might seem that mathematically this dissonance is only theoretically and supposed by the notation image.

But, as Pipetus says in his comment even the fourth is dissonant.

And yes, all augmented and diminished intervals are considered as dissonant. (Ttw).They are stressed, containing lead tones, leading to the nearby next tone.

https://en.wikipedia.org/wiki/Augmented_third

So we could also compare the augmented second with a minor third:

The augmented interval is dissonant with a tension of resolving into a nearest note step, defined by the melodic and harmonic context ( sharps leading up, flats leading down).

On a piano these dissonances are not always audible. (Bartok Mikrokosmos vol. IV, nr. 111

enter image description here

Read more about Unusual Transformations in Bartok's "Minor Seconds, Major Sevenths”

https://www.esm.rochester.edu/integral/wp-content/uploads/2019/06/INTEGRAL_12_gollin.pdf

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  • The fourth is treated carefully in voice leading. It's treated as a dissonance against the bass (like in a 6-4 chord) but as a consonance against upper voices(like in a 6-3) chord. – ttw Jul 22 at 14:03
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    Yes, we should say the fourth is considered as dissonance as suspension. As an inversion of the 135 triad it is consonant of course. – Albrecht Hügli Jul 22 at 14:15
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    The augmented second is an excellent example because it's such a characteristic feature of the harmonic minor scale. You simply cannot mistake that oversized step on the scale for a minor third. – cmaster - reinstate monica Jul 23 at 7:54
  • @ttw or we could just say the fourth is consonant but the eleventh is dissonant. – leftaroundabout Jul 23 at 8:19
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Upon first glance a perfect fourth and augmented third seem for all intents and purposes equal...

enter image description here

...they are enharmonically equal. On a piano they are literally executed with the same keys.

But by definition augmented and diminished intervals are considered dissonant.

Why? I think the reason is clear when we consider whether the modified interval is diatonic or chromatic.

Play something to just establish a diatonic setting...

enter image description here

...then play an augmented third that is not enharmonically equal to a diatonic perfect fourth...

enter image description here

...the sound is pretty jarring, because it's outside the key. It's a sort of dissonant against the diatonic context.

I don't know if that is the origin of the theory that all augmented and diminished intervals are dissonant, but it's my way of making sense of it.

One final thought going back to the diatonic, enharmonically equal example. If we add a note to create a triad, we get...

enter image description here

If the context was clearly a C chord, like a tonic in C or dominant in F, then spelling it with a B# is aggravating. It doesn't make a good example of an augmented interval as a dissonance. It's just an example of bad harmonic spelling.

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