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I am currently reading the Jazzology and on the chapter per the consonant and dissonant intervals I came across this statement:

while a minor 3rd is consonant, an augmented 2nd is dissonant.
(page 6)

So my question is this:

Why is a minor 3rd consonant but an augmented 2nd dissonant, since they --technically-- are the same note?

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Just to keep as reference, the complete quote is: Enharmonically equivalent intervals usually appear in different contexts and thus should not be considered the same as their counterparts, i.e. while a minor 3rd is consonant, an augmented 2nd is dissonant. –  JCPedroza Jul 10 at 16:52
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They're only actually the same note if you're tuning system is equal temperament. Jazz often isn't. –  OrangeDog Jul 11 at 10:08
    
@OrangeDog can you expand your comment in an answer? It seems interesting –  Shevliaskovic Jul 11 at 10:10
    
Someone else can take the rep, but here are some links. en.wikipedia.org/wiki/Musical_tuning en.wikipedia.org/wiki/Musical_temperament en.wikipedia.org/wiki/… –  OrangeDog Jul 11 at 10:14
    
And as @Dave mentions, the "same" note can be 40 cents different depending which direction you're coming from in his example. –  OrangeDog Jul 11 at 10:15

4 Answers 4

up vote 12 down vote accepted

Well, without any further context there is no possible distinction between a minor third and an augmented second as they are indeed the same note, technically.

However, the phrases minor third and augmented second make reference not only to that space of three semitones, but also to the relationship that this interval plays within a given chord or scale. Since almost every scale known to the Western world has some form of third, a scale or chord with an augmented second would most probably have another kind of third as well, making the augmented second seem like an added dissonance in context.

Consider this chord: C7#9. (The #9 can be considered equivalent to an augmented second). The naming convention of the chord assumes there will be a major third. So the chord is 1, 3, 5, 7 and #9. The last note is not an essential part of the chord's structure, and will sound dissonant.

If you just have a C and a D#/Eb, it doesn't really matter whether you call it a D# or an Eb. But when you're talking about the role that note plays within another structure, then there are reasons for naming it an augmented second (to make clear it is not a minor third).

Hope this helps!

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Good point and well said. I would only add that the augmented 2nd shows up as often or even more often as a melodic interval, and it is always a melodic dissonance in common practice music while a melodic minor third is usually consonant (barring some sort of chromaticism) –  Pat Muchmore Jul 10 at 15:17
    
@PatMuchmore Good point, I think it can be reasoned both from a common practice perspective as well as the perspective of contemporary jazz theory. I think it would add clarity if someone could give an example of how a note used in a melodic context might be an augmented second escaping from the implied harmony and thus dissonant, or a minor third in keeping with the harmony. But I don't feel like firing up Finale! Maybe later. –  Grey Jul 10 at 15:24

A key thing to keep in mind is that technically a minor 3rd and an augmented 2nd are different pitches (have different notional fundamental frequencies), at least in anything other than equal temperament. In just intonation, these two pitches differ by approximately 40 cents (list of intervals), enough to make a perceptable difference in the degree of consonance. (Also note that some types of mean-tone temperament can also represent this difference). Thus these different notes are different and have different harmonic behaviour in the context of a chord.

Even in the context of music intended for performance in ET, notating the enharmonic notes in particular ways can provide the performer with information on the composer's intent.

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Good point, Dave. Unfortunately, the distinction between them is now lost on most of us because hundreds of years ago a bunch of barbers and blacksmiths conspired to ruin music by cursing it with only 12 notes. :( –  Grey Jul 10 at 15:29
    
@Grey - true to a degree, but it doesn't half make changing key a doddle... –  Tim Jul 10 at 15:53
    
1) I don't think this answers the question. 2) Would that small frequency difference (measured in commas) influence the argument? Would that difference make a difference in consonance or dissonance? 3) Given the predominance of equal temperament, one would assume that the author is taking it into consideration. –  JCPedroza Jul 10 at 15:57
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@JCPedroza 1) they behave different harmonically because they are (in JI and some other tuning systems) different pitches 2) 40 cents in a harmonic context is pretty discernible (added to answer in edit) 3) the composer is indicating whether the given given interval is intended to be consonant or dissonant, and how it's intonation should be if performed by an instrument with fine pitch control. –  Dave Jul 10 at 16:24
    
3) The author is talking about context and not frequency difference, and he is explicit about it. The complete quote (page 6) is: Enharmonically equivalent intervals usually appear in different contexts and thus should not be considered the same as their counterparts, i.e. while a minor 3rd is consonant, an augmented 2nd is dissonant. –  JCPedroza Jul 10 at 16:50

One reason is that if you're specifying an augmented 2, its probably because you have an augmented second and a major third in the chord. These notes are only a half step apart, and that is very dissonant.

Since we don't have, for example, a "minor fourth" interval, the third will always be major if an augmented 2 is involved. I guess there could be exceptions, but if there isn't also major third in the chord, it would just be written as a minor third interval.

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There's not going to be a #2 and a maj3 in a particular chord. The clash is too great. There is a #9, which could be argued amounts to the same thing, but since it's an octave away from the note it would have clashed with, it's sonically not a problem. Close to the 'Hendrix chord'. –  Tim Jul 10 at 16:07
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Sorry, yes #9 is basically what I meant but as far as a scalar representation of the chord I used a #2 as the example. –  Eichhörnchen Jul 10 at 16:08

It seems to stem not from the meaning that we attach to the words now, but the past. Consonant meant it sat well in the key, dissonant, the opposite. So, when WRITTEN in music, a minor 3rd belongs in a given set of notes, whereas a #2 is not found.It appears to be more of a technicality than a reflection of what it actually sounds like.

Turn a minor 3 upside down, and it's a major 6th.Supposedly consonant. Turn a #2 upside down, and it's a diminished 7th. Both augmented and diminished intervals were labelled dissonant.

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