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When voice leading in the eighteenth-century style, why is the melodic augmented second (e.g., B♮ to A♭ in the same voice) forbidden?

Over the years I've heard reasons ranging from "it's awkward" to "it's a hard interval to sing" or "it sounds bad," but none of these seem all that convincing to me; plenty of other intervals are more awkward, harder to sing, and perhaps sound worse, but they aren't forbidden.

In looking through three common textbooks, I see no clear explanation. I couldn't find clear logic in either Laitz (The Complete Musician) or the Clendinning/Marvin (The Musician's Guide to Theory and Analysis), and Gauldin (Harmonic Practice in Tonal Music) only states to avoid singing any augmented intervals (diminished intervals are okay, provided they are usually descending).

Is there a better—ideally acoustic, much like the rules against parallel perfect octaves—reason for this limitation?

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    I've always heard the same reasons as have you. I've always taken it to be an aesthetic matter "lost to history", in which "the authorities" declared it so, and thus it was written. (Also, possibly prejudice, as it sounds "Eastern".)
    – Aaron
    Nov 22 at 0:30
  • It's also harder to read than B to G#. The G# is more logical, depending on the context of course.
    – Jomiddnz
    Nov 22 at 0:41
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    I suspect the reason is historical -- it wasn't explicitly forbidden because it wasn't recognized as a possibility until some later time, and other rules prevented it anyway: the interval exists between the lower sixth degree of the scale, from which one must descend, and the higher seventh degree, from which one must ascend. I just scanned through Gradus ad Parnassum, and Fux does not even include the augmented second in the list of intervals, nor did I notice anything in the musical examples (hoping to find one as an example of a mistake requiring correction).
    – phoog
    Nov 22 at 11:29
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    @phoog Interesting, and I like this thought process. Does Fux mention, say, a diminished fourth?
    – Richard
    Nov 22 at 11:41
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    @Richard yes. Intervals smaller than an octave are major and minor second, third, sixth, and seventh, perfect unison, fourth, and fifth, diminished fourth and fifth, and augmented fourth, fifth, and sixth. This is from the table on page 39 of the 1725 edition.
    – phoog
    Nov 23 at 0:04

3 Answers 3

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Don't think 'forbidden', rather 'out of style'. Like parallel 5ths and octaves, they worked against the aim of 4 independent but smoothly integrated voices, WHEN writing 4-part vocal arrangements. Which is something we tend to get obsessed with in theory class - the old composers wrote a lot of other stuff as well!

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  • How does an augmented second work against the aim of 4 independent but smoothly integrated voices? Nov 24 at 16:58
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The awkwardness in singing is definitely a valid reason. Try it. Another reason is the hexachord. Particularly in 18th century common practice that you mention, the system of tonality was (and still is ) defined by understanding the hexachords, the modes and how they relate. Look at when and how master composers used the intervals you are asking about and you will begin to see how they treated them in their music.

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  • Flamenco singers, for example, certainly don't seem to find it awkward. If you find it awkward to sing then this may well be mostly down to lack of experience with scales containing augmented seconds. Nov 23 at 23:02
  • @leftaroundabout The awkwardness only has to do with the cultural context, and this is that of the 18th century common practice. Most flamenco singers, for instance, will find a ^𝄳2 awkward, but Iranian singers will not. Nov 24 at 17:19
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It's not forbidden as one can find many classical pieces (I remember one of Mozart's piano concertos) using such an interval. An augmented interval is always considered "dissonant" (as are all diminished intervals.) There may be some acoustic differences between the "same" interval when that interval is used in different tunings. (An aside: the major third in "just" temperament is a 5/4 ratio; in "Pythagorean" temperament is 81/64; the difference is audible.)

Supposedly (according to what I remember from some music history of theory books and articles), something (in the key of C minor) a phrase like D-F-G-Ab-B would be a bit hard to sing (probably for congregations but professionals would have no problem). However, this is just a Gm9 arpeggio and a dominant chord arpeggio seems like it oughtn't to be unusual or unusually hard. This particular pattern is common in instrumental music from the classical area.

Conventionally, one only has 7 notes in the base scale of the key (ABCDEFG in some permutation). Thus one avoids writing D-F-G-G#-B instead of D-F-G-Ab-B. Also, the German Sixth (again in C major or C minor) is written Ab-C-Eb-F# and resolves to (usually) G-C-Eb-G (or G-C-E-G). The enharmonically equivalent Ab7 chord is written Ab-C-Eb-Gb (with a minor third on top rather than an augmented second); it resolves to some version of a Db major or Db minor chord (usually, maybe a form of Bb chord.)

What's important is to realize that even in equal temperament (only applying to fretted and keyboard instruments), there are differences between the minor third and the augmented second. There is the notational convention that augmented intervals expand while diminished intervals contract; thus the correct notation makes reading easier.

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  • Regardless of the presence in literature, I have also heard and read about avoiding melodic augmented seconds. Assuming there was a context where augmented seconds were avoided, forbidden, or just considered poor practice, this answer doesn’t answer the question of why. Nov 22 at 3:44
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    Arpeggios and scalar passages aren't "voice leading in the eighteenth-century style," though. The fact that such intervals appear in an ornate solo passage doesn't imply that Mozart would have allowed them in a choral texture.
    – phoog
    Nov 22 at 10:52

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