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Rule 12 of Paul Hindemith's Craft of Musical Composition - Book 2 states the following:

Avoid augmented and diminished intervals. If, after an augmented or a diminished interval, the third tone is taken by skip, a chord group will result.

So, naturally, I look to my intervals chart (I am new to this) and see that the majority of intervals are, as far as their "alternate name" goes, either diminished or augmented.

table in three columns: number of semitones, interval name, enharmonically equivalent interval name

At this point I realized that I was misunderstanding something. For background information: the music I want to compose is mostly diatonic (does this rule apply if my music is strictly diatonic?). Can someone please shed some light on this Rule 12 for me?

Thank you.

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    I don't think it's likely that you'd find yourself using an augmented or diminished interval by mistake. Hindemuth is suggesting that you resist the urge to use them on purpose, not that you avoid using them accidentally. So you don't have to learn to avoid them, just remind yourself to not use them when the temptation arises. Unless you doubt Hindemuth's advice - there are no rules in composition. – Todd Wilcox Apr 13 at 1:32
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    You might find some helpful information here: What's the Reason for Naming Major Second a Diminished Third? and here: Why call a major second a diminished third?. – Aaron Apr 13 at 1:51
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    Aaron do you know if SE has any provision for secondary subsections like hindemith.music.stackexchange? Some theoretical contributors are so important that it would make sense to somehow have dedicated areas. I'd probably have one for Bach and one for Schonberg as well. – Bennyboy1973 Apr 13 at 2:00
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    What you call an alternative name actually has a name. It is called a enharmonic equivalent. Most tones have two names, some even have three. No matter by what you call them, they still only represent one tone. – Neil Meyer Apr 13 at 7:23
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    Dump that chart. It's not that good. – Tim Apr 13 at 8:23
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The chart you show is only telling half the story.

Intervals are more than just a certain number of semitones between two notes. But that's all the chart tells.

Intervals also need the names of the two notes - or where they're written on the staff.

True, each interval will have at least a couple of names - we could even stretch that top one to augmented unison, and the penultimate one to diminished octave, for the sake of argument.

Trouble is, without knowing the actual notes concerned, we can't say accurately what an interval will be called. Just hearing two notes isn't enough. Play C and E♭, it's m3. Play C and D♯ , it's augmented 2nd. On piano, tuned 12tet, they sound identical, but how would they get written when someone is transcribing them? There's the rub. It'll depend mostly on the context - what key is it in, where's it come from, where's it going to, mainly. Make that C into B♯, and leave the E♭ as is - now it's a 4th interval - but will still sound the same as the other two.

So, while most, if not all intervals will have a 'diminished' or 'augmented' alternative name (as the chart states), mostly, those same intervals will have a more common name, depending on what the notes are called. Diatonically, they're major, minor and perfect. In key C, for example, C>G is P5. It sounds fine in that key. Make that C B♯, though, and it belongs in another key - and the interval is a 6th - a diminished 6th. Not so good in key C.

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  • Thank you. I followed basically till the the last sentence. You say the diminished 6th is "not so good in key C" . . . but its equivalent (to the ear) to a P5 . . . so it should sound just the same? – 286642 Apr 14 at 2:13
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In a non-tempered tuning, the intervals C-G# and C-Ab are not identical. (Voices, and strings, and some other instruments will often produce different sounds for these intervals.)

With the interval C-G#, the spelling is that of a fifth and the # indicates that the fifth is augmented (perfect intervals only have augmented and diminished versions). The interval is musically a fifth, and as an augmented interval, its (usual, tonal) resolution is to expand. (In a G7 chord, the augmented fourth tends to expand to E-C whereas the diminished fifth B-F tends to contract to C-E). The interval C-Ab is a sixth, and the flat indicated a diminished sixth which will tend to contract.

Both the spelling and accidentals of an interval do indicate the usual usage of such intervals. For these specific intervals, I would expect the tendency for C-G# to move to C-A or C# to A or B-B or something like that. C-Ab would move to C-G or D-F# or something similar. (Tendencies only).

Augmented and diminished intervals, because of their movements, do have a characteristic sound. Hindemith is warning of using too many similar-sounding intervals in a row. At least that's how I read it.

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C to G♯ is an augmented fifth. Mostly you'll have C to A♭, though, and it will be a minor sixth. In other words, the spelling matters. The fact that it would be an augmented or diminished interval if it were spelled differently isn't particularly relevant. What matters is whether it's an augmented or diminished interval when it's spelled correctly.

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  • Thanks. I don't understand the concept of spelling. – 286642 Apr 13 at 1:39
  • Take the interval C-G#, the spelling is that of a fifth and the # indicates that the fifth is augmented (perfect intervals only have augmented and diminished versions). The interval is musically a fifth, and as an augmented interval, its (usual, tonal) resolution is to expand. (In a G7 chord, the augmented fourth tends to expand to E-C whereas the diminished fifth B-F tends to contract to C-E). – ttw Apr 13 at 2:09
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The basis for Hindemith's rule is the avoidance of a melodic segment that sounds like the outline of a chord.

Suppose a melody contains C followed by D# — an augmented second. Further, let the next note ("the third tone") be G, which is more than a second away from the D# ("is taken by a skip"). That sequence of notes will sound like the outline of a C minor chord — a minor third followed by a major third, rather than an augmented second followed by a diminished fourth.

As explained in other answers, enharmonically identical intervals (e.g., augmented second and minor third) have distinctive sounds in context. But a melodic procedure like the one above undermines the sound of both the augmented second and the diminished third.

Similarly, consider the melodic sequence C D# G#. This will appear to the ear to be an Ab major chord (in first inversion: C Eb Ab — minor third and perfect fourth) rather than an augmented second and perfect fourth.

Hindemith is in effect saying "melodies should not outline chords, so avoid augmented and diminished intervals, because a subsequent 'skip' will likely produce a chord" (that is, a "chord group", a group of notes which together form a chord).

It's not likely you'd run into this problem in strictly diatonic composition, but it's not impossible. For example, in C minor, a melody might progress from Ab to B — an augmented second. Were the next melody note an Eb, the result would sound like an Ab minor triad (Ab Cb Eb), which would almost certainly disrupt the diatonicism of the melody.

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You're correct that a jump of 3 semitones might be a minor 3rd or an augmented second. But this isn't a free alternative choice of spelling. Depending on context, one or the other will be the RIGHT spelling.

Let's look at the C harmonic minor scale. I've marked two places where an interval of 3 semitones occurs (no matter that they aren't consecutive notes in the scale). Between C and E♭ and between A♭ and B. IN THE CONTEXT OF C MINOR TONALITY these intervals have very different flavours and deserve different spellings, as a minor 3rd and an augmented 2nd. Calling the first an augmented 2nd, the second a minor 3rd wouldn't be 'alternative', it would be wrong!

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Hindemith isn't talking about what an interval of a certain number of semitones might be, out of context. He's talking about what they ARE, in a given tonal context.

Read 'Craft of Musical Composition' and learn from his ideas. But don't take it as a bible. Partly because he's a little too fond of 'rules' that don't always stand up to practical scrutiny.

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