31

In music theory when naming intervals, a lowered diminished interval is a doubly diminished interval (dd) and a raised augmented interval is a doubly augmented interval (AA). One example is a C♯ to a G♭ would be a doubly diminished 5th (dd5) and a C♭ to a F♯ would be a doubly augmented 4th (AA4). However, these intervals can be converted to their enharmonic equivalent so the make more sense so instead of having a C♯ to a G♭ you could write it as C# to F# and have it be a P4 and instead of having a C♭ to F♯ you could write a B to F# and have it be a P5.

I have never actually seen a naturally occurring doubly diminished or doubly augmented interval I have only isolated examples in theory books. Is there ever any scenario where any doubly diminished or doubly augmented intervals are used in melodies or chords?

Improve this question
2
  • F♭ to a B♯ is a triply augmented fourth...
    – mathlander
    Jan 10 at 19:28
  • @mathlander yes, but that example isn't here so not sure what you are getting.
    – Dom ♦
    Nov 8 at 15:45

8 Answers 8

Reset to default
17

The last piece in Ligeti's Musica Ricercata is a good example of double diminished everything. But these intervals in the piece occur only because of polyphony.

I'm quite sure that if you dig up some early or very late Shostakovich you'll be able to find examples of more harmonic and melodic (rather than polyphonic) use of double diminished intervals. Shostakovich is a very frequent user of diminished and double diminished intervals.

Improve this answer
1
  • 4
    Excellent, there they are! Including the inversion of the exact same interval I hypothesized about in my answer, Gb–C# doubly-augmented fourth implying resolution to F–D. Thanks so much for providing an example, I'm going to show it to my students next week!
    – Pat Muchmore
    Feb 23, 2014 at 14:20
5

In standard functional harmony, diminished intervals only naturally occur between the 4th and 7th scale degrees, which is typically found in a vii° or V7 harmony. Double-diminished or double-augmented intervals don't occur anywhere in this system in its most basic version. Much of our Western music is based on this harmonic system, so intervals of this type are naturally much less common.

But the more inventive and expansive harmony becomes, and the more chromatic a piece of music is, the more likely you are to find intervals of this sort. Usually they arise out of linear motion than a vertical, simultaneous chord with a functional harmonic structure, though.

I recall seeing lots of chromaticism of this type (leading to the intervals you seek) when I was analyzing the music of Scriabin and Berg in school. That's a good place to start.

Unfortunately I can't think of any functional harmonic chord structure or progression that contains a doubly-diminished or doubly-augmented interval.

Improve this answer
2
  • 2
    'Standard functional harmony' progressed way beyond the simply diatonic several hundred years ago!
    – Laurence
    May 21, 2017 at 17:16
  • so to put it in layman's terms, is the purpose of writing an interval this way to visually indicate the direction two melodic lines are moving?
    – Andy
    Mar 15, 2019 at 18:02
4

I know I'm late to answer, but one of the places you might find a doubly augmented/diminished interval is in the respelled German sixth chord. The normal spelling (♯4-♭6-1-♭3) easily lends itself to parallel fifths, so the ♭3 may be respelled as a ♯2 to avoid this. This has the effect of creating a doubly augmented fourth (or doubly diminished fifth) between the ♭6 and ♯2.

Improve this answer
2
  • Indeed the second spelling you mention is harmonically valid, and the avoidance of consecutive fifths is not the only reason for it. The German sixth chord may resolve onto a cadential 6/4 in a minor key thus: ♭6-1-♭3-♯4 5-1-♭3-5 5-7-2-5 1. The other chord resolves onto a cadential 6/4 in a major key thus: ♭6-1-♯2-♯4 5-1-3-5 5-7-2-5 1.
    – Rosie F
    Apr 25, 2018 at 11:17
  • Now I wonder why parallel fifths are avoided by respelling the tones. I always thought they were forbidden because of what you hear and not because of what is notated. This would be a very smart trick in a test of 4 part harmony.
    – Albrecht Hügli
    May 19, 2019 at 8:44
3

Besides for user181381's excellent example, I was looking around last week and found that altered chords may have a doubly augmented or doubly diminished interval in them.

Let's look at a C7b5#9 and a C7#5b9

C7b5#9 - C  E  Gb  Bb  D#

C7#5b9 - C  E  G#  Bb  Db

In the case of a C7b5#9, the interval between Gb and D# is a doubly augmented 5th and the Gb wants to go to an F(tonic) and the D# wants to go to an E(tonic's 7th aka leading tone). In the case of a C7#5b9, the interval between G# and Db is a doubly diminished 5th and the G# wants to go to an A(the 3rd of tonic) and the Db wants to go to a C(the 5th of tonic).

So these intervals just help lead back to tonic and function as an extension of a dominant chord.

Improve this answer
2

I haven't seen them in an actual piece, but I'm hoping somebody else on here has, because I'd be very interested. However, I can think of a functional reason to use your example, C#-Gb; it would make sense as a chromatic dissonance that resolves to a D-F minor third. Doubly diminished sevenths such as C#-Bbb would imply "resolution" to a o5, in this case D-Ab. They should absolutely never be used unless there's a specific implied resolution like this, and there's a pretty strong case to be made that they shouldn't be used even then because they're just too unfamiliar to a performer. Personally, I think there's something to be said for truly showing the actual function despite odd intervals (for example, I often use augmented 3rds in my own music, implying an outward resolution to a P5), but I just don't know if I could bring myself to throw a doubly diminished or augmented interval at somebody.

Improve this answer
0
1

Doubly-diminished intervals will seldom occur in a piece whose tonal center remains in one key. Weird things can happen when pieces modulate, however, especially if the most "natural" way of writing the modulation would result in an excessive numbers of sharps or flats. Consider, for example, a piece of music that starts in E major and modulates upwards twice times by a whole step; each modulation is preceded by a V7 of the original key. If the second key is written as Gb major, then the old-V7 to new-I transition will be

    B  D#  F#  A
    Gb Db  Gb  Bb

The interval from D# to Db will be a doubly-augmented prime. If there were only one modulations, one could avoid the doubly-augmented prime by modulating into F# rather than Gb, but that require that one either modulate from F# to Ab (posing the same problem as modulating from E to Gb) or else modulate to G#--a key with eight sharps.

In general, harmonies are worked into key signatures in such a way as to avoid doubly-augmented or doubly-diminished intervals, but every once in awhile, key signatures need to "go around the bend" from lots of sharps to lots of flats or vice versa, and such transitions can make it necessary to use some wonky intervals. Augmented and diminished seconds, thirds, sixths, and sevenths are very common in such cases; even those cases don't often cause doubly-augmented or diminished intervals, however. Certain required modulations, however, can compel their usage.

Improve this answer
3
  • 2
    Db to D# is a doubly-augmented prime, not diminished. In fact, diminished primes are impossible, because moving either note is always expanding the interval, never contracting.
    – Pat Muchmore
    Aug 2, 2014 at 21:42
  • @PatMuchmore: You're quite right of course (corrected I think). A transition from D# to Db could be a doubly-diminished or doubly-augmented octave, depending upon direction. I know I've heard music which modulated with an old-key V7 going to the tonic of the key a major second higher, so although the choice of starting key was contrived to cause "trouble", the chord sequence was "real". I found it surprisingly difficult to create any sort of doubly-augmented or diminished interval, since just about all the intervals which could get "double-whammied" were either major intervals which got...
    – supercat
    Aug 3, 2014 at 15:36
  • ...reduced twice (and thus became only singly-diminished) or minor intervals that got expanded twice (and thus only singly-augmented). I have actually encountered a doubly-diminished second (pitch moving the opposite direction of the staff note) in print (choral sheet music); there was a section of about eight bars that was in Cb, but two non-consecutive bars within that section notated pitches enharmonically as though it was in a "sharps" key. I'm sure it was "accidental", but it was definitely weird having the staff notes go one way and the pitches go the other.
    – supercat
    Aug 3, 2014 at 15:42
0

A doubly augmented first (prime) occurs in Verdi's Stabat Mater No. 2, tenor, bars 187-188: a Db to a D#.

Improve this answer
0

Sorry for my bad english

However its too late but , At first i want you to know you can never change the name of an interval with the other one [just for some modulations you can] and it does not depend if those are enharmonically equal or not , its' because of tendency of each one of them. in your example ( C_# to G_b) imagine which tonality you are in, it can be for example d minor , so in d minor your dominant chord is a-c#-e-g so normally you have c# but also in some cases in minor you can decrease G halftone in dominant chord so in this situation you have dd5 c# will go to d and G-b will go to F. You can find the same notes together in some other cases especially in melodic motions (sorry again for bad english)

This kind of intervals helps are more when we talk about Atonal music .

Improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.