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Thread: Interval problem

  1. #1
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    Interval problem

    So I was doin some practice problems in my theory book and ran into one problem I can't seem to grasp. The section I'm working on is telling me to identify which intervals are perfect unisons fourths fifths and octaves, and identify them as diminished or augmented when they arise. I'll try to draw out the staff..

    ---------------
    ---------------
    bbO
    ---------------
    -----bO----------
    ---------------

    It's a bass clef..from what I can gather it's a Bb and Ebb, which = D..but Bb to D is only a third, from what I can gather..anyone know what this would be? An augmented third perhaps?

  2. #2
    The Riff Master zog's Avatar
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    Since the exercises you are doing are asking for fourths and fifths Bb to Ebb would be a diminished 4th if you change it to D then it is only three notes away from Bb and becomes a major 3rd.

    This is one case where the enharmonic spelling of a note comes into play since the note is written on the staff as an Ebb then that is what you should use instead of its enharmonic spelling of D.

    An augmented 3rd from Bb would be a D# when dealing with intervals you need to count the letters between the two notes for example D# is three notes away from Bb so its some kind of third in this case an augmented 3rd but if you change the enharmonic spelling of the note to Eb then it becomes four notes away from Bb and becomes a perfect 4th. Hope that makes a little bit of sense.

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    Bleh..so it's just more trickery in the music theory world..it seems that world is full of trickery. So the fact that the pitch is actually a D makes no difference? Just count it as a diminished 4th..I get it I think. Thanks.

  4. #4
    Registered User JonR's Avatar
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    Quote Originally Posted by jwilliams
    Bleh..so it's just more trickery in the music theory world..it seems that world is full of trickery.
    Indeed.
    Quote Originally Posted by jwilliams
    So the fact that the pitch is actually a D makes no difference? Just count it as a diminished 4th..I get it I think. Thanks.
    The "pitch" - as in the sound - is simply a frequency. It may have more than one name depending on how we're using it. The governing rule is that a scale has to have one of each note (letter) - and only one.
    An Ebb note is admittedly extremely rare (wouldn't occur in any practical musical situaiton I can think of), but enharmonic issues (one pitch, 2 or more names) occur all the time.
    In fact, there are 21 (common) note names covering 12 pitches - because each of the 7 notes needs to have a natural, flat and sharp version of itself, to cover all 15 keys. So obviously there is some overlap!

    Er, yep, 15 keys, not 12. (More trickery...)
    C major, plus 7 sharp keys and 7 flat keys.
    3 of the 15 are "enharmonic" - all 7 notes can be spelled one of two ways.
    Eg...
    F# major = F# G# A# B C# D# E# F#
    Gb major = Gb Ab Bb Cb Db Eb F Gb

    - see what's happening? These keys sound identical to one another. But every note is spelled differently to keep the note count working.
    It's true this is not a common key, but it does occur. And what are you going to call it, and how would you spell it so it makes most sense? It's either 6 sharps or 6 flats.
    If you mix up sharps and flats (thinking that might make it simpler), you get into various kinds of confusion. You get 2 or more of one note, and one or more missing.
    And you should find that it's easiest to think of Gb major as a half-step down from G major - for every note. Which includes flattening C to Cb.
    (Or F# major as F major raised by a half-step, including raising E to E#. Because, er, we already have an F...)

    More commonly, you get diminished 4th intervals in every harmonic minor scale - between 7th and 3rd steps. Eg, G#-C in A harmonic minor is a diminished 4th. And G#-F is a diminished 7th (which matters because it's the basis of the "dim7" chord). And F-G# is an augmented 2nd. It sounds like F-Ab (minor 3rd), but there is no Ab note in the A harmonic minor scale.
    (Might seem like a whole load of trickery, but it makes perfect sense when you see the whole picture.)

  5. #5
    bitter old fool Jed's Avatar
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    Quote Originally Posted by jwilliams
    Bleh..so it's just more trickery in the music theory world..it seems that world is full of trickery. So the fact that the pitch is actually a D makes no difference?
    If it were a D, why would the composer notate it as an Ebb?

    For the most part humans perceive music in relative terms. The language that we use to describe music likewise needs to reflect this relative nature of how we perceive the sounds. The nature of how we perceive things doesn't follow any kind of mathematical logic (it a perceptual thing), but it does follow perfectly the kind of intervallic logic that music theory was designed to communicate.

    The purpose of this exercise is to encourage you to see, hear and think of sounds and notes in terms of relative intervals, as opposed to looking at them in terms of discrete pitches (an absolute construct). Your comment about Ebb being equal to D natural illustrates that you are looking at this in terms of discrete pitches (in terms of mathematics). While this is not an inaccurate generalization, it misses the nuance of how that sound was derived. While the generalization makes sense to our logical minds, it obscures the nuance.

    The specific lesson in this case, is that Bb to Ebb is a diminished 4th, which while distinct in name is the same sound as a major 3rd (from Bb to D). In other words, that sound that we identify as a major third is the same sound that we identify as a diminished 4th.

    cheers,

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