interval inversions

Discussion in 'General Instruction [BG]' started by yor123, Jun 12, 2001.

  1. yor123


    Mar 29, 2001
    New Orleans
    Hey guys ( and gal, Jason if you are out there)

    Did a search on interval inversions but came up empty.
    I have a question about recognizing interval inversions by intervallic distances. I will use G at the third fret on the E string and C at the third fret on the A string as examples. Going up from G to C is a perfect fourth. A perfect fourth is a distance of 5 semitones. So you count UP: G to G# (1) G# to A(2) A to A#(3) A# to B(4) and B to C (5).

    Now, if you then go from that same C back to the same G, you have an inverted interval, right? It should be a perfect fifth. (I use the short cut rule that all inversions add up to 9, perfects stay perfect, diminished stay diminished, major become minor and vice versa.) A perfect fifth is a distance of 7 semitones. So you count UP: C to C#(1) C# to D(2) D to D#(3) D# to E(4) E to F(5) F to F# (6) and F# to G (7)

    But wait, Why do you count UP? Should you not count DOWN, since that is the direction you are heading (A string to the E string) Thus: C to B(1) B to Bb(2) Bb to A(3) A to Ab(4) and Ab to G(5). So that gives us a distance of five semitones which is a perfect fourth.

    I know the correct answer is a prefert fifth, I just don't why the last senario isn't also correct. Maybe one of you college ed-u-macated folks can help up this self-teaching student.

  2. To calculate the inversion of an interval, use the following forumulas:

    new interval = 9 - original interval
    Perfect goes to Perfect
    Major goes to minor
    minor goes to Major
    Augmented goes to diminished
    diminished goes to augmented.

    So, the inversion of a Perfect 5th is a Perfect 4th. The inversion of a Major 3rd is a minor 6th. The inversion of a diminished 5th is an augmented 4th. etc ...

    For more info about the terminology, check out:

    - Dave
  3. Chris Fitzgerald

    Chris Fitzgerald Student of Life Staff Member Administrator

    Oct 19, 2000
    Louisville, KY
    Be prepared to do a big Homeresque "DOH!!!". All intervals can be inverted, but in order to invert them, the direction changes.....i.e. - to get the inversion of G UP to C, you need to go from G (this time as in the open 1st string) DOWN to C. Then you get your perfect 5th, or 7 semitones.

    The pattern behind interval inversions is easy to remember if you can retain a couple of pieces of info:

    Major intervals invert to minor intervals, and vice-versa.

    Perfect intervals invert to perfect intervals.

    The sum of the two intervals that are inversions of each other will always be "9". (except for the tritone, which can be explained in a number of ways). Sooo....

    mi2..... inverts to Ma7
    ma2.....inverts to mi7
    mi3......inverts to Ma6
    Ma3.....inverts to mi6
    P4.......inverts to P5
    Aug4...inverts to dim5 (but like I said, different folks think of this one in different ways).

    Hope that helps. I'd hate to think of all that edumacation goin' for nuthin'.
  4. yor123


    Mar 29, 2001
    New Orleans

    Thanks guys. I knew that you would come through. BTW Chris, I laughed out loud at you "luke666" thread. Funny stuff.

    Thanks again,

  5. Christopher


    Apr 28, 2000
    New York, NY
    I don't exactly follow your example. G up to C is an interval of a fourth. C back down to the same G is also a fourth, not a fifth, as you suggest. However, C UP to G (the G an octave above the aforementioned "same G") is a fifth.

    The point is that the polarity of the interval--for want of a better term---matters. CG is not the same interval as GC. When one refers to an inversion, one doesn't mean simply ascending from one note to the other and back down again to the same note.

    An inversion means inverting the relationship of the notes, ie. moving the lower note an octave above or the higher an octave below. Thus, if you invert GC to get CG, you are necessarily putting the G above the C; you *have* to count up from C. There's nothing left below.
  6. Chris Fitzgerald

    Chris Fitzgerald Student of Life Staff Member Administrator

    Oct 19, 2000
    Louisville, KY

    Maybe if Ah Had me one 'o them fancy powdered wigs, Ahd'a posted that sucker faster. Oh, well, two for the price of one...
  7. yor123


    Mar 29, 2001
    New Orleans
    So Christopher,

    My example was wrong then. Ascending to the C from the G IS a perfect fourth, and decending back to the same G IS still a perfect fourth, right?

    Your explaination of inverting by moving the lower note up an octave or the higher note down an octave makes perfect sense.

  8. Desdenova


    Feb 18, 2003
    Hampton, VA
    I have a question more about what the name of an interval implies, i.e. a six-four inversion or six inversion. All I have written down in my book is "Root" "^6-4 inversion", and ^6 inversion". Kinda hard to figure out various inverted seventh chords when I don't remember what the different inversions mean =O
  9. moley


    Sep 5, 2002
    Hampshire, UK
    No, ascending from G to C is a perfect 4th, and descending from the C back down to the G is still a perfect 4th.

    But I think that's what you meant, it was just a typo :)