Well, regardless of inversion used, accidentals used or quality, intervals sounded simultaneously are harmonic. In my thinking, it simply means they create a harmony- like a triad missing a note. If the notes are sounded independently, they’re melodic. No big deal. And I still submit (it really doesn’t matter), that the perfect prime is a unique entity separate from all other perfect intervals. Since a perfect prime is a specific pitch (say, C4) in an ‘intervallic’ relationship with itself (C4) the size of the interval is 0. It cannot be made smaller than itself- at least in any real-world common practice era sense. If I write C4- Cb4, I have made the prime interval bigger, not smaller.
Understanding music theory is important, but a great depth of understanding- such as the minutiae we’ve been discussing here- isn’t necessary to compose meaningful music. Christian at Spitfire Audio is an astounding example.
All those intervals follow the rule. An augmented unison inverts to a diminished octave, and a diminished 2nd inverts to an augmented 7th.
Michael is correct here. When inverted:
Major becomes minor
Minor becomes major
Perfect remains perfect
Diminished becomes augmented, and,
Augmented becomes diminished.
And, if an interval is inverted correctly (i.e., F4 up to G4 then G4 up to F5) we have a major 2nd and a minor 7th. 2+7=9- and an octave between the 2 Fs. This ‘formula’ is true of any interval and its inversion. Michael’s example of a diminished 2nd (say C4-Dbb4) is a diminished 2nd; when inverted, it becomes Dbb4-C5- an augmented 7th. 2 + 7 =9, and we have an octave between the 2 Cs. A minor 3rd (G4-Bb4) when inverted, becomes a Major 6th (Bb4-G5). 3 + 6 = 9, and we have an octave between the 2 Gs.
I’m a bit puzzled by this. If I move from C down to Cb, I would call it an Augmented Unison. (I realize this is the contentious issue.) Inverting it, that is, taking the lower sounding pitch and raising it an octave, the C up to Cb is a Dim Octave - in my nomenclature, aug inverts to dim. So far, so good. But if I take that original interval, and call it a Dim unison (C down to Cb), how is C up to Cb an Aug Octave? - it’s clearly a Dim Octave ( we agree on that, yes?)
You are correct. That’s why the perfect prime (unison), being in intervallic relationship with its self, and therefore having an interval size of 0, cannot be diminished- only augmented. C-Cb is not a diminished prime unison. It’s an augmented one. That is why the inversion of say middle C to the Cb above it is, as you said, a diminished octave. The perfect prime unison is a unique duck.
Yes, you are quite correct. Thank you for bringing that to my attention. They are a diminished unison and an augmented unison respectively. I was in such a hurry to get some much-needed sleep that I didn’t stop to check that what I had written was what I intended.
One detail I omitted was that I took the notes on the lower staff to be the reference note when determining the “interval from one note to another” (which is not identical in meaning to the “distance between two notes”).
I hope this clarifies the answers I gave.
No problem. I certainly mean no offense. One could spend half a semester of college theory in intervals, their inversions, and what to call them. All that matters is what we create with them- regardless of what we call them😉
Agreed.
I remember that a tutor at university once asked me to name the chord formed by the notes C, E and A♭. My answer, which he rejected, was C augmented. His correct answer was A♭ augmented, first inversion. It all depends on how it is written as to how one determines the theoretical root note of a chord. Same sound, different spelling.
I taught college theory for 10 years. Augmented triads are odd things. Sound wise, there is no difference in an augmented triad and its 1st, 2nd or 3rd inversion. Augmented triads are composed entirely of major 3rds. I suspect the reason he rejected your answer is that, strictly speaking, E-Ab is a diminished 4th. Sounds like a major 3rd, though😉
That’s more or less exactly what he said.
In your example, you made the interval bigger by flatting the D, thus augmenting the size of the interval. I think of it this way: whatever accidental I add to EITHER note of an interval either makes that interval bigger (augmented), or smaller (diminished)- speaking here of P4, P5, and P8. (PU is an exception). The accidentals used to accomplish this are whichever ones are needed to create the new interval. For example, F4- C5 is a Perfect 5th. If I write F#4-C5, I’ve made the interval smaller- diminished- even though I used a sharp. If I write Fb4- C5, I’ve made the interval bigger- augmented- even though I used a flat. Ahhh! Why do we need intervals and inversions anyway? But, we do😉
I remember that a tutor at university once asked me to name the chord formed by the notes C, E and A♭. My answer, which he rejected, was C augmented. His correct answer was A♭ augmented, first inversion. It all depends on how it is written as to how one determines the theoretical root note of a chord. Same sound, different spelling.
Your professor was correct. However, if he had played it, and asked for identification, there would be no way to tell the difference between a root/first/second inversion Aug triad. Funny little guys, yes?
As I found out!
Indeed they are🙃
But a diminished octave inverts to diminished unison, not augmented. And an augmented octave inverts to an augmented unison, not diminished - both up and down:
And in addition to that, a fixed number from the full list of intervals are equal in one sense (enharmonically) but opposite in the context of consonance-dissonance, and their inversions will preserve this paradox. So the aug 7 is a dissonance that’s exactly the same as a consonance, either directly or as a product of inversion. So are the dim 2, aug 3, aug 7 and a couple more.
It’s clear why it is happening, but all of this creates a situation where you have to either discriminate between intervals in some way or you accept all of them as valid building blocks specifically for the purpose of chord creation (not analysis of a written chord), which really makes no sense:
Of course these are basic and so the issue is obvious, but as the complexity grows in tonal music (especially with modes and dissonance), the question of organizing principle is not as trivial as it might first seem.
No. A diminished octave inverts to an augmented unison.
An augmented octave is greater than an octave and therefore counts as a compound interval: an octave plus an augmented unison. Its inversion is thus the same as the inversion of an augmented unison: a diminished octave.
A perfect prime (unison) cannot be diminished. It is in an intervallic relationship with itself (ex., C4-C4). The interval ‘distance’ is 0, and cannot be diminished. Even as a melodi interval, the diminished prime does not exist. Melodically, say, C4-Cb4 is in the melody. The Cb is simply a chromatic half step. In commom practice theory, you can’t make what is, in effect, an interval of a perfect 0 (which a prime unison’s interval relationship is with itself) smaller. It can only be made bigger- augmented. C4-Cb4 is not diminished because C4-Cb4 is not a smaller interval than C4-C4. The perfect prime is unique among intervals🙃
Diminished octave. Inverting down and up.
Augmented octave. Inverting down and back up.
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I know I should not believe my lying eyes, but this doesn’t look diminished:
Nor does this look very augmented:
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I remember you said earlier that in your opinion augmented can be ascending or descending. That’s certainly very creative, but it’s too confusing for a dummy like me: it makes me feel like up is down and black is white.
In my opinion, the question of diminished unison is a totally artificial problem, it only exists in one context - where does the counting start from. But it becomes a non-issue as soon as the unison is conceptualized as a center rather than a beginning.
I find it’s not at all different from the idea of all tonal music - the tonic, like a unison, is likewise a center, with D and S (and mediant and submediant) at right and left of it (or up and down). This harmonic or intervallic “oscillation” relative to the tonic or a unison is not unlike a vibrating string analogy (or the knob for stereo balance) and it makes a lot of things simpler and more intuitive.
Anyway, I’ve actually learned something here and it’s been a very enlightening thread. Thank you.
You are teriffic🙂
You’ve just shown a diminished octave inverting to an augmented unison.
That’s not an inversion. The point here is that the interval to be inverted is greater than an octave. To invert intervals greater than an octave, you need to move one note by enough octaves so that the note that was originally higher becomes the bottom note. To achieve that in this case, you need to transpose the D-sharp down two octaves. Or the D-natural up two octaves. The essential thing is this: in the original interval, the D-sharp is above the D-natural, so in the inversion the D-natural must be above the D-sharp.
See the Wikipedia article on intervals, notably the quote from Ebenezer Prout: “the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded.”
They are both augmented. Once more: “augment” has nothing to do with “raise”. It means “make 1/2 step wider”.