Question on inversion of intervals

[pianoplayjl]

What is the inversion of a diminished 8ve?

Thanks, JL

[p2u_]

What is the inversion of a diminished 8ve?

That will be an augmented unison or augmented prime.

Paul

[iratior]

Agreed.  An augmented unison typically occurs when the leading tone of one minor melody goes up to the tonic while another melody is going down the minor scale.  For example, you might have one melody with whole notes B# and C#, while the other melody has quarter notes B, A, G#, F#, followed by whole note E.  Play them together and the B-B# combination gives you an augmented unison.

[keyofc]

Just wondering - when would you really need to know this for practical use?
If I look at C and going up to a B -
a major 7th - how does it help me in thinking of this as a diminished 8th
instead of a CMajor 7th chord  - other than a theory test?

[nystul]

Just wondering - when would you really need to know this for practical use?
If I look at C and going up to a B -
a major 7th - how does it help me in thinking of this as a diminished 8th
instead of a CMajor 7th chord  - other than a theory test?

If the key is C# minor, then the leading tone would not be C.  It would be B#.  Say a V-I cadence in C# minor would be G#7 going to C#m.  G#7 would have G#, B#, D#, F#.

This choice of key is making it more complicated than it really is.  So let's say it's C minor.  G7 has a B, not a Cb.  Easy enough.  So when we have a V-I cadence, you get the note B going to C.  If this were, say, a choral piece from England in the 1500s, the cadence would also have this raised B going to C.  But maybe another singer has a line that is going down through B and ending on the G of what we would now call the I chord.  In that time period, that singer's B might actually be a Bb.  Which sounds really dissonant, but that's OK because it's resolving to this beautiful C chord.

In a case like that, you end up with this false relation.  It doesn't make any sense in that case to call the B a Cb.  It doesn't make any sense to call the Bb an A#.  So what you have is a diminished octave or augmented octave or unison.