I took theory in high school, kind of a long time ago, and since it was an adjunct to choir, they didn’t say much about things like suspensions (chords, not school) and modes and etc.
Now, I have started composing for the first time since my little band days back when, only this time on a PC keyboard/piano. I have a question:
If I have a melody in the key of C (major) that goes, BCGD, then a straight third harmony would be two and a half steps away, EFCG, right?
So, if I play FDAC as harmony, what relationship are those notes to the root of BCGD?
I agree with this, with the same disclaimer, except that a perfect 5th flattened by a semitone is technically known as a dminished 5th rather than a minor 5th. Someone once told me that the reason for this is too obscure to bother explaining as it does not really illuminate anything, but if anyone disagrees I’d like my curiosity satisfied! The same is true of 4ths and octaves.
…would be D (minor 3rd), E (major 3rd), B (major 3rd), F (minor 3rd).
A minor third is 3 half-steps (e.g. B, C, C#, D).
A major third is 4 half-steps (e.g C, C#, D, D#, E).
F is a diminished 5th from B.
D is a 2nd (2 half-steps) from C.
A is a 2nd from G.
C is a 2nd from D.
Does that answer your question? Using FDAC as harmony to BCGD would be unusual, to say the least. Once you have your melody line, you might want to work out a bass line next–that the usual thing: melody + bass, then the rest. YMMV, of course, this being art and not science.
And that diminished-5th might actually be an augmented fourth, depending on the context. If you drop a 4th a half step, you just get the major third but, theoretically, you could have a diminished fourth. An octave lowered by a half step is a major seventh. The rule I learned is that perfect intervals (unison, fourth, fifth, octave) can only get diminished or augmented; other intervals get major or minor. Now, I have never heard anyone refer to a diminished octave or diminished fourth, but wikipedia claims they exist. Wikipedia also has an entry for a diminished third, something else I have never heard of.
No matter how much theory I learn, there seems to be an infinite amount left to learn. If anyone has insight on diminished octaves or diminished thirds, or the reason for the nomenclature, I’d be interested, too.
It’s not hard to find diminished fourths or octaves: I’ve just picked up a Vivaldi score, not somewhere you’d expect to find bonkers harmonies, at found a C#m chord (acting as a dominant 7th in F minor) with a violin figuration rising through C#-E#-B then B-A-B as an auxillary note. Prior to equal temperament the distance, for a string player, between E# and A was not the same as F to A. There’s various points on the same page where a rising chromatic bass line gives diminished octaves between a note in an upper part and the bass of a subsequent chord.
Diminished thirds…I’ll have a think, but I’m sure I can come up with an example
OK. I follow the diminished fourths. But what exactly makes something a diminished octave as opposed to a major seventh? Are you saying, if we have a C2-C3 octave, then the C2 goes up to C#2, the space between the C#2 and C3 is formally a diminished octave rather than a major seventh?
As for diminished thirds, the only thing I could think of lowering an already minor third. edit: Oh, well, I guess that is it. Wikipedia says its enharmonic to a major second, so that makes perfect sense to me.
Probably the most likely place is when augmented sixth chords are “inverted” or arpeggiated.
Concerning interval names:
Perfect intervals (perfect unison, perf. fourth, perf. fifth, perf. octave and their octave compounds, elevenths, twelfths, etc.) become augmented or diminished when chromatically altered. That’s just the way of things. Unisons, fourths, fifths, octaves can never be major or minor.
Major and minor (as far as intervals go) only applies to 2nds, 3rds, 6ths, and 7ths (and their octave compounds, ninths, tenths, etc.).
I could see it being used with a chromatic descending bass and a chromatic ascending melody figure. I know I’ve played figures on the piano that start on the unison and the left hand breaks chromatically down and the right hand chromatically up. But, yeah, it’s not an everyday occurrence, or anything.
It (mostly) has to do with the way it’s written. B-double-flat, while the same as A, would be a diminished octave rather than a major 7th (or whatever scale degree it is). There’s also (technically) something called double augmented and double diminished, but good luck finding one. The point is mainly about staying in structure more than anything, you usually want your chord tones to be structured in “thirds” (I put it in quotes because the interval may not actually be a third, but the notes, without regards to pitch, that are written look like they are) regardless of whether or not it requires 6 flats to do so. This doesn’t matter in most music, in which each chord is usually a specific tone quality, but there is a nomenclature and progression difference between a 7th written as a 7th and a 7th written as an 8th with a flat (as far as I remember, at least).
B major, moves to G# major (first inversion), then C# major. The G# chord is acting as a new dominant taking us away from the key of B major. The bass ascends B-B#-C#, the B# being a diminished (compound) octave below the Bs which have been all over the upper parts in the B major harmony.
That it’s B# in the bass and not C natural is important not only for non-equal-temperament intonation as I mentioned above, but to visually indicate its role as leading note in C# major. It’s important that we have a way of describing intervals between notes which acknowledges that enharmonics such as this can impart particular information such as this.
Oh, right, the definition/identification of them rather than an example - the quick rules to remember as I teach them are:
(1) Count letter names. If it’s a D (flat, natural, sharp, whatever) up to a B (flat, natural, etc.), that’s DEFGAB, so it’s a sixth, of some kind.
(2) Going up a major scale from the lower note, you’ll have the major 2nd/3rd/6th/7th and the perfect 4ths and 5ths.
(3) Minor intervals are the major intervals narrowed by a semitone but retaining the same letter names (bear in mind that ‘major’ and ‘minor’ can mean large and small as well as referring to keys).
(4) Diminished < minor < major < augmented.
(5) Diminished < perfect < augmented.
As for examples, leafing through the Bach solo violin sonatas & partitas I can see a few, in just the role Knorf suggested.
There’s a Mozart piano sonata (I don’t remember which one) that has a theme and variations in A major. One of those variations is in A minor, and involves the opening C-B-A-B-A-D-E-D#-F-E-D-C. I’ve seen others, but that’s the one that springs to mind.
Duh! Of course, the most likely place for a diminished third is undoubtedly where you have motion from a raised fourth scale degree (tonicizing the dominant) to the diatonic sixth scale degree of a natural or harmonic minor scale (or vice versa)–just as the example above shows.
A Neapolitan Chord progression is another good example of where you might a see diminished third. The motion from the flat second scale degree to the leading tone gives you a diminished third. It’s often filled in chromatically, but not always.
Silly that these examples didn’t occur to me right away.
Thanks – the naming rules I knew, but I just hadn’t encountered the terms diminished octave, diminished fourth, and diminished third in context, and I wanted to be clear. After thinking about it, diminished third seemed self-explanatory (flattening a minor third), but the other two weren’t as immediate to me.
Well, yes, but picture it with a cello, and a soft violin descant.
But I think, seeing the relationships spelled out, that I understand. It is inconsistent to have all intervals of a second, & then one flatted fifth. (much as I like them!)
I finally had to abandon all hope of a descant anyway because the MIDI apparently didn’t like playing a nearly identical melody on two almost adjacent instruments. About halfway through, it started a drone note that was very pretty for a measure or two, but unfortunately lasted for the entire rest of the song.
My whole trip with the MIDI is I’ve challenged myself to see if I can make music that appeals to me on it. I always hated MIDI music (and hence, angelfire sites) because it sounds to me like those first whiny Casio keyboards that people had. Cheesy electronic “music simulation.”
One day, I had a song come to me in the shower that I just had to try and realize, & my PC was all I had.
Since then, I’ve found that MIDI can produce some limited coolness if you use instruments for other than their intended purpose/ range. Also, that I can too play drums, by proxy.
It’s worth remembering that ‘MIDI’ actually refers to a way instruments and computers communicate with each other, not directly to the software/hardware/samples then used to create sounds. To demonstrate the point, these demos are MIDI-produced.
However, it’s true that you can squeeze some interesting sounds out of poor synthesizers if you’re creative. However, my advice is to be aware that you’re dependent on your hardware. I wrote a piece years ago that only sounded good on my computer’s crappy built-in general MIDI synth. I still have the MIDI file, but the computer’s long gone and I consider that piece lost.
