New series of blog articles about music theory

[dinaiz]

I'm trying to write a kind of "music theory for dummies" blog post series. There are only 4 articles in it, but it's a work in progress.
You can check it out here : http://www.springbeats.com/node/14

Any kind of feedback really appreciated.

[arkmabat]

What a neat way to remember intervals!

[jancivil]

"If I play G# then C, I will play a descending minor sixth."

No, any G [downwards] to any C is [some type of] a fifth. That is an augmented fifth. (Ab down to C is that minor sixth.) C to Gb is a diminished fifth.
So, if you were to write 'C [up] to A# is a minor seventh', you'd be committing the same error; that's an augmented sixth. Etc.
The letter name the determinant of the interval, regardless of quality.

Also as to the conversational 'they did this to confuse us', I'd suggest to lose that and show the not-really-confusing facts of it. With a perfect quality interval {8ve, 5th, 4th} by default, raising/lowering a semitone is now augmented or diminished quality; the 2nd, 3rd, 6th and 7th have two default qualities, minor and major. Extending the size of these by the semitone gives diminished and augmented, resepectively.

[JumpingJackFlash]

Some further errors from additional pages:
"All the major scales are like this. They have a root (here it's C) and from the root, they follow the interval sequence from above..."

You mean tonic here rather than root.

"The definition of a chord is a chord is a stack of 3 or more thirds played simultaneously or in a short sequence (think arpeggios or strumming)"

No, that really isn't the definition of a chord at all.

"If the 3rd is major, the chors will be called a major chord. If it's minor...well you can guess !"

Except if it's augmented or diminished... (Also see the typo in there)

"The third and last note is a 5th away from the root."

Probably best not to call this the "third" note, for obvious reasons.

"Dominant 7th - Diabolus in Musica"

The "Diabolus in Musica" refers specifically to the tritone, not to the Dominant Seventh itself.

"I won't dwelve on that topic."

nice word!

[MadBrain]

Right. Aside from the #4/b5, augmented/diminished intervals exist only in writing, so they are rare because the "common" equivalent is almost always more correct (and easier to read). But they do exist in writing! Here's the ones I can think of, on the top of my head:

Augmented 2nd (minor 3rd)
- Shown as a "#9" in Jazz chord symbols, part of 7#9, alt7 and sometimes 7b9 chords.
If this note appears in a melody part, it will often be written as a minor 3rd.

Diminished 4th (major 3rd)
- Used in some transcriptions of the Arabic Saba Maqam (1 b2 b3 b4 5 b6 b7).

Augmented 4th/Diminished 5th (tritone)
- If it appears with a 5th, use a #4. If it appears with a 4th, use a b5.
- Most major contexts use a #4, especially the lydian mode: 1 2 3 #4 5 6 7.
Exceptions: 7b5 can appear in Jazz chords (equivalent to 7#11).
- Most minor contexts use a b5, especially the locrian mode: 1 b2 b3 4 b5 b6 b7.
Exceptions: minor lydian modes use a #4
(Nawa athar/Hungarian Gypsy, Gypsy Minor, Ukrainian Dorian/Nikriz, Todi)
- Classical music uses #4 upwards (4 #4 5) and b5 downwards (5 b5 4).
Jazz seems to prefer #4 in both directions (5 #4 4).

Augmented 5th (minor 6th)
- Used in augmented chords (aug/+/7#5/alt7/maj7#5).

Augmented 6th (minor 7th)
- Used in classical music chords: the #6 is preferred to the b7 since it resolves upwards.
- Equivalent to bVI7 in Jazz.

Diminished 7th (major 6th)
- Used in diminished chords (dim7).
- Often spelled with enharmonic equivalents to use less flats and double flats:
Ddim7 is D F Ab Cb in theory, but D F Ab B is easier to read.

[jancivil]

Right. Aside from the #4/b5, augmented/diminished intervals exist only in writing

I'm unsure of what that is supposed to indicate.

An augmented sixth chord for instance, is a real thing. The whole idea of it is augmenting the interval, 'sixth'.
For example, in A minor, your iv6 chord {f a d} is taken to augment f to d: f - d#. This is done for the voice-leading potential. f and d# in contrary motion to octave e, for one thing (forming a type of secondary dominant, to V). So, the idea is not a minor seventh. In this case, spelling it right is conveying it right.

If you're spelling a scale in a row, surely you want it to be alphabetical in a row rather than any avoidable duplication of a letter name. So every seven-note scale should in all likelihood be seven letters. An octatonic scale means a duplication of one of them, and the meaningfulness of that preference may well belong with a harmony it is chosen to decorate. G7 type chord, G Ab Bb B C# D E F; or A# may mean a #9 to you. Db may mean a b5.

I don't think I'd advise that 'jazz seems to prefer #4 either way'. The whole 'flat five substitution principle' is significant and appears to bely that. I haven't noticed anything different than 'classical' type principle #4 up to 5, b5 down to 4 in linear writing. I don't think it's all that important, not to everyone. I remember Zappa telling Tommy Mars what to do in Baby Snakes, 'that flat five up to five thing, you know', where I would call it a sharp four, but no one is confused by that.

[fmr]

I remember Zappa telling Tommy Mars what to do in Baby Snakes, 'that flat five up to five thing, you know', where I would call it a sharp four, but no one is confused by that.

Nobody would be confused, but that is incorrect, nevertheless. If the note is going to raise, then it should be an F#, not a Gb, because a Gb is always supposed to go down. It's so natural that someone reading at first sight, when see an alteration with a sharp immediately prepares to go up, while when see an alteration with a flat, expects always to go down.

[jancivil]

Typical lingo for jazz players is 'that flat five'. That comment kind of helps MadBrain's 'exist only in writing' for me. Nobody's reading, he's inventing what to do in realtime.
If that's what pops up in his mind to tell Mars, that's what it is. Cf., 'This was your Mott the Hoople extravaganza.'

[MadBrain]

Right. Aside from the #4/b5, augmented/diminished intervals exist only in writing

I'm unsure of what that is supposed to indicate.

It's just like how "x" or "q" are not real sounds in English (since "x" is really just "ks" or "gz", and "q" never really existed in any European language and is just a strange way to spell "k"), or how "h" is not a real sound in French. You will never find a real "q" (as opposed to a "k") in the mouth or ears of any speaker, it only exists once you write words on paper.

Likewise, there's no such sound as a #6 independent from a b7 in equal temperament. It will never show up on any spectrogram. Guitar necks have one 10th fret, not two. The difference only exists once you write down a part on paper.

An augmented sixth chord for instance, is a real thing. The whole idea of it is augmenting the interval, 'sixth'.
For example, in A minor, your iv6 chord {f a d} is taken to augment f to d: f - d#. This is done for the voice-leading potential. f and d# in contrary motion to octave e, for one thing (forming a type of secondary dominant, to V). So, the idea is not a minor seventh. In this case, spelling it right is conveying it right.

It's still a 7th chord, the only difference is that the 7th resolves upwards instead as downwards. I guess writing it as a #6 emphasizes the way it resolves, and groups it with other chromatic dissonances going upwards and basically the whole D/F, F7, E7 motion (which is more important in classical music, since it has all sorts of strange chromatic progressions in which individual chords often don't make any sense).

And writing it as F7 instead emphasizes the color of the chord itself, how it can be replaced by other 7th chords like F9, F7#11, F13, F7#5 (also, it can resolve downwards in Jazz).

If you're spelling a scale in a row, surely you want it to be alphabetical in a row rather than any avoidable duplication of a letter name. So every seven-note scale should in all likelihood be seven letters. An octatonic scale means a duplication of one of them, and the meaningfulness of that preference may well belong with a harmony it is chosen to decorate. G7 type chord, G Ab Bb B C# D E F; or A# may mean a #9 to you. Db may mean a b5.

I don't think I'd advise that 'jazz seems to prefer #4 either way'. The whole 'flat five substitution principle' is significant and appears to bely that. I haven't noticed anything different than 'classical' type principle #4 up to 5, b5 down to 4 in linear writing. I don't think it's all that important, not to everyone. I remember Zappa telling Tommy Mars what to do in Baby Snakes, 'that flat five up to five thing, you know', where I would call it a sharp four, but no one is confused by that.

Looked at some parts in a real book to check (specifically the case of a blues scale tritone) and guess I'm wrong on this, it can go either way (and seems to follow mostly if the next note is up or down). Actually the whole figure (#4/b5 not conditioned by a chord so it's ambivalent between the two possibilities) is way less common than I expected.

[jancivil]

An augmented sixth chord for instance, is a real thing. The whole idea of it is augmenting the interval, 'sixth'.
For example, in A minor, your iv6 chord {f a d} is taken to augment f to d: f - d#. This is done for the voice-leading potential. f and d# in contrary motion to octave e, for one thing (forming a type of secondary dominant, to V). So, the idea is not a minor seventh. In this case, spelling it right is conveying it right.

It's still a 7th chord, the only difference is that the 7th resolves upwards instead as downwards. I guess writing it as a #6 emphasizes the way it resolves, and groups it with other chromatic dissonances going upwards and basically the whole D/F, F7, E7 motion (which is more important in classical music, since it has all sorts of strange chromatic progressions in which individual chords often don't make any sense).

And writing it as F7 instead emphasizes the color of the chord itself, how it can be replaced by other 7th chords like F9, F7#11, F13, F7#5 (also, it can resolve downwards in Jazz).

I don't know which items don't make sense. The idea 'augmented sixth' is 'augmented sixth'. It isn't about that.
It is a specific move. This idea is what is taught. It makes sense to teach it this way, because that is the coherent thing to do.

As the 'Tristan chord', Wagner Tristan und Isolde it's this:



That is known as augmented sixth chord. Note here the tune, A up to F suggesting the iv harmony.
Sometimes simply taught as eg., F D# moves out to octave dominant but the rest of the chord isn't sufficiently explained. I always taught it as iv6, augment the sixth.
F A D# is Italian; F A C D# is German; F A B D# is French. Tristan chord is French and the strong appoggiatura G# gives the sonority of a half-diminished; but it functions as secondary dominant. It is possible that Wagner was interested in that sonority and then subverting expectation. Some people do think so and call it both of these things. It was a bit avant-garde to come out with that one, though. The Tristan chord is significant in chromatic harmony class because of the particular voice-leading, NB. the appoggiatura...

But! When you argue 'only exists as written' because 'equal temperament', you're assuming every instrument forces this restriction. In an earlier post I pointed out people discussing this, vis a vis Wagner and these type of harmonies. During the time Tristan appeared, musicians appear to have been more interested in intoning things for effect. It sounds to a lot of people to be Fø7 but then 'what is that?' F7b5 to E7#11. I might intone F/D# to E/E with a pronounced sharpening of D# at least. D# to D here; it may seem jazzy. I wonder if flat five substitution begins here, actually. Check it out, B D# F A.

I don't think I'd advise that 'jazz seems to prefer #4 either way'. The whole 'flat five substitution principle' is significant and appears to bely that.

Actually the whole figure (#4/b5 not conditioned by a chord so it's ambivalent between the two possibilities.

If it's a b5 chord there is no P5. The idea is it's a flat five chord. The idea of 'flat five substitution principle' is to obtain chromaticism by making a dominant 7th chord multivalent. Dm7, Db7b5 (G7b5), Cm, Cb7b5 (F7b5), Bb etc.

[fmr]

As the 'Tristan chord', Wagner Tristan und Isolde it's this:



That is known as augmented sixth chord. Note here the tune, A up to F suggesting the iv harmony.
Sometimes simply taught as eg., F D# moves out to octave dominant but the rest of the chord isn't sufficiently explained. I always taught it as iv6, augment the sixth.
F A D# is Italian; F A C D# is German; F A B D# is French. Tristan chord is French and the strong appoggiatura G# gives the sonority of a half-diminished; but it functions as secondary dominant. It is possible that Wagner was interested in that sonority and then subverting expectation. Some people do think so and call it both of these things. It was a bit avant-garde to come out with that one, though. The Tristan chord is significant in chromatic harmony class because of the particular voice-leading, NB. the appoggiatura...

But! When you argue 'only exists as written' because 'equal temperament', you're assuming every instrument forces this restriction. In an earlier post I pointed out people discussing this, vis a vis Wagner and these type of harmonies. During the time Tristan appeared, musicians appear to have been more interested in intoning things for effect. It sounds to a lot of people to be Fø7 but then 'what is that?' F7b5 to E7#11. I might intone F/D# to E/E with a pronounced sharpening of D# at least. D# to D here; it may seem jazzy. I wonder if flat five substitution begins here, actually. Check it out, B D# F A.

I don't think I'd advise that 'jazz seems to prefer #4 either way'. The whole 'flat five substitution principle' is significant and appears to bely that.

Actually the whole figure (#4/b5 not conditioned by a chord so it's ambivalent between the two possibilities.

If it's a b5 chord there is no P5. The idea is it's a flat five chord. The idea of 'flat five substitution principle' is to obtain chromaticism by making a dominant 7th chord multivalent. Dm7, Db7b5 (G7b5), Cm, Cb7b5 (F7b5), Bb etc.

Yes, an augmented sixth is an augmented sixth, because the voice leading will make it an augmented sixth, not just because of the writing. The late romantic period has almost as much polyphonic treatment as Bach. They had a very rich and deep harmony, but that is also dressed up with very careful voice leading, especially in the orchestra - it's not just a matter of piling chords, but of treating each voice of the chord as an entity. That's why the note names were/are so important, and why they used double flats and double sharps also. Each note has to have it's justification, and it's also a matter of showing (by the composer) that he actually knew what he was doing, and what he wanted.

Regarding the b5, that's one of those things that I always found strange. Either the b5 is a real note (i.e. it belongs to a new tonality we are modulating into, and in that case, we are talking of a tonality full of flats - D flat Major, at least) or it is a chromaticism, a passing alteration, and in that case it is silly to give it the importance of changing the name of the chord - passing notes are just that, they don't belong to the harmony. Question is: Does it come from G to G flat? Will it go to F? Or is it there just because it adds colour to the music?

[BERFAB]

I like the series. Solid work, though it's hard for me to judge just how much a newbie would grasp. Seems about right though.

I had one organizational suggestion. I had to hunt and peck a bit to find all the articles in the series. And even then, I wasn't sure if the articles were meant to be read in any particular order.

Creating permanent side-bar links in chronological order to your past articles would make this much easier to navigate.

Nice work.

Cheers
-B

[jancivil]

Regarding the b5, that's one of those things that I always found strange. Either the b5 is a real note (i.e. it belongs to a new tonality we are modulating into, and in that case, we are talking of a tonality full of flats - D flat Major, at least) or it is a chromaticism, a passing alteration, and in that case it is silly to give it the importance of changing the name of the chord - passing notes are just that, they don't belong to the harmony. Question is: Does it come from G to G flat? Will it go to F? Or is it there just because it adds colour to the music?

G flat in a C7 does not 'come from' G per se. It is a way to make bII7 and V7 the same, functionally. C E Gb Bb; Gb Bb 'C' 'E'. Voicing aside, the bass player may well play Gb on the C7 chord and basically everybody knows what the deal is. It's all about function. Typically there, yes it goes to F in terms of voice leading and in terms of root if the move is to F. But, what this does is open up possiblities. Gb7 is dominant to F, C7 dominant to B.

It is not a passing anything, as I said 'the idea is flat five'. I don't know why 'belonging to key' or not means it's real or not real.
In the Tristan chord, does D# belong to A minor? It's not any passing tone, you granted the term 'Augmented sixth chord'. It's the same argument. Insisting the G natural is what's real will be the same as getting rid of modulating diminished sevenths {borrowed from minor in major usage} etc.

[jancivil]

As what Tristan chord does, it's secondary dominant to V7. So spell it B D# F A, there is your flat five!

[fmr]

As what Tristan chord does, it's secondary dominant to V7. So spell it B D# F A, there is your flat five!

What made this passage revolutionary is the chromaticism, and the unexpected resolutions of the voices. Tristan is full of things like this. That's why it is regarded as the beginning of the end of tonality.