The purpose of 'the key'

[jazz oud]

Originally Posted by alez

I suppose it's kind of treating the key's 7th like it's done in minor: minor 7th on the signature, raise it for V7 (typically). From that perspective, the result has more similarity to a tonal approach than using a major signature.

Yes, except that the harmony in a blues is derived from tonal music, with the exception of the 7ths. So the way that we hear it is not modal, but tonal with altered 7ths. If a piece was really mixolydian or another mode (say something like "milestones"), then using the modal key signature might be appropriate.

Not to get into a big discussion, but the actual m7 interval in mixolydian is different from the one in the blues, which is based on African usage, so it really is not mixolydian. There are actually four distinct intervals that are equivalent to a m7 (the tuning differences between which are erased in equal temperament, but which our ears still infer to some degree based on context). So even though on a superficial level the blues seems similar to mixolydian, it really isn't. If you listen to older blues, jazz and gospel recordings, this difference is easily heard.
Essentially a real dominant chord has a 7th based on the difference between a stack of three 5ths (IV - I - V), while the blues has a 7th based on the overtone series 7th harmonic. The former is unstable and wants to resolve, the latter is stable.

[alez]

Originally Posted by jazz oud

Essentially a real dominant chord has a 7th based on the difference between a stack of three 5ths (IV - I - V), while the blues has a 7th based on the overtone series 7th harmonic. The former is unstable and wants to resolve, the latter is stable.

Nice one!

[Mariotte]

Originally Posted by jazz oud

Essentially a real dominant chord has a 7th based on the difference between a stack of three 5ths (IV - I - V)

jazz oud please can you explain what do you mean by that (I don't understand the operation).

[jazz oud]

Originally Posted by Mariotte

jazz oud please can you explain what do you mean by that (I don't understand the operation).

The 7th of a tonal dominant is the difference between scale degrees 4 and 5, with the 5th on the bottom.
So in the key of C, we have a stack of 3 5ths: F C G (this would be pretty stable), but it is inverted to put the G on the bottom and the F on the top. This becomes unstable, and strongly wants to resolve to the tonic C.

Western intervals can be derived from combinations of P5ths, M3rds, and their inversions. When discussing tuning systems, this is how most of the "ideal" intervals are calculated. Since there are in many instances more than one "ideal" interval depending on context and because changing keys causes an exponential increase in the number of ideal intervals, we have (mostly) settled on equal temperament for the majority of our purposes in western music (at least for fixed-pitch instruments like guitar and piano; voice, strings, horns, etc. have enough flexibility to accommodate the pure intervals in many cases, and in actual practice most western music is a combination of ET and Just Intonation adapted to whatever works best at any given time).

Equal Temperament can be thought of like an aural illusion that allows one particular interval to musically represent the function of a group of nearby intervals: our ears are forgiving enough to intuit the harmonic meaning even if the tuning is a little off.

The really neat trick is when the same interval changes meaning in the middle; much like a C#o7 chord can simultaneously represent viio7 in D minor and viio7 in F minor, thereby effecting a modulation by retroactively changing the meaning of what you just heard, intervals do the same thing all the time but in a much subtler way.

In the case of the "minor 7th", the four main instances are:
• the standard dominant m7, which occurs between the outer notes of an inverted stack of 5ths, most commonly on ii7 and V7 (ratio 16:9 or approx. 1.78)
• the other minor 7th (sometimes called the modal m7), which occurs when you go up two fifths and down a M3 (this one is higher than the dominant m7 and normally would occur on a vi chord that didn't have a secondary subdominant function (tonic vim7, rather than a vi7 that acts like a ii7), or in certain inverted chords; much more common as an interior interval rather than with the root (ratio 9:5 or 1.8). Some people claim to hear this on Mixolydian and some other modes, but I think it is debatable.
• the overtone 7th, which is lower than the standard m7 (this is the "blue 7th" from African and some other music-- ratio 7:4 or 1.75)
• the Augmented 6th, which comes from going up a M3, up two P5ths, and up another M3 (usually shown starting on the b6 degree: Ab C G D F# ratio 225:128 or approx. 1.76). Despite being called a 6th, it is slightly higher than the overtone 7th, but noticeably lower than the others.

When you look at how the music happens, context usually makes clear which of these we are supposed to "hear". Some contexts are ambiguous, and (some) composers exploit this to give a note multiple "meanings".

Some people will disagree that the above has any significance, but it is there to consider whether one finds it relevant or not.

[duane massey]

I tend to be a realist when I commit music to paper. The key signature I select is typically to make the musician reading the part have the least amount of confusion from the details. I will use modal key signatures when it makes sense, and standard major/minor key signatures when they make sense. One of our composers in town uses no key signatures, and his charts, although very well-crafted and sound, are a challenge to read because of all the accidentals. To make it even worse, there are no adjustments made for enharmonic spelling relative to the instruments, so (for example) the trumpet parts will have a figure with E#, F##, G##, A#, instead of F-G-A-Bb. Sheet music is a method of communication, and I am a firm believer in making it as readable (and natural) as possible.

[beeboss]

I really hate to see Fb's and Cb's (E sharps etc) and double sharps and flats on charts. It hurts my head, although one has to tolerate it in classical music often. Most stuff I write without a key sig because it is never in the same key for long enough to bother with key sig. Basically the clearest chart with the fewest possible accidentals is what I aim for. I think it is pretty common these days in the days of software score writing that people transpose parts from a concert score and then don't bother to proof read the parts to see if they make sense or could be written out in an easier way.

[Mariotte]

Originally Posted by jazz oud

The 7th of a tonal dominant is the difference between scale degrees 4 and 5, with the 5th on the bottom.
So in the key of C, we have a stack of 3 5ths: F C G (this would be pretty stable), but it is inverted to put the G on the bottom and the F on the top. This becomes unstable, and strongly wants to resolve to the tonic C.

I understand almost everything, but not this thing about "stacking" the intervals (I know about stacking intervals, i.e.: thirds to make chords, but I don't quite since to grasp what are you exactly doing there with them). Also I became confused with scale degree as I don't know if you are referencing the key or the chord (I think you are talking about key when you make that reference).


The 7th of a tonal dominant is the difference between scale degrees 4 and 5, with the 5th on the bottom.

the difference? It I sustract a perfect fourth from a perfecto fith I got a whole tone, don't I? I mean, if I ascend a fifh and then go down a fourth, I would be a whole tone away from the start point. So this is why I'm not following there. Obviously, you are refering other thing.

PS: I have understood parcially the part about the 3 fifh stacked, although there is no "c" in a G7 chord (and that was giving a hard time to understand). I guess the idea is that from g to f you have to ascend 2 P4, right? Mmm eitherway I get stuck about that implicit "c" in the stacking.

Ps2: thanks for the long explanation and sorry to bother you, but I was curious about this matter!

[engelbach]

Originally Posted by beeboss

I really hate to see Fb's and Cb's (E sharps etc) and double sharps and flats on charts. It hurts my head, although one has to tolerate it in classical music often. Most stuff I write without a key sig because it is never in the same key for long enough to bother with key sig. Basically the clearest chart with the fewest possible accidentals is what I aim for. I think it is pretty common these days in the days of software score writing that people transpose parts from a concert score and then don't bother to proof read the parts to see if they make sense or could be written out in an easier way.

Yes, no music software transposes for perfect clarity. It's always necessary to go through the transposition and make enharmonic changes by hand.

[jazz oud]

Originally Posted by Mariotte

The 7th of a tonal dominant is the difference between scale degrees 4 and 5, with the 5th on the bottom.

the difference? It I sustract a perfect fourth from a perfecto fith I got a whole tone, don't I? I mean, if I ascend a fifh and then go down a fourth, I would be a whole tone away from the start point. So this is why I'm not following there. Obviously, you are refering other thing.

A whole tone is the inversion of a minor 7th.

G7 occurs in the key of C.
If you go down a 5th from C, you get F.
If you go up a 5th from C, you get G.
If the F is on the bottom, G is a major 9th above.
If you invert the interval, putting the G on the bottom (as it is in a dominant 7th chord), you get a minor 7th.
The m7 interval is just the distance from scale degree 5 to scale degree 4 with the 5th on the bottom.

PS: I have understood parcially the part about the 3 fifh stacked, although there is no "c" in a G7 chord (and that was giving a hard time to understand). I guess the idea is that from g to f you have to ascend 2 P4, right? Mmm eitherway I get stuck about that implicit "c" in the stacking.

Hopefully my explanation above made it clearer, it's because G7 comes from the key of C. So both F and G are existing in relation to the tonic, C.

[jazz oud]

Originally Posted by engelbach

Yes, no music software transposes for perfect clarity. It's always necessary to go through the transposition and make enharmonic changes by hand.

People who let the software make choices about accidentals and rhythmic notation . . .

[Mariotte]

Ahhh there you go, I finally understand the process you where talking about, thank you for your patience

So, you were saying that this minor 7th interval, which is the essence of a dominant chord, and which is born from this stacked fifth's, is eager to resolve to the tonic, because of theese implicit fitfhs that naturally want to resolve in that direction?