Yet another ignorant question - Keys

[Grazioso]

I'm afraid I have the same problem.  Am I listening for these chords from a specific instrument?

The chords are heard in all the instruments and vocals together--except the drums --but probably most easily on the rhythm guitar strumming the complete chords itself throughout the tune, and the bass emphasizing the root and 5th of each chord, such as the C and G of the C chords (notes=CEG).

Don't sweat trying to tell by ear what precisely the chords are, just that they're shifting. That's the important first step.

This might help:

http://www.youtube.com/v/Q3qlIdIB80w

Here's another by the same teacher for a song with a more involved melody and chords, which might make it more clear how the chords work with a shifting melody:

http://www.youtube.com/v/9DgpDqXtee4

Every time his fretting hand is shifting shapes during his performance at the beginning, you're hearing a chord change. (The single fingers moving up and down are just for embellishments.)

[71 dB]

In fugues the comes imitatates the dux (usually) fifth higher. So, in C major:

C => G
D => A
E => B
F => C
G => D
A => E
B => F???

The last one is a problem for me. A melody in C major scale "should" become a melody in G major scale (G A B C D E F#) when rised a fifth! But the fugue is in C major and we don't want key changes, at least not yet. How is this problem solved?

1) The resulting F# notes are "rounded" into F notes? Some of the intervals of dux and comes melodies are different.

2) We "allow" these F# notes, the possible dissonanses it causes in C major and we accept that we have a chromatic 8-note scale (C D E F F# G A B)?

3) We simply don't use B notes in dux?

[petrarch]

As long as the notes making up those intervals do not sound simultaneously or leave them as passing notes everything should be ok).

Check this out:

http://www.teoria.com/articulos/analysis/BWV846/index.htm

Take a look at the score and note the use of F# right on the 3rd measure and onwards, soon to be joined by other non-C major notes in the 8th measure.

[jochanaan]

In fugues the comes imitatates the dux (usually) fifth higher...

Usually a fifth, but often a fourth; think JSB's famous Toccata and Fugue in D minor.  And then the second comes is most often in the tonic.  No question of following the circle of fifths.  (One notable exception is the first movement of Bartok's Music for Strings, Percussion and Celesta, whose fugal entries follow the entire circle of fifths. )

[71 dB]

As long as the notes making up those intervals do not sound simultaneously or leave them as passing notes everything should be ok).

Check this out:

http://www.teoria.com/articulos/analysis/BWV846/index.htm

Take a look at the score and note the use of F# right on the 3rd measure and onwards, soon to be joined by other non-C major notes in the 8th measure.

Thanks for the link. I'm not good at reading notes so I need some free time to study that score 

Anyway, if I am correct, the 14 notes of subject are C D E F G F E A D G G A G F E. This indicates that there might be something in my "theory" #3 since there is not note B used.

Usually a fifth, but often a fourth; think JSB's famous Toccata and Fugue in D minor.  And then the second comes is most often in the tonic.  No question of following the circle of fifths.  (One notable exception is the first movement of Bartok's Music for Strings, Percussion and Celesta, whose fugal entries follow the entire circle of fifths. )

Yes I know but I kept things simple. My question remains: How is potential chromatism handled?

Wikipedia says: To make the music run smoothly, it [comes] may also have to be altered slightly. When the answer is an exact copy of the subject to the dominant, it is classified as a real answer; if it has to be altered in any way it is a tonal answer. A tonal answer is usually called for when the subject begins with a prominent dominant note, or where there is a prominent dominant note very close to the beginning of the subject. To prevent an undermining of the music's sense of key, this note is transposed up a fourth to the tonic rather than up a fifth to the supertonic. Answers in the subdominant are also employed for the same reason.

This teaches me a lot. There is much musical logic in this. Comes can be altered slightly if needed. So, if there is/are B note(s) in C major Fugue subject, the answer can be "purified" to avoid unwanted chromatic F# notes.

[Grazioso]

Proof that Bach really does sound like math 

[jochanaan]

Proof that Bach really does sound like math 

On the contrary: proof that Bach sounds like great music rather than strict math.

[Grazioso]

On the contrary: proof that Bach sounds like great music rather than strict math.

Seriously, it's interesting that when Bach is criticized as stuffy or boring, you often hear the criticism couched as "It sounds like math." But when you pay attention to and study music, instead of just being swept along emotionally, you can't help but perceive complexly interweaved patterns, intervals, ratios, and sequences. (It's no coincidence that the medieval quadrivium brought together the academic study of music with arithmetic, astronomy, and geometry.)

Bach is interesting in that, to my ears, he forefronts that side of music and shows the beauty inherent in. It's like getting to hear the harmony of the spheres 

Pythagoras is in the house! 

[71 dB]

This is what I think about math and music:

- In the end harmony IS math since it's about the degree of consonance and dissonance (mathematical rations between the frequencies of notes).

- Rhythm is also based on math because it is about how (musical) events are distributed over time frames.

- Melody is much less mathematical structure in music but since it is coupled with rhythmical and harmonic dimensions of music, even it isn't free of math. 

[Grazioso]

This is what I think about math and music:

- In the end harmony IS math since it's about the degree of consonance and dissonance (mathematical rations between the frequencies of notes).

- Rhythm is also based on math because it is about how (musical) events are distributed over time frames.

- Melody is much less mathematical structure in music but since it is coupled with rhythmical and harmonic dimensions of music, even it isn't free of math. 

Even melody can be described numerically as scale degrees and intervalic leaps. And there are the patterns of scalar melody sequences that mark baroque music. Look at, e.g., a solo arrangement of "Jesu, Joy of Man's Desiring", aka "How to Run Pleasantly Up and Down the G Major Scale" 

[North Star]

All music is about mathematical ratios between different pitches. Bach is just more obviously 'math' because the relations are more obvious compared to the classicists, the romantics or modern composers - like school math compared to university math, or simple geometric shapes compared to fractals in nature.