We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
Not to worry. None of us is really capable of fully understanding Bach. His music speaks to the heart and mind in a way that is mysterious and timeless. Listening with attention is all that is required to hear it.
The Great Con....Symphony orchestra "conductors". All.Every bit of "conductor" leading or directing musicians is ludicrous. Kabuki theater for the naive.Musicians follow their sheet music or play by ear. Some combination. They sure as heck don't pay any attention to the bozo in front of them with his baton. It is a scam for the benefit of the dimwits , the pretenders in elite society. Jazz bands don't have a conductor. County music bands don't either. Why not? Because they are not needed. Bernstein Schmerstein. Have a clue!
I'm only a lightly-schooled musical amateur, but there are differences between playing with and without a conductor. A conductor can
1. Start everyone on time
2. Encourage the players to observe expression markings
3. Point at misbehaving players
4. Stop the group if things go wrong
5. Issue cues for players who don't keep count of measures
6. Try to control tempos
7. Explain what fermatas mean, and enforce them
8. Give advice to the poor chump who shows up with a 100-year-old horn but deserves first chair.
As the work of Pythagoras implied, every musical tone entails the notes that make up modern harmony and melody. Bach showed how it all fits together, exploring the far reaches of this insight. Many of Bach's discoveries were not mined until the Romantics and then Jazz.
Pythagoras, experimenting with the length of strings, found that the most pleasing musical relationships were formed from simple ratios, such as 3:2 (perfect fifth) and 4:3 (perfect fourth).
When a string vibrates, it doesn't typically vibrate in a simple manner, all at once as it were, but many different vibrations are superimposed, multiples of the primary vibration.
All of the pictured vibrations can occur on the same string, but are in a rational number relationship. The different amounts of each vibration creates the timbre of the instrument. For instance, a scratchy violin has more amplitude on the higher harmonics than does a sonorous flute.
On the first diagram, look at the musical notion below the string. When you sound a C-note on the string, the string will also sound the C an octave higher (2x frequency), and the G above that (3x frequency), the C above that (4x) above that and so on. From the fourth harmonic, you can see the basic C-E-G triad chord, which, it turns out, sounds as harmonics from a simple pluck of a single string.
The following diagram shows how three harmonics add up to a non-sinusoidal wave form. The ear hears the first harmonic, the fundamental, as the pitch or note, and the sum of the harmonics as the timbre.
If were to have two strings tuned, one to C and one to a harmonic of C, and plucked the C, then the harmonic string will also ring in sympathy. The closer they are harmonically, the more it will ring. If you press the damper pedal on a piano, lifting the dampers on all the strings, and strike a note, then not only will that string ring, but so will all the strings harmonic to the struck note. This creates a richer timbre than if you strike the same note without pressing the damper pedal which lifts the damper on only the struck string. If you divide a string exactly in the middle (such as on a guitar), it will sound the C one octave higher. If you divide it to a third of its length, it will sound the G above that. And so on.
This is the basis of chords, harmonic progression, and even melody (the upper harmonics of the fundamental note).