A childish question about music theory!
This question is anything but childish. Musical theorists have debated it and related questions for millennia. The more I've browsed the internet trying to understand it the more questions I have. I certainly haven't yet found a simple, clear explanation. I wonder whether any such thing is possible! However, I'll try to summarise where I've got to and some of the questions I have.
Theorising about scales in the western world may have started with Pythagoras who is said to have realised that two notes sound well together if there is a simple arithmetical relationship between their frequencies. The most obvious relationship is what we call the octave: two notes where the frequency of one is double that of the other (ratio is 2:1). In a perfect 5th (G above C for example) the ratio is 3:2. Many of these ratios are heard in the overtones that arise whenever a string is struck or the air in a tube is caused to vibrate: there will be waves of the length of the string or tube which can be heard as the fundamental note, waves of half the length (double the frequency) which sound an octave higher, one third the length (triple frequency) which sound a 5th above the octave, and so on.
An octave is obviously fundamental but how should it be divided? Because the interval of a 5th is so simple and harmonious the "cycle of 5ths" provides one way to devise a scale, giving C, G, D, A and so on up to B flat then F and then .... unfortunately, because of the way the arithmetic works, the 13th note in the sequence is a fraction above C. Therefore, any system of tuning that uses the cycle of 5ths involves compromise: one or more of the intervals between consecutive notes has to be adjusted slightly. I have read about various systems of temperament: for example "just temperament" and "well temperament" (of which I think there are variants according to how many intervals are adjusted and which ones). I haven't tried to understand the differences.
I think that the difference between C sharp and D flat illustrates the need for compromise: C sharp is the note that would be reached by working up in perfect 5ths from C (or any other starting point) whereas working downwards from C to F to B flat and so on would arrive at D flat. In the same way that working up the cycle of 5ths from C arrives at not-quite-C, working up to C sharp is not quite the same as D flat.
The fact that it takes 12 steps in the cycle of 5ths to get back approximately to C probably explains why there are 12 semitones in an octave. But why is it called an octave? Obviously because there are 8 notes when playing an octave on the white notes on a piano. But why are only 7 of the notes white and 5 of them black? Is the answer simply because the Greeks (or maybe Gregorian chanting monks) found that singing up certain scales of 8 notes sounded better than singing the chromatic 13 note scale?
I understand why in an unequal tempered scale music in different keys should have a different character (for those who, unlike me, have ears to hear it) but I wonder why all the "flat" keys share a characteristic that differentiates them from all the "sharp" keys. Does this depend on the form of temperament that is adopted?
One point seems clear: there is no such thing as a perfect system of tuning/temperament. All such systems involve compromise. Equal temperament has the great advantages that it is unambiguous and allows free modulation between all keys without any increase in disharmony. (Since my unsophisticated ears couldn't hear the difference between equal temperament and any other, I'm quite happy to live with this particular compromise.)
No modal music please,
How can you say that, when VW is the composer of the day?
Wow, thanks Hugh. I’d wondered whether to dive into the circle of fifths, and decided I’d couldn’t possibly explain it without drawing lots of diagrams… and even then I’d only confuse matters 😂
Your description is excellent, and so clearly explains why a C# and a D flat are not the same.
I’m very fond of the circle of fifths, too, as a musical device that composers like Vivaldi used to move quickly between quite distant keys. You can clearly hear those moves as each dominant becomes the next tonic, until the destination key is reached. Perhaps I can find an example to illustrate how this sounds?
But I agree entirely: the further you delve into these things, the more questions arise.
A rabbit hole indeed!
How can you say that, when VW is the composer of the day?
@hugh I meant theoritically. I'm only just beginning to learn about major and minor chords and stuff (remember I'm no professional), so all these modes I read about, following @capriccio 's explanation, while researching the internet made my head spin 😵😵😵 Have pity on me guys!
Of course I'd listen to any and all kinds of classical music, be it modal, tonal or extraterrestrial, even 🤪
(Since my unsophisticated ears couldn't hear the difference between equal temperament and any other, I'm quite happy to live with this particular compromise.)
🙋♀️ Same here.
And thank you so much for the detailed explanation.
two notes sound well together if there is a simple arithmetical relationship between their frequencies.
So, in essence, music sounds beautiful because of its mathematical perfection? 🤔
I guess that's why when I accidentally hit a wrong note the result is very cringey! ( for a better understanding of chords, I try what I'm reading about on the keyboard, most of the time it sounds horrendous of course 🤣).
music sounds beautiful because of its mathematical perfection?
Pythagoras would have agreed. Bach too, probably.
Hello everyone 👋,
I'm asking a question related to your other post about the minor key (I created a separate post so as not to derail the conversation in the original).
And then there’s the matter of how sharp, how flat?
The childish question from a music theory newbie, here 🙋♀️ would be :
It is my limited understanding (please correct me if I am wrong) that on the piano for example the (actual physical) "black" key between, let's say C and D would be called either C#, since it's a half step above natural C, or Db, since it's a half step below natural D, right? So the silly childish question is: the note this key plays is always, obviously, going to sound the same, whether we call it C sharp or D flat? Why then does it have two names?
My guess is that it's either sharp or flat relative to its neighbors?
(n. b. @capriccio, I think you should set up a "music theory for dummies" section or something, if only for my benefit 🤣).
Of course other members' input is always welcome.
Thanks, guys, for allowing me to take advantage of your musical expertise! 🙏
In common practice harmony, C# and Db are two very different tonal centers with key relationships that go off in different directions. For Db major, its relative minor is Bb minor, and its dominant is Ab major. You can modulate to Bbmaj, Gmin, Fmaj, and Fmin.
The relative minor to C#maj is A#minor, and its dominant is G#maj. When you get that many sharps in the key signature, it's difficult to add more, because the keys become "theoretical". I.e. there is no real A#maj scale.
So, yes, C# and Db are very different notes, mostly because of their function and usage in their respective key relationships.