Talk:Key signature/Archive 1

If two scales have the same key signature, they'd use the exactly same notes of the octave.

Do minor and major keys have identical key signatures?

--- Anon

If this is so, why do they sound different?

--- User:Karl Palmen

C major and A minor certainly sound different because they have a different tonic. What you really hear in tonal or modal music is the intervals of various notes against the tonic. --Damian Yerrick

How does the composer ensure that this is the case? Perhaps the answer could be put in the tonic page. --User:Karl Palmen


 * I'm really not sure if this is the sort of thing that can be explained. It's up there in the realm of "how does a writer achieve a particular effect?". Still, I look forward to reading an answer! -- Tarquin
 * The real answer is that the major or minor of a key comes from the, chord progression, cadences to the tonic and the establishment of the tonal center in the piece. It's no accident that 90% of western music begins the melody on the tonic or the dominant. The description of how a tonic is established and cadences are prepared really belongs in the Counterpoint article, since it's definitely a compositional technique. It has to do with certain chord progressions and such. Man this stuff is complicated, and here I was just about to jump in and do up Counterpoint. Basically, if you've set up A as your tonal center, the only way you can have a D min - E7 - A min. progression is if you are in a minor key and make use of the melodic minor scale.JFQ


 * Surely a discussion of establishment of tonal centre and so on ought to be in harmony rather than counterpoint. Other than that, I agree with all you're doing (and I'm very happy that there's somebody doing all this theoretical stuff so I don't have to feel guilty about writing about dead composers all the time) --Camembert

A good way of putting it is that the "word" ABCDEFGA is different from the "word" EFGABCDE, even though they are both simple sub-sequences of the sequence ...CDEFGABCDEFGABCDEFGABC...
 * That's actually a little misleading. The order that the notes are commonly arranged in in scales results from arranging them as they ascend in pitch. This is arbitrary. What is important is:

It's actual much more difficult to write atonal music than it is to write tonal music, contrary to what you might think. The scales and harmonies are so ingrained in your ear that you have to work hard to do things contrary to the common tendencies.JFQ
 * 1) The relationship of each note to the tonal center
 * 2) The relationship of each note to each other note, particularly w/r/t consonant and dissonant intervals.
 * 3) The quality of the chords built on each note

I find this topic very difficult. As a musician, I intuitively feel it. As a mathematician, I want some sort of axiomatic base to it all. I was trying to explain scales to someone last week: Like JFQ says, part of the problem is that much of it is ingrained. How much of the scale derives naturally from number theory, and how much is human construction? -- Tarquin
 * 1) the major scale has this pattern of tones and semitones. -- But why that particular pattern?
 * 2) well, the major scale is pretty much a historical blip of a few centuries, which started to fade with Debussy, Schoenberg, jazz and blues. Before that there were modes. -- right. But why only seven modes? after all, there are more than seven orders of stacking 2 semitones and 4 tones.
 * 3) ... arg... the 7 modes are special because they're different starting points in the C major scale... but then it's back to "why the major scale?" Why 7 notes from 12 for that matter? Why 12 semitones?


 * 12 semitones are explained by realising that the octave, a ratio of 2/1, is the simplest interval. If you just stack octaves on top of one another, you don't get anywhere, they all sound the same. So you take the next simplest ratio after that, which is 3/2, the perfect fifth. Now here you've got something - if you start with what we now call a C and go a 3/2 up, you get a G, which sounds different. If you go a 3/2 up from that, you get a D, which sounds different from both the C and the G. Great. But no number of 3/2s will ever fit exactly into any number of 2/1s (octaves) - you can keep stacking 3/2s on top of each other for ever, you'll never get exactly back where you started. You've got to get out of it somehow. After 6 3/2s, you're nearly back where you started (albeit several octaves higher, but octaves are equivalent, and you can just bring everything within one octave). What you have after stacking 6 3/2s are seven notes which are a major scale, in fact. But after 12 3/2s, the difference is almost imperceptible (albeit seven octaves higher). So you just ignore the difference and pretend the note at the top of the 12th 3/2 is the same as where you started. And so you get a 12 semitone scale. It's that wilful ignorance of the difference between 12 3/2s and 7 perfect octaves that has led to a lot of people in this and the last century using completely different tuning systems (Harry Partch for example).


 * I've written all this in a bit of a rush - it might not be wonderfully clear, but I'm sure it's correct.


 * All the early modes business and emergence of the major-minor dichotomy is really not my area; I do 1700 to date, more or less, when it comes to tuning. But I do know that most of the things which have become ingrained over time started out as simple maths and careful listening.


 * I guess I should go and write a proper article somewhere now... --Camembert


 * That gap at the end of the stack is called the Pythagorean comma -- Tarquin