When the people sing the song, we use do, re, mi, fa, sol, la, ti (or si).... but some time I hear that the music people say A, B, C, or C flat..., what is their relationship? or are they two different things? Thanks.
Do-re-mi-etc. is "sol-fa" or "solfege".
Sol-fa represents a major scale, with Doh being the first note, Re being the second, and so on. I'm sure you can sing that scale.
The A-G note names are absolute names for a certain note. An 'A' is an 'A' no matter what key you are performing in.
There are two variants of sol-fa. Fixed doh and Movable doh.
Fixed doh is used in China, France, Italy, Portugal, Spain, Romania, Russia, South America and parts of North America, Japan, and Vietnam.
In fixed-doh, Doh is always equivalent to C; Re is always equivalent to D; and so on.
Movable Doh is used in Britain, Germany, Indian classical music, and the United States.
In movable-doh, you can pick a different pitch to start on, and sing Do-re-me-... starting at that note. What you are doing when you do that is singing the major scale in different keys.
If you are singing in C major, d,r,m,f,s,l,t,d is C,D,E,F,G,A,B,C
If you are singing in D major, d,r,m,f,s,l,t,d is D,E,F♯,G,A,B,C♯,D
... and so on.
In both forms, there are other phonetic names for sharp and flat names. The complete list is on Wikipedia.
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Solfege (do, re, mi, ...) is a numbering system which starts from the first note of the scale (do=1, re=2, ...). Solfege identifies the position of the note in the scale.
Pitch names are a numbering system which starts from a particular sound (A440 or concert A=1, B=2, ...). Pitch names identify the sound of the note in the scale.
Take an example. Say you are singing a song that’s in F major. The pitch names for that scale will be F G A B♭ C D E F, and the solfege for that scale will be do re mi fa so la ti do.
Now, sing that song in G major. The pitch names will change to G A B C D E F♯ G, but the solfege for that scale will still be do re mi fa so la ti do.
On a Fixed Do scale the A Note is assigned to La because of the precision of the frequency (440 Hz) which corresponds to such note and you end up with a correspondence as follows
A = La
By the way the note names on the Fixed Do scale come from a poem of the benedictine monk "Paul the Deacon" which goes like this:
Ut queant laxis
And the Ut was replaced by Do to make it easier to say on the Romance languages
If you have ever looked at pop sheet music in Spanish, you'll see that they don't use "C, D, E, F, G, A, B" at all. They only call notes by their Fixed Do names.
In Spanish sheet music, a C dominant 7 cord is called "Do7". A G# dominant 7 chord is called "So#7".