Pianos have 5 black keys per octave, yet my music teacher tells me that there are 7 sharps. I know E sharp is actually F and B sharp is actually C, but he said they don't count. So how are there 7 sharps?
It's because we didn't always know there were any black keys at all.
Go back 1000 years or so and we only knew about the white keys - that's why the black keys didn't get their own letters.
At some point around 1000 years ago some composer wrote a sequence like F-G-A-B and gave it to the choir to sing. The choir sang F, G, A... and then something not quite B. But it sounded OK, and it was easy to sing.
We didn't know what to do with it. But composers now had a new note to play with. At first it was called musica ficta (false music) and the actual B was musica recta (right music). We eventually adopted B quadratum (square B for the musica recta) and B rotundum (round B for the musica ficta). You could write those as symbols, with either a circle or a square as the bottom of a lower case B.
The round B eventually morphed into our flat symbol, and the square B became our natural sign. Over the course of roughly the next 400 years we discovered the other black key pitches. And in the mid 15th century we decided that if you could lower a note with a flat, you could also raise a note with a sharp, so we invented that.
The piano wasn't created until another 300 years later, so it's always had the five black key arrangement. But the idea of flats (and sharps) is a symbolic one - if you can call a note B flat or G flat, you can call ANY note flat, and it's understood that you're lowering it by a half step.
Since we have seven letters in the musical alphabet, we can have seven sharp names - and seven flat names. The fact that they don't always line up with a black key isn't an issue... because black keys are pitches (sounds) and sharps and flats are symbols (instructions for what sounds to make).
Try to not get hung up on the black notes of the piano keyboard.
Yes, those 5 keys are named with sharps or flats, but sharps and flats don't exist because of those black keys.
Instead of thinking of sharps and flats as belonging to black piano keys think of them as belonging to the musical letters:
A B C D E F G.
The spaces between the letters are either whole steps or half steps (also called whole tones or semi-tones.)
There are whole steps between all the letters except
B C and
Any time you want to shift a tone (a letter) up or down a half step you use a sharp to go up or a flat to go down.
Each letter can be shifted in that way so there are seven sharps or flats for each letter.
I know E sharp is actually F and B sharp is actually C, but he said they don't count.
Your teacher added to the confusion by saying 'they don't count' instead of properly explaining musical spelling.
E sharp is not actually F, but it's called enharmonically equivalent. Yes, you play the same piano key for both notes, but they are written differently in staff notation! That may seem like a picky technical detail, but it's important. Example: sometimes people spell an
Amajor chord as
A Db Ewhich is confusing to read compared to the proper spelling
A C# E.
There are times when you do want to use spellings like
E#. Example: in
F#minor the dominant chord is
C#major which is spelled
C# E# G#. An enharmonically equivalent spelling is
C# F G#but that spelling is actually hard to read on staff notation.
If you are working with simple chords in simple keys like
F, etc. these enharmonic issues don't come up often. But when you start working with keys whose tonics take a sharp or flat, work with minor key, or work with chromatic harmony enharmonic spelling issues are regular.
You might try to find some easy classical music in
C# minor (4 sharps) or
F# minor (3 sharps) for practical examples. Those keys use tones
I suppose the simplest examples for flats would be tone
Cb in chord
V7/IV in key
Db major (5 flats) or tone
Fb in chord
V7/IV in key
Gb major (6 flats). But I think it will be harder to find easy classical pieces in those 'flat' keys compared to the keys
C# minor and
You have this confusion because you treat the piano as a natural object like trees and mountains and the interesting sounds made by crows and the lullabys that mothers sing their babies to sleep to — also called a capella singing.
The confusion would disappear if you go from the natural to the artificial; ie instead of starting with piano start with
- Between the notes 440 hz and 880 hz ie between A and the next A on the piano you have an uncountable infinity of sounds — interesting for a mathematician, less for a physicist, useless to a musician.
- Cut down to rationals between 1 and 2 — still infinite but now countable
- Cut down to 5-limit rationals and we get Just Intonation (small modification for Pythagorean tuning)
And now we've begun to reach the beginnings of a system that musicians can use but is still highly inconvenient.
Towards more convenience implies going towards the…
A keyboard can only be finite. This means two issues need resolving
- how many keys
- what notes those keys should sound
IOW nothing sacred about 12 and assuming 12, the sounds produced need not be what they are on the modern piano.
Brings us to the topic of
Alternate tunings or intonation
The modern piano is tuned to something called equal temperament. Even in the western tradition this tuning has gained currency only quite recently. And in other cultures mostly never.
Its only in equal temperament that B♯ = C and E♯ = F
Western music is not based/conceived around ET but a less crude system called Meantone. Like all usable musical systems it is approximate but is a finer approximation than ET.
When you study a little more music your teacher will tell you about
very similar to spellings in English. eg you will be taught when A♭ is right and when G♯ On the piano they look like the same note but they are logically different.
[In C major] A♭ is the minor sixth whereas G♯ is the augmented fifth; former is (somewhat) consonant the latter is quite dissonant
And in JI they are quite different:
A♭ = 8/5
G♯ = 25/16
I'll end with two interesting evidences from common (western) practice
was evidently taught by his father to play the flats sharper than the sharps ie when you take a note down (flatten) you dont reach the midpoint. Likewise sharpening does not reach the midpoint (25/16 < 8/5)
in his last piano sonata (no 32 2nd movement) on the same page has within 3 lines an A♭ and a G♯. In itself this seems pedantic
When I got hold of a piano that had JI capability I was struck by the fact that Just-major made the A♭ sound good and the G♯ bad and Just-minor the other way round.
I conjecture that the Just-major uses the augmented black notes whereas the just-major the minor