Why are there both sharps and flats?
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Why are there both sharps and flats?
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Re: Why are there both sharps and flats?
#2Gee.. page full of very low quality/BS answers there! Hadn't seen Music StackExchange before.. super non-impressive. The 2 top-voted answers are absolute without-a-clue nonsense, people-who-don't-know rambling aimlessly, not explaining anything.
I am also no music historian, don't know all the history, but:
Not until the third-top-voted answer, the one beginning "Historically, keyboards didn't always work that way" is it mentioned that..keyboards didn't always work that way. But they go on "Our musical notation is older than enharmonic equivalency that you get with "well-tempered" keyboards" - evidently confusing well temperament with equal temperament.
Which is understandable - it seems everyone's 'educated' with that misconception; I certainly was. (Classical then jazz pianist) Even in my 30s I remember reading a book from the 1880s talking in detail about the specific emotional qualities of the different keys, thinking they were just imagining things, deluded. Then I learnt that no, Bach's "well-tempered" actually wasn't our equal temperament, with each note 2^(1/12) higher than the next.[0] Every key (C major, E minor etc) actually sounded different, the intervals were different etc. So that 1880s book wasn't crazy at all. Apparently that's about when equal temperament was brought in everywhere (mid to late 19th C), and the old "different keys sound different" was abolished.[1] Many composers complained about the loss of..key personality, didn't want the new system. Now all the keys sounded exactly the same. (Well, not to me, I've got perfect pitch. But to most people they do now.) It seems a strangely huge cultural forgetting, that somehow I never heard about all that, during decades in various music worlds.
So before the equal temperament system of e.g. middle C is 3 semitones above A, so 220 x 2^(3/12) Hz, many different systems of ratios were used to compute the note frequencies, producing lots of different tunings, 'temperaments'.
The problem in all this is the Pythagorean comma, the gap resulting from the awkward fact that when trying to construct a scale from octaves (2x the frequency) and 5ths (3/2x), 2^x=3^y has no positive integer solution. With continued fractions they worked out that 2^7~(3/2)^12 (128~129.7463..) is a good approximation, which is, in short, why pianos have 12 notes per octave, and going up 12 5ths takes you up 7 octaves. With equal temperament, the gap is spread evenly among the notes, only now none of the intervals have simple ratios of frequencies like they did before (except the octave). There's now nothing perfect about a "perfect 4th" or "perfect 5th".
Anyway..going up in 5ths you get C,G,D,A,E,B,F#..
Going down you get C,F,Bb,Eb,Ab,Db,Gb..
Gb and F# on modern pianos are (just different names for) the same note, but in the pre-equal temperament days, going up a 5th wasnt just Freq x 2^(7/12) but multiplication by some ratio, most simply 3/2. And then the note you got going up (F#) was different to that you got going down (Gb). Some keyboards had black notes split in half, one playing the sharp, one the flat.
But I won't go into more historical detail, because I don't know it and I'm rambling aimlessly enough already. And you could fill a book with the answer to the Q.
[0] well, pedantic piano tuners won't agree, but that's the theory.
[1] Some instruments had been equal temperamentish for centuries, e.g. guitar I think, (it using the same frets for different keys) but others, like pianos, not until then.
Re: Why are there both sharps and flats?
#3Wow -- it's amazing how bad the answers are on stackoverflow.
The first reason why there are both sharps and flats is historical. Equal tempering produces the same pitch for, say, D# and Eb. The same was, however, not true for some of the historical tunings prevalent at the time the very notation became standard.
For more information about this, you can read "How Equal Temperament Destroyed Harmony (and Why you should care)". It explains, for example, that Bach's Wohltemperierte Klavier did not, in fact, refer to the equal tempering, but to a different tempering (whose details I can't exactly recall), but I seem to remember something about slightly less sharp thirds. In fact to summarize that book in a sentence -- he doesn't like overly sharp thirds... and sevenths.
There was a veritable zoo of different tunings, and each involved a different set of compromises. So one produced lovely chords as long as you stayed in root position, whereas another produced slightly less faithful thirds but instead allowed you to play secondary dominants of the relative minor, and so on.
Anyway, the point is that there was a time when playing a third up, and playing a sixth down were not the same thing (modulo an octave), and that's why they used different symbols. But we now use equal temperament, which forces that to be true, to hell with those overly sharp thirds (as compared to natural overtone series).
The second reason has to do with the fact that notes are not really useful on their own. They're useful when considered in relation to other notes. In other words, we're really interested in intervals, rather than individual notes. And when considering intervals, it's customary to begin at a certain note, say, C, and count our way towards some destination note. Once you start doing that, you arrive very naturally at the "sharp" and "flat" formulations.
Re: Why are there both sharps and flats?
#4It was my question too! Thanks for clarification.
Re: Why are there both sharps and flats?
#5To everyone saying these answers are bad because they don't delve into the history, equal temperament, and how D# and Eb weren't always harmonically equivalent:
You're answering the wrong question. Yes, the question was "why are there sharps and flats" but read the rest of the question and it becomes clear, he/she isn't looking for the origin of sharps and flats. They are asking why it's practical to have both sharps and flats.
The answer is: Because it's easier to write in F if you call them "A and Bb" rather than "A and A#"
Re: Why are there both sharps and flats?
#6Gee.. page full of very low quality/BS answers there! Hadn't seen Music StackExchange before.. super non-impressive. The 2 top-voted answers are absolute without-a-clue nonsense, people-who-don't-know rambling aimlessly, not explaining anything. I am also no music historian, don't know all the history, but: Not until the third-top-voted answer, the one beginning "Historically, keyboards didn't always work that way" i…
It seems that we could get our perfect ratios now that we have computers.
As the computer plays, it uses a psychoacoustic model to determine which notes would have significant local tonal impact in the listener's mind. (the automated choices can be overridden as desired) Both past and future notes are considered. Exact ratios are used to determine every note frequency, using nearby significant notes as references.
You'd get nice integer ratios all throughout the music. The pitch standard would slowly vary, such that you could start in A440 and end up in A337. In most music, the pitch wouldn't change all that much, since it is something of a random walk by tiny amounts. There would be the occasional piece of music that causes a continuous unidirectional change in the pitch standard, requiring a few tweaks if that is undesired behavior.
Re: Why are there both sharps and flats?
#7Wow -- it's amazing how bad the answers are on stackoverflow. The first reason why there are both sharps and flats is historical. Equal tempering produces the same pitch for, say, D# and Eb. The same was, however, not true for some of the historical tunings prevalent at the time the very notation became standard. For more information about this, you can read "How Equal Temperament Destroyed Harmony (and Why you shoul…
Why is the top comment on HN a wrong answer?
Music notation existed before keyboards did, or other tempered instruments.
Re: Why are there both sharps and flats?
#8To everyone saying these answers are bad because they don't delve into the history, equal temperament, and how D# and Eb weren't always harmonically equivalent: You're answering the wrong question. Yes, the question was "why are there sharps and flats" but read the rest of the question and it becomes clear, he/she isn't looking for the origin of sharps and flats. They are asking why it's practical to have both sharps…
Yes. Equal temperament does not explain why there is Ab and G#. It merely explains why they have not always been harmonically equivalent.
You, and the top SO answer, give the correct reason why. And it's not just for writing, but reading also.
The diatonic scale, combined with the staff of lines and spaces, necessitates both flats and sharps.
Re: Why are there both sharps and flats?
#9Gee.. page full of very low quality/BS answers there! Hadn't seen Music StackExchange before.. super non-impressive. The 2 top-voted answers are absolute without-a-clue nonsense, people-who-don't-know rambling aimlessly, not explaining anything. I am also no music historian, don't know all the history, but: Not until the third-top-voted answer, the one beginning "Historically, keyboards didn't always work that way" i…
It seems that we could get our perfect ratios now that we have computers. As the computer plays, it uses a psychoacoustic model to determine which notes would have significant local tonal impact in the listener's mind. (the automated choices can be overridden as desired) Both past and future notes are considered. Exact ratios are used to determine every note frequency, using nearby significant notes as references. Yo…
Ohh that's a very interesting idea. Wonder if you could actually make something sound significantly better like that. But like you say, people might have rather different ideas on what sounds better.
And after a lifetime of equal temperament, that's what sounds good to me, anything else sounds out of tune. (I haven't experimented to see if even proper perfect 4ths and 5ths sound out of tune to me! That would be weird. Though those notes are very close to their equal temperament versions I think.) I used to have some music software that came with hundreds of different historical temperaments and tunings, from many different traditions, it was fascinating playing around with.
Re: Why are there both sharps and flats?
#10Wow -- it's amazing how bad the answers are on stackoverflow. The first reason why there are both sharps and flats is historical. Equal tempering produces the same pitch for, say, D# and Eb. The same was, however, not true for some of the historical tunings prevalent at the time the very notation became standard. For more information about this, you can read "How Equal Temperament Destroyed Harmony (and Why you shoul…
Music teacher with degree here, the Stack Overflow answers are correct as far as modern usage goes, with respect to common-practise tonal harmony at the very least. Your second reason is just an alternative way of phrasing all of the answers that cite F major as an example.
Yes, in non-equal temperaments they can be different pitches, but I highly doubt that someone asking the difference between sharps and flats is concerned with niche subsets of early music and contemporary classical.