I don’t know jack about music (as you might have already guessed from the title).
In a piano, there are black keys in between the whites. Why aren’t there black keys in between all the whites? How are those tones not desirable/usable/musical?
I don’t remember the scale or some of the proper terms in English and am feeling too lazy to look it up, but the info is still valid inasmuch as this non-musician, non-acoustics specialist can make it.
The white keys correspond to “basic notes,” the black keys to “half notes.” If you have two notes A and B separated by a full tone, the half note is called “A sharp” or “B flat” (the terms are synonimous). But the difference between each basic note and its neighbors isn’t always a full tone.
Using the basic scale in Spanish (Do, Re, Mi, Fa, Sol, La, Si, Do), there’s full tones everywhere except at Mi-Fa and Si-Do. You can have a flat Mi and a sharp Fa, but sharp Mi/flat Fa just doesn’t exist.
I know that the names for the notes in Spanish come from a medieval song where they’re the first sillables and the first notes for each of the first seven verses. Whether the scales we use for pianos and most Occidental music were defined there or had actually been in use before, I don’t know. Hopefully a music historian will come along and inform us.
Those aren’t “missing keys” or “missing tones.” There is a proportional progression from each key to its adjacent key, irrespective of the key’s color. The arrangement of black keys - two, then none, then three, then none, repeated throughout the keyboard - makes it easy to identify the tone of each key at a glance. If all the keys were the same color, or even if every other key were black, there would be no such ready reference to identify the notes.
I think what the OP may be asking - although not knowing they’re asking - is “why does Western music choose those particular intervals in the chromatic scale to be dominant [white notes] or secondary [back notes] in the major scale of C?”
I myself find the intervals in a major scale sounds “right” but have no idea why. Is it nature or upbringing? If the former, is there something mathematical at work? If the latter, do other chromatic or even more fine-grained scales, sound “right” to other cultures?
I know Indian music works to different scales; does it sound totally normal to people brought up with it?
That’s just a matter of tradition related to where the black keys are - in other words, which keys were chosen to be black. But this: “Why aren’t there black keys in between all the whites? How are those tones not desirable/usable/musical?” indicates that the OP had the notion that there could have been two additional black keys which would correspond to two additonal notes that were chosen to be omitted. That is not the case at all, as all notes in the Western chromatic scale are present. Starting with that understanding - all the notes are there - the answer to why there aren’t black keys between every pair of white keys is that the pattern of coloration aids in identifying the notes.
To sum up, there are no missing keys. There’s just a pattern that makes it appear that there are missing keys.
There aren’t any missing tones. The difference in pitch between any two adjacent keys (regardless of color) is the same amount (this amount is called a semitone or half-step.)
Here is a diagram of a musical keyboard with the white notes labeled. It looks like the difference between B and C is the same as the difference between C and D, with an extra black key in the middle. In fact, the difference between B and C is one semitone, the difference between C and the black key to the right (called C-sharp or D-flat) is a semitone, and the difference between that black key and D is one semitone.
If you start on C and play all the white notes, you get this pattern of intervals: tone, tone, semitone, tone, tone, tone, semitone. This pattern is called a major scale and you can construct one starting on any note on the keyboard, but this one (C-major) is the easiest because it’s just the white keys.
As for why the keys are laid out that way, the system evolved for a number of reasons:
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It makes things easier to play – if there were only white keys for all 12 tones in the modern Western tuning system, you would have to stretch your fingers further to reach various notes, and some large chords would be impossible unless you had truly gigantic hands.
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It makes it easy to see where you are visually: C is always to the left of a group of two black keys. If there were black keys in between every white key, you’d need some other means of knowing where the notes were.
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Horribly complex historical reasons involving the development of temperament systems which are fascinating in their own right but beyond the scope of this post.
Which came first–the development of musical notation in which seven tones were somewhat arbitrarily considered “natural” (Is that what you call non-sharps and flats? It’s been a long time since I knew anything about music.) and five were considered sharps or flats, or the development of keyboard instruments in which five of the keys were recessed and colored differently for ease of play?
In other words, did the notation evolve to fit keyboard instruments, or vice versa?
As has been said, the difference between any key and the next is the same interval, a half step. This is true whether it’s two white keys next to each other or two black keys next to each other.
However, to play a major scale (do-re-mi-fa-sol-la-ti-do), you don’t go up by the same interval between each note. You go: whole step, whole step, half step, whole step, whole step, whole step, half step. The piano keys are arranged so that if you start on a C, you can play a major scale with white keys only.
If the letters represent the white keys and the #s represent black keys, you have:
C # D # E F # G # A # B C
See how the black keys are positioned so that just playing the whites gives you the progression: whole step, whole step, half step, whole step, whole step, whole step, half step?
Incidentally, you can also play a minor scale by starting on A and playing only white keys. The minor scale progression is: whole step, half step, whole step, whole step, half step, whole step, whole step:
A # B C # D # E F # G # A
Just playing the black keys you can play a pentatonic scale. Music based on this scale is common in some parts of the world, not so much in western classical music. To my ear it sounds kind of “Asian”.
But who decided that these are the ones which comprise the “major scale”? It seems to some of us that it is rather arbitrary, suggesting that we’ve gotten accustomed to it, rather than those notes being inherently more musical.
The notation was earlier, I believe. There’s medieval music sheets with # signs on them. I understand some of those are much earlier than the development of keyboard instruments.
I’m moving this from General Questions to Cafe Society.
Gfactor
General Questions Moderator
A little of each, or both together.
Western music evolved largely thru the Church, which had various “modes” (a lot like scales) with different intervals (but always multiples of half-steps, not third or quarter) between the various modal steps. We now call this scale from C to C (= one octave), including all white and black notes, chromatic.
Some early folk music (cf. Scots) had even larger skips between some tones (but still multiples of half steps to us), and fewer tones per octave. This is one of the characteristics of bagpipe music.
Note that Eastern music has a different development history and different intervals.
Around the Baroque era, Western music realized that a harpsichord, clavichord, and then piano, could play any mode if the keys were arranged and tuned much like today. A futher micro-refinement of tuning led to the concepts of "equal temperment,"which is getting into acoustic theory maybe a little deeper than you want to go.
Many alternate schemes have been proposed and discarded since, but the basic keyboard layout hasn’t changed for a few centuries. I just looked up my long reference list of such and found that most of the links are obsolete, so here are just a few of those schemes in layouts and tunings:
http://www.pianoworld.com/fun/oddpianos.htm
Which was a necessary invention when a standard church mode was used and the starting and ending pitch (tonic) was not C. If you try to play/sing a major scale starting anywhere else, you will need to use one or more black keys (sharps or flats) to keep the intervals the same as mode C.
Most of this is from memory. Some of it is guesswork. Follow the wiki links for more info.
IIRC, 5 and 7-note scales existed before keyboards. The thing to note is that you can modulate a scale up or down (“start at a different semi-tone”), but you then need a different selection of 7 out of 12 semi-tones to make up the full scale.
In an equal-temperament tuning, the layout of the keys only means that the white keys form the major C scale which is equal to the minor A scale and a bunch of other scales, and the black keys are needed to “fill in the gaps” that you need to play the rest of the possible 7-note scales. So the layout is more or less arbitrary.
But equal-temperament tuning is really a compromise, needed because pianos have fixed tunings for each key while just intonation and meantone temperament map keys to different frequencies depending on the scale that’s being used. (contrast with a violin, which allows for completely arbitrary frequencies). In other words, if you tune the piano using just intonation starting at some note, say C, then the C major scale on that piano will sound a lot better than, say, F major. If you use equal-temperament tuning, all the scales will be slightly off, but none worse than any other.
In any case, given that all kinds of different tuning systems for keyboarded instruments were in use will into the 18th century, it makes sense to have a keyboard layout that prefers the “best” scales.
See also Musical keyboard - Wikipedia
The notation mostly evolved at a time when vocal music dominanted, and has been tailored further, when necessary, to suit various instruments.
That’s not a bad way of describing it, actually, in the same way as jazz harmonies sound OK to us, but to a 19th century European ear they’d have been strange and discordant. There’s many centuries of music very much within a distinct European musical history which is not centred around major and minor keys.
Ut Queant Laxis provided the medieval six-note Ut Re Mi Fa So La, from which our solfege systems derive. At the centre of this hexachord was the only semitone, providing a symmetrical arrangement, and it neatly fitted with the type of melodic line used in a lot of sacred chant. Ascent higher or lower was thought of not in terms of an octave scale, but with overlapping hexachords, starting on (modern) C, F and G, with that on F giving a (modern) B flat, and that on G giving B natural. Further principles of transposition gave rise to other flats. The development of concepts of enharmonic equivalence, where B flat is also A natural, came much later on.
I’m curious about this as well. What (if anything) is special about T-T-S-T-T-T-S ?
(where T denotes tone and S denotes semitone)
ETA: I see that Gorillaman already responded
Doesn’t the composition of the major scale have to do with integral ratios between the notes. I’ve tried to sit down and figure out the ratios before, but I’m not good at logarithms and I always gave up before I got it.
Various musical scales, including the common major and minor scales, pentatonic scales, and so on, evolved more or less organically from the fundamental harmonies, and only later were common notation systems (and keyboard instruments) developed for them.
Way back in ancient times, people realized that the best harmonies were produced by frequencies with small whole-number ratios. If you were making a musical instrument, you’d one note to start with and make the instrument capable of playing other notes with those frequency ratios. Those groups of notes became the first scales.
For example, suppose you start with a string that vibrates at 200Hz. You could add the following additional strings:
One with a ratio of 5:4 of 200, or 250Hz.
One with a ratio of 4:3 of 200, or roughly 267Hz.
One with a ratio of 3:2 of 200, or 300Hz.
One with a ratio of 2:1 of 200, or 400Hz.
You’ve just invented a simple pentatonic (five-tone) scale; in the modern system we’d call these harmonies a major third, a perfect fourth, a perfect fifth, and an octave, but in Olden Tymes you could call them whatever you wanted, since there was no particularly common system.
Eventually, the Western world settled on a few common conventions: a popular scale used in many compositions was an eight-note scale that became known as the major scale; a different eight-note scale which shared several frequencies in common with the major scale became known as the minor scale. (Actually there are a few different kinds of minor scales.) People started to want instruments that could play any kind of scale, so they started making them with supersets of notes that could be played in different ways, and the development of equal temperament as a compromise between overlapping frequency ratios (which don’t line up perfectly) led to the 12-tone keyboard as we know it.
That’s the super short version. For a less short (but still relatively short) version, I highly recommend the book Temperament by Stuart Isacoff.
Thanks for all the answers in their varying degrees of interestingness and overmyheadness.
My confusion arose from thinking that the difference in tone from white to white was always the same and blacks were half steps.
That straightened, it all makes sense. Fascinating stuff.
As an aside, I wish I knew enough about music to make more intelligent questions about this. The music crowd here is head to head with the car and the math crowd in knowledge and ability to bring complex stuff down to the level of my ignorance.
More precisely, the ratio of pitch between two adjacent keys is the same. Each key has a frequency 1.05946… times greater than the previous one. Go one full octave (from C to C, say), and that amounts to a factor of exactly 2.
And speaking of ratios, I’m going to actually tackle the question of “why”. Combinations of tones sound good to the human ear if their frequencies form a simple fraction, for instance, if one is twice the other, or one is 3/2 times the other. Originally, this was the governing principle behind tuning instruments: You’d tune the instrument such that certain intervals of notes the instrument could produce corresponded to these simple ratios. One such combination of pleasing tones is three tones in the ratio of 1 : 5/4 : 3/2. This forms what’s called a major chord, and corresponds to the notes we now call (for instance) C, E, and G (this is the C major chord, since it starts on C). But there are other ratios we could use. For instance, there’s also the ratio 4/3. This falls in between 5/4 and 3/2, and we assign that tone a letter between those letters (in the key of C, this would be F). If we keep taking these ratios, we can fill in all of the notes, and the first ones to get filled, using the simplest ratios, are the major scale, as it was originally defined.
Now, if we keep going after we have the major scale, and define five more notes, we find that those notes are almost evenly spaced (that is to say, the ratio between adjacent notes is almost the same). So what we do nowadays, is we adjust all of the notes so that they are evenly spaced (that is to say, the ratios are all exactly the same). This is how we get that value of 1.05946… I mentioned above: That’s the twelfth root of 2, so 12 such steps bring us a full octave (factor of 2). In this tuning, the notes C, E, and G don’t exactly match the ratio 1 : 1.25 : 1.5-- They’re instead 1 : 1.25992… : 1.49830… But this is very close to 1 : 1.25 : 1.5, so it still sounds pretty good. And I can also play the chord starting with any other note on a piano, without tuning between, and it also sounds pretty good, whereas with the old tuning methods, some of those chords would be out of tune.
When did this change in tuning happen? Do composition from before that change sound somehow off when played in instruments tuned in the new way?