I don’t have the least knowledge about music, and as such the recent column on Musical Notation leaves more questions than answers:[ul]
[li]Didn’t the Chinese or Hindus (or Mayas, Incas, etc.) develop their own notation? [/li][li]Can their music, or every other “non-occidental” music be written down without loosing anything?[/li][li]Being sound a continuous wave spectrum, why are only seven notes?[/li][/ul]
I don’t know the answer to your first two questions, but regarding your third, there are 12 semitones in an octave. I believe that they are related by perfect fifths – if you start with C and move up by a fifth to G (possibly the first harmonic, but I’m not positive), then move by another fifth to D, and so on, you’ll eventually go through all 12 semitones and get back to C. It’s called a circle of fifths.
I can’t answer this either - but a lot of Eastern music uses quarter-tones, for example (I think Western composers are just starting to toy with those). I’m not sure how you’d write that out, perhaps a classical musician would know?
You can’t really write a true gliss in our musical notation. You can put the starting note and the ending note and a symbol that means “go from here to there in a glide”, but you can’t differentiate one “shape” from another. So while pretty much anything you can do on a piano can be represented with the notes and staves, instruments such as trombones and violins and definitely voices can do things that can only sort of be gestured at on the page with inadequate symbols.
Actually, come to think of it, there are a few piano-sounds that would be difficult to write down: the chordecho effect you get when you slam down a chord and hit the damper pedal a split-second after you release it; or the resolution-clarification effect you get after playing several tonally related chords with damper down and then lift it briefly during another chord containing some and omitting some of the same tones.
You can make noises at any frequency you wish, but they won’t necessarily sounds good together. Frequencies that are fractions and multiples of one another sound good together. An octave (e.g. A below middle-C to the next higher A) doubles in frequency. That first A is 220Hz, and the higher one is 440Hz. In the standard Western scale, there are 12 semitones. The frequency of each note is derived by multiplying the proceding note by the twelfth root of two. So is A is 220Hz, then A# is (220 x 2sup[/sup]) 233.08Hz and the frequency of B is (233.08 x 2sup 246.94Hz.
This difference in frequency is called a half-tone. There is a trade-off between making notes and their harmonics match the exact frequency of other notes, and having sharps and their corresponding flats be identical. One of the most pleasant sounds in music is a perfect fifth; for example, a C and a G played simultaneously. The third harmonic generated when you play a middle C is about (if I remember how to calculate this properly) 784.88Hz. The second harmonic above the G in the same octave is 783.99Hz. This is the modern scale which is used today, and results in A# and Bb having the same frequency. The alternative, which Bach was a big fan of (among others) was instead to adjust the scale so the harmonics of a given interval aligned themselves perfectly. The disadvantage to this system is that it disaligns sharps and flats, meaning instruments would need to be retuned to change scales.
About scales. Major and minor scales (and their various related modes) are groups of eight notes from the subset of the 12 notes in the western scale. A major scale consists of the intervals of a full tone, full tone, semitone, full tone, full tone, full tone, semitone). On a piano, the distance between any two adjacent keys, including black keys, is a semitone. You may notice that the black keys are arranged in such a way that if you start on C, and play all the white keys, you play a major scale. That’s C major. There are twelve major scales, one for each note. There are other scales, like minor scales, which use different intervals from the 12 available tones.
Now, can you believe I know all that and don’t even play an instrument? 
friedo, I’m not disagreeing with you.
But let me point out that when you say this: “You can make noises at any frequency you wish, but they won’t necessarily sounds good together” you’re making a value judgement. And different combinations of notes will sound good to different people (and groups of people).
With western cultural domination it’s easy to become so accustomed to the 4/4 rhythmic and I-IV-V chord structure that all else seems odd. But there are places where it’s not.
There’s no value judgment here. Other scales besides the western one are based on the same principles of harmonics, just organized in a different way. If you play two notes that are not harmonically compatible, you get an ugly waveform. Ugly waveforms sound irritating. This isn’t a matter of opinion, it’s universal. Find me someone who enjoys the sound, of, say, a baby screaming, and maybe I’ll change my outlook. I’m not talking here about chord progressions or melodies, but harmonies.
And so am I. But oddball combinations of notes to make what we would call ‘off key’ combinations are sometimes considered desirable in other cultures.
You’re right that certain harmonics resonate in ways we would consider proper. But that by no means implies that other musical traditions would do so.
Jonathan, are you then arguing that those other cultures just randomly put together notes with no sense of harmonics? Even quarter-tones are related by fractions. You’re the one using terms like “oddball” and “off-key,” so don’t start arguing value judgement issues until you get over your own prejudices.
You don’t even have to go to another culture to find unusual combinations of notes. A great deal of 20th century western composers have used harmonies that sound shocking to someone who is used to hearing earlier “classical” music. For example, I remember playing a piece that had two different keys at the same time. It’s not a value judgment to say that you can’t just pick any two keys to throw together and sound good.
Besides, one could argue that since music is a performance art, its value depends strongly upon the opinions of your audience.
Are you sure? I had understood that Bach was rather a proponent of the uniform scale we use today. Re-tuning at every key change would make it pretty well impossible to play, say, the Ascending Canon.
I agree that ‘oddball’ might be too much, but ‘off key’ is a technical term.
And no, I’m not saying that other cultures put together notes at random, only that, regardless of harmonies, other cultures will find other combinations positive or negative.
And music is ‘performance art’ only for the audience half the time. I’ve spent more time playing just to play than ever for an audience.
You’re probably right – it’s been a long time since I studied this stuff.
Jonathan Chance
I’m not sure what you mean by “regardless of harmonies.” Other musical scales are certainly based on different harmonies than the western one, but they are harmonies none-the-less.
Even other eastern scales can be represented correctly as subsets of the modern 12-tone scale in use in the west. The popular Pentatonic scale, used in Greek and Chinese cultural music a great deal, is a subset of a western major scale.
Quarter-tone scales, which can be classified as a super-set of the standard western scale, are still based on the same mathematical principles that govern all sound. You’re given more options with quarter-tones, but a perfect-fifth is still a popular interval, and two adjacent notes played simultaneously sound dissonent and grating. There is certainly a place for dissonence in music; the minor third, for instance, can sound beautiful and haunting when used well. But that is because all notes on a scale are harmonically related (that’s the whole point of a scale.) My original point, which perhaps I didn’t make clearly, is that all notes on a scale must be related to each other in some way in order to make pleasant sounds. If you construct a scale of completely random frequencies and harmonics, it will sound awful. That’s guaranteed or your money back.
Well if you don’t take harmony or at least relative harmoniousness of pitch into account, you no longer have music, but noise. And what definition of off-key are you using?
Also, playing just to play still takes an audience into account… yourself. As my orchestra director is fond of saying, the most important audience you’ll ever play for is yourself.
hmmm - there is one exception/qualification to this general statement that I’m aware of, namely the way the standard notation system is used for the Great Highland Bagpipe. Although the standard notation is used, it has a different meaning than with other instruments. It’s rather like the fact that standard spelling is used in English, but there are regional pronunciations, where a particular written word may sound quite different with different speakers.
To start with, the basic tonic note of the GHB, its pitch, is conventionally written as A above middle C. However, the note that pipers call A is actually closer to B flat, as played on a piano. Since all of the notes in the piping scale are named in relation to A, they are all correspondingly out of step with the classic notation.
In addition, the scale played on the GHB doesn’t match the notation. The GHB has a nine note range, from G to high A, and if you look at a piece of pipe music, it may look like it uses the standard notation. But if you look closely, you’ll see that there’s no key notation given, nor do you usually see any indication for sharps and flats, which might suggest everything is in C major. However, if you hear the nine notes played in sequence on the chanter, it doesn’t match a C major scale. That’s because the GHB notes don’t match the normal “tone-tone-semitone” pattern - some of the steps are different. What a piper calls C is really C#, and the F is really an F#. So based on the internal steps, the scale could be written A, B, C#, D, E, F#, G, A. But we don’t do that, because the GHB aren’t a chromatic instrument, so there’s no point in making that distinction.
Which doesn’t mean that the standard notation isn’t used, just that bagpipes use a special variant of it, where the standard notation does not match the actual sounds produced. This isn’t a problem for pipers, but it can be a problem if a piper is trying to play with someone using another instrument. If the two don’t appreciate the differences in what the notation means for each instrument, they aren’t likely to get very far in their duet.
Yeah, well, bagpipes are a “special variant” of about everything. There are some folks who even think the cacophony that bagpipes make is “music.”
::: ducking :::
Just kidding, Piper, I actually like bagpipe music and have several CDs of bagpipes.
I use them when I want to scare the cats from the garbage cans.
Oooh another piper… not that I qualify as one just yet, but oh well 
This discrepancy isn’t as bad as you think. Lots of other instruments don’t play the notes as written, they’re known as transposing instruments. Granted, they’re usually “off” by more “normal” intervals than the GHB (for example, a written C played on clarinets and trumpets is actually a B-flat in concert pitch).
As for the other idiosyncracies of the GHB, it uses a different scale from the “classical” major and minor, I believe it’s the mixolydian scale (will do a bit of research here…). I have seen some 'pipe music written with the sharps (F# and C#). Of course, as you mention, it doesn’t matter either way since we can only play certain notes.
Actually, the way my teacher (and his teacher and HIS teacher) learned was aurally, so the written music didn’t really matter. IIRC, in the olden days, the “only” way to learn GHB was by ear, so the modern written notation is just a (surprisingly good, given the circumstances) way of fitting the music into a visual format.
Sigh. Not to dignify this with a response, but IIRC, the GHB was developed as a war instrument to scare away enemy soldiers…
Oh, and one other thing…
I think everyone so far has mentioned that A=440Hz. That’s typically what American orchestras tune to (that’s what I normally set my tuner to, as an oboist). I believe it may be in Europe that they tune A=435Hz or something like that… either way, different cultures have different preferences for what “A” should sound like.
In England, A’s got as high as 455Hz and in the US as high as 461Hz. This was not a huge deal for stringed instruments which could be tuned to any pitch, but obviously it made wind instruments which have to be built to an exact frequency that much more difficult to make. A flute built for A=455Hz could not be used with violins tuned to A=461Hz. An international standard of A=440Hz was finally agreed upon sometime in the 1950s, IIRC. I believe it’s an official ISO standard.
Of course, you’re still free to tune your instruments however you like, but don’t be surprised if the obo guy gets annoyed. 
'salright, CK - I have neighbours who sometimes decide to discuss their family problems in their back yard, letting everyone else hear.
I just go out and start practising.
They tend to take it inside.
