I recently became curious as to why humans perceive exactly 12 notes in a musical octave. As far as I can tell this is not culturally specific - the music of all cultures is still made up of these 12 notes.
After some searching, I finally found this page which identifies the problem. The page led me to the horrifying revelation that the reason why the scale is divided this way is unknown. The author of the page seems to be well qualified as he has recently published his PhD dissertation on a closely related topic.
But anyway, I was just wondering if anyone had any further insight into this issue.
One thing I had a problem with is his statement:
It seems to be there is quite a bit known about why we see colours the way we do - it boils down to our having three types of receptors in our eyes (cones), each of which corresponding to what we call primary colours. The other colours are simply different combinations of the three primaries. So what it “feels like” to see red is that the brain areas connected to cones responsible for red are being strongly activated, while the areas connected to the other cones are relatively inactive.
I’m sure someone will come along and answer this more better [sic] than I can, but I believe the answer to that guy’s basic question (why 12?) is that 5 isn’t enough and 19 is too many.
In my experience, people who want deep, meaningful answers to such questions just miss the obvious. I would think it’s pretty obvious that 5 notes per octave just doesn’t give you enough musical range. And If I remember correctly, the 12-note scale was developed when the predominant instrument was the piano, which has keys. So trying to have 19 notes per octave would make for an unwieldly instrument where the keys that are an octave apart are too far apart physically for a human to reasonably play the kind of music that we want to play.
So the 12 note scale was developed as the most reasonable compromise that gives us enough notes to make good music while still being able to make keyboards that can be played. Simple as that.
What do you mean exactly by “the music of all cultures is still made up of these 12 notes?” The Arabic maqam system, for instance, is based on a 24-note system (which is still imprecise), although they may only use 7 of these at any one time. You’ll also find lots of microtones in Indian raga, as well.
I didn’t look at your link, but my explanation (and I’ve provided this before, maybe we need a sticky )
The ancient Greeks picked tones based upon ratios in the Harmonic series, i.e. Natural harmonics of a fundamental frequency. For example the 2/1 ratio is the octave, 3/2 is the interval we now call the “Perfect Fifth”.
they picked seven tones for their scales. Other cultures did something similar, but picked 5,6,8,11,13… so this step is arbitrary.
the Greek scales (which they based upon starting points) became generalized into the modern Major and Minor scales.
it was realized that the intervals between adjacent notes were not even. There were 5 big gaps and 2 small gaps. Even worse, the big gaps came in two varieties. This was a big headache for various reasons, so extra semi-tones were inserted leaving 12 semi-tones in an octave.
The is a great simplification, and at every step I’ve had to gloss over many subtleties.
These answers boil down to the idea that dividing the scale into 12 was simply a historical choice, like the number of characters in the alphabet, and these notes sound “right” to us simply because we are used to them. I initially considered this to be the most plausible explanation. However, upon further research it seems that the “12 golden tones” have arisen independently in isolated cultures.
For instance, the pentatonic scale was the basic scale of China and other Asian cultures. The pentatonic scale contains 5 of the 12 golden tones. The major and minor scales were used in European cultures each consist of a particular 7 of the 12 tones. It wasn’t until much later that the 12 tone chronomatic scale was actually recognized and found to contain all the notes needed for these and other scales.
Neither would most people, but that’s unrelated to the question. It’s about relative spacing between notes, not the particular frequencies. You would definitely notice if you heard music that contained 29 notes per octave. Specifically, it would not sound musical.
This is not true. There are plenty of musical cultures that do not use a 12-tone scale. For example, Indian Ragas can be thought of as using a 22 tone scale. Gamelan uses pentatonic and heptatonic scales. Arabic music uses a system of 24 tones per octave. Furthermore, there is a rich tradition of microtonal music in the west also.
Furthermore, anyone who has played violin, or any fretless bowed string instrument, will know that there are far more than 12 tones in an octave. Try this experiment: if you tune your open A string to 440 Hz, the D string below will thus be at 293.3 Hz (440 * 0.6666 a perfect fifth below) and the open E string at 660 Hz (440 * 1.5). Now place your finger on the A string so as to play a B, and play this note together with the open D, you now have a major sixth: 293.3 * 5/3 = 488.8 Hz. Now, this sounds “right”. Without moving your finger, now play the B-E interval with the other open string. It’s now going to sound terribly out of tune. What happened? B-E is a perfect fourth, so if E = 660 Hz, B = 660 * 3/4 = 495 Hz. Which is the real B?
Of course, neither are, that why in just intonation we talk about intervals rather than tones. If your read the article on microtonal music, you’ll see that for most of western music’s history intervals rather than tones were the norm. If you listen to a viol, a fretted bowed string instrument, you’ll notice that the tuning sounds a bit off to western ears. For instruments that use the tempered scale, this is much less noticeable. This has probably to do with the timbral characteristics of the sound as well as a fair bit of cultural conditioning.
A much better, and more difficult question is: why do we perceive an octave as being the same note? Sure, it’s a nice mathematical ratio, but that’s not a perceptual explanation. Interestingly, monkeys also perceive octaves as similar (pdf), which points to the fact that at least part of our pitch perception is hard-wired, and not solely a product of education.
Not just that - we like tones that are whole ratios, and the basic ratios are better approximated by 12 equal tones than 19. 3/4 = 9/12, 1/2 = 6/12, 1/8 = 1.5/12 (hurrah for 24 tone systems!), but none of those are approachable in a 19-tone system.
This doesn’t make the slightest sense - sorry for the bluntness!
Music using a recognisable sound and notation using the familiar division of tones and semitones was composed for a long period before major and minor keys became dominant. The semitone, at the centre of a hexachord (CDEFDA), goes right back to chant from over a thousand years ago.
Also, many pentatonic systems use a choice of five pitches which have no relation whatsoever with the western scales. Slendro is, in effect, a Javanese 5-note equal temperament…
I think you’re suffering from a case of ‘pattern finding’.
Read the Even Tempered link above to get a better sense of the compromise involved to make the ‘golden tones’ you indicate are universal. It is indeed a case of familiarity and chromatic use-ability.
The A at 440 was another Western arbitrary choice.
Even when you listen to something that is nominally noted on a Western scale, like, say, bagpipe music. The fourths and sevenths there don’t exactly correspond to fourths and sevenths on a piano. Look here for some examples of bagpipe scales.
Ah, very interesting. Although it’s still a bit suspicious that it’s 24, and not a number unrelated to 12.
Also, according to my understanding of this link, the notes used in any particular piece of Indian Raga music do correspond to notes on the chromatic scale.
I had a pupil tune her viola just this week, after playing an A on the piano, and after she was finished it sounded WRONG to me. Her response was ‘that’s how it is on my electronic tuner’ - she’d tuned correctly, by memory, to equal temperament (she was spot-on with the electric piano C), which isn’t how I normally tune, preferring pure fifths and bringing the E down a touch in ensemble situations. I gave a hurried explanation of the dilemma of temperament, especially as we were working on solo Bach, but I need to go into it in more detail with her another time!
Wow! I wouldn’t have expected so many answers while I was typing my post!
I disagree, rather, it wouldn’t sound western. There’s a lot of music out there the very notion of tonality isn’t particularly relevant. This track may not be to everyone’s taste, but I hope that you’ll still recognize it as music.
‘Correspond to’ doesn’t mean that they’re the same - it’s easy to get into the position of falsely finding equivalence with the chromatic scale in a way which can obscure particular features of another system.
I said extra semi-tones were inserted. I called the greek intervals “5 bigs and two smalls”, implying tones and semi-tones. The Greeks didn’t care about the gaps. That became a problem later when you tried to start a major scale (TTSTTTS) on the second note of the scale… at that point you realize that you need a note between each of the big gaps.
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