# Music: 12 Notes/Octave - No Known Explanation?? **URL:** \ **Category:** Factual Questions\ **Created:** [February 6, 2009, 12:10am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645 "2009-02-06T00:10:57Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Bad\_Astronaut](https://avatars.discourse-cdn.com/v4/letter/b/e19adc/32.png) [@Bad\_Astronaut](https://boards.straightdope.com/u/Bad_Astronaut)\ **Post date:** [February 6, 2009, 12:10am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/1 "2009-02-06T00:10:57Z")
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](http://www.skytopia.com/project/scale.html) 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: > [@](#): > > Firstly, it’s always a possibility that there may be no mathematical explanation why there are 12 notes. In the same way that science can’t explain what it ‘feels’ like to see the color ‘red’, perhaps the notes of the scale are beyond mathematics, and reach into the qualia/metaphysical/spiritual realm (if it exists). 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. ---
**Author:** ![Roadfood](https://avatars.discourse-cdn.com/v4/letter/r/9fc348/32.png) [@Roadfood](https://boards.straightdope.com/u/Roadfood)\ **Post date:** [February 6, 2009, 12:27am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/2 "2009-02-06T00:27:41Z")
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. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 6, 2009, 12:36am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/3 "2009-02-06T00:36:43Z")
> [@Bad\_Astronaut](#): > > 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. 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. ---
**Author:** ![K364](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k364/32/5_2.png) [@K364](https://boards.straightdope.com/u/K364)\ **Post date:** [February 6, 2009, 12:39am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/4 "2009-02-06T00:39:05Z")
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. ---
**Author:** ![foolsguinea](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/foolsguinea/32/14751_2.png) [@foolsguinea](https://boards.straightdope.com/u/foolsguinea)\ **Post date:** [February 6, 2009, 12:42am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/5 "2009-02-06T00:42:43Z")
I dunno, I’m sort of note-blind. I don’t really notice when a tune is transcribed to a different key, so defined notes mean very little to me. ---
**Author:** ![Bad\_Astronaut](https://avatars.discourse-cdn.com/v4/letter/b/e19adc/32.png) [@Bad\_Astronaut](https://boards.straightdope.com/u/Bad_Astronaut)\ **Post date:** [February 6, 2009, 12:48am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/6 "2009-02-06T00:48:28Z")
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. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 6, 2009, 12:50am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/7 "2009-02-06T00:50:51Z")
> [@Bad\_Astronaut](#): > > 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. But the 12 chromatic tones _don’t_ cover all the notes in Indian or Arabic music. See [here](http://en.wikipedia.org/wiki/Arab_tone_system) for Arab tone system. ---
**Author:** ![Bad\_Astronaut](https://avatars.discourse-cdn.com/v4/letter/b/e19adc/32.png) [@Bad\_Astronaut](https://boards.straightdope.com/u/Bad_Astronaut)\ **Post date:** [February 6, 2009, 12:51am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/8 "2009-02-06T00:51:02Z")
> [@foolsguinea](#): > > I dunno, I’m sort of note-blind. I don’t really notice when a tune is transcribed to a different key, so defined notes mean very little to me. 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. ---
**Author:** ![Superfluous\_Parentheses](https://avatars.discourse-cdn.com/v4/letter/s/8edcca/32.png) [@Superfluous\_Parentheses](https://boards.straightdope.com/u/Superfluous_Parentheses)\ **Post date:** [February 6, 2009, 12:53am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/9 "2009-02-06T00:53:59Z")
> [@Bad\_Astronaut](#): > > 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. Except that these 12 tones are a compromise. See [equal temperament](http://en.wikipedia.org/wiki/Equal_temperament) ---
**Author:** ![jovan](https://avatars.discourse-cdn.com/v4/letter/j/0ea827/32.png) [@jovan](https://boards.straightdope.com/u/jovan)\ **Post date:** [February 6, 2009, 12:57am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/10 "2009-02-06T00:57:17Z")
> [@Bad\_Astronaut](#): > > 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. This is not true. There are plenty of musical cultures that do not use a 12-tone scale. For example, [Indian Ragas](http://en.wikipedia.org/wiki/Raga) can be thought of as using a 22 tone scale. [Gamelan](http://en.wikipedia.org/wiki/Gamelan) uses [pentatonic](http://en.wikipedia.org/wiki/Sl%C3%A9ndro) and [heptatonic](http://en.wikipedia.org/wiki/P%C3%A9log) scales. Arabic music uses a [system of 24 tones](http://en.wikipedia.org/wiki/Arab_tone_system) per octave. Furthermore, there is a rich tradition of [microtonal music](http://en.wikipedia.org/wiki/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](http://www.youtube.com/watch?v=nyQ1b6_qKFA&feature=related), 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](http://www.cogsci.ucsd.edu/~creel/COGS160/COGS160_files/Wright2000.pdf) (pdf), which points to the fact that at least part of our pitch perception is hard-wired, and not solely a product of education. ---
**Author:** ![Superfluous\_Parentheses](https://avatars.discourse-cdn.com/v4/letter/s/8edcca/32.png) [@Superfluous\_Parentheses](https://boards.straightdope.com/u/Superfluous_Parentheses)\ **Post date:** [February 6, 2009, 1:00am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/11 "2009-02-06T01:00:37Z")
> [@Roadfood](#): > > 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. 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. ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [February 6, 2009, 1:01am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/12 "2009-02-06T01:01:33Z")
> [@K364](#): > > 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. 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](http://en.wikipedia.org/wiki/Slendro) is, in effect, a Javanese 5-note equal temperament… ---
**Author:** ![CheapBastid](https://avatars.discourse-cdn.com/v4/letter/c/8baadc/32.png) [@CheapBastid](https://boards.straightdope.com/u/CheapBastid)\ **Post date:** [February 6, 2009, 1:01am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/13 "2009-02-06T01:01:42Z")
> [@Bad\_Astronaut](#): > > 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. 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. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 6, 2009, 1:04am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/14 "2009-02-06T01:04:44Z")
> [@Superfluous\_Parentheses](#): > > Except that these 12 tones are a compromise. See [equal temperament](http://en.wikipedia.org/wiki/Equal_temperament) 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](http://www-personal.umich.edu/~emacpher/pipes/acoustics/pipescale.html) for some examples of bagpipe scales. ---
**Author:** ![Bad\_Astronaut](https://avatars.discourse-cdn.com/v4/letter/b/e19adc/32.png) [@Bad\_Astronaut](https://boards.straightdope.com/u/Bad_Astronaut)\ **Post date:** [February 6, 2009, 1:05am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/15 "2009-02-06T01:05:59Z")
> [@pulykamell](#): > > But the 12 chromatic tones _don’t_ cover all the notes in Indian or Arabic music. > > See [here](http://en.wikipedia.org/wiki/Arab_tone_system) for Arab tone system. 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](http://cnx.org/content/m12459/latest/), the notes used in any particular piece of Indian Raga music do correspond to notes on the chromatic scale. ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [February 6, 2009, 1:08am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/16 "2009-02-06T01:08:35Z")
> [@jovan](#): > > 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? 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! ---
**Author:** ![jovan](https://avatars.discourse-cdn.com/v4/letter/j/0ea827/32.png) [@jovan](https://boards.straightdope.com/u/jovan)\ **Post date:** [February 6, 2009, 1:09am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/17 "2009-02-06T01:09:19Z")
Wow! I wouldn’t have expected so many answers while I was typing my post! > [@Bad\_Astronaut](#): > > You would definitely notice if you heard music that contained 29 notes per octave. Specifically, it would not sound musical. I disagree, rather, it wouldn’t sound _western_. There’s a lot of [music](http://www.youtube.com/watch?v=nfwD05XA2YQ) out there the very notion of tonality isn’t particularly relevant. [This track](http://www.youtube.com/watch?v=IPMETWcAwKA&feature=related) may not be to everyone’s taste, but I hope that you’ll still recognize it as music. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 6, 2009, 1:10am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/18 "2009-02-06T01:10:49Z")
> [@Bad\_Astronaut](#): > > 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](http://cnx.org/content/m12459/latest/), the notes used in any particular piece of Indian Raga music do correspond to notes on the chromatic scale. Read a little further: > [@](#): > > In some ragas, some notes may be flattened or sharpened by one shruti, in order to better suit the mood and effect of that raga. So, for tuning purposes, the octave is divided into 22 shrutis. This is only for tuning, however; for any given that or raga, only twelve specifically-tuned notes are available. The 22 shrutis each have a specific designation, and the intervals between them are not equal; the frequency ratios between adjacent shrutis ranges from about 1.01 to about 1.04. > > In spite of the fact that these tunings are based on the physics of the harmonic series, Indian music can sound oddly out of tune to someone accustomed to equal temperament, and even trained Western musicians may have trouble developing an ear for Indian tunings. As of this writing, one site devoted to helping Western listeners properly hear Indian tunings was The Perfect Third. So, it depends for you on where temperament ends and where scales begin. But more on Arab music. It seems to me that the 24-note system is simply a shorthand. [Read up here.](http://en.wikipedia.org/wiki/Quarter_tone) Note that: > [@](#): > > The quarter tone scale may be primarily considered a theoretical construct in Arabic music. The quarter tone gives musicians a “conceptual map” which with to discuss and compare intervals by number of quarter tones and this may be one of the reasons it accompanies a renewed interest in theory, with instruction in music theory being a mainstream requirement since that period.[2] > > Previously pitches of a mode where chosen from a scale consisting of seventeen tones, developed by Safi 'I-Din al-Urmawi in the thirteenth century.[3] ---
**Author:** ![GorillaMan](https://avatars.discourse-cdn.com/v4/letter/g/50afbb/32.png) [@GorillaMan](https://boards.straightdope.com/u/GorillaMan)\ **Post date:** [February 6, 2009, 1:10am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/19 "2009-02-06T01:10:51Z")
> [@Bad\_Astronaut](#): > > 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](http://cnx.org/content/m12459/latest/), the notes used in any particular piece of Indian Raga music do correspond to notes on the chromatic scale. ‘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. ---
**Author:** ![K364](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k364/32/5_2.png) [@K364](https://boards.straightdope.com/u/K364)\ **Post date:** [February 6, 2009, 1:11am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/20 "2009-02-06T01:11:03Z")
> [@GorillaMan](#): > > 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. 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. [Next page](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645.md?page=2)