# 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:** 2
**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, 1:19am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/21 "2009-02-06T01:19:06Z")
> [@pulykamell](#): > > 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. That’s what I meant? 😕 edit: what I meant is that equal temperament etc **are** the compromises. ---
**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, 1:20am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/22 "2009-02-06T01:20:40Z")
> [@K364](#): > > 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. Hexachord theories allowed for the transposition of the whole system, allowing B/B flat to become E/E flat, etc…and I’m certainly not talking about Greeks, but about 15th and 16th century guys! Also, I have to say that the idea of ‘big gaps’ and an ‘extra note’ does have a whiff of piano-centricity. ---
**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, 1:25am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/23 "2009-02-06T01:25:09Z")
> [@Superfluous\_Parentheses](#): > > That’s what I meant? 😕 > > edit: what I meant is that equal temperament etc **are** the compromises. Sorry, I’m actually agreeing with you and adding other examples for **Bad Astronaut** ’s edification. I didn’t mean to quote as a contradiction of your post. edit: I think. Unless now I’m misunderstanding what you were saying. But I think we’re on the same page. ---
**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, 1:28am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/24 "2009-02-06T01:28:17Z")
At this point I’m reasonably well convinced that scales are merely cultural constructs, which is interesting in itself. Also, I was curious about Native American music since we can be pretty confident that there was no cultural contact between the Old and New worlds between the last ice age and the 15th century. Sure enough, their music is vastly different: > [@](#): > > Native American music is often described as pentatonic or five note in nature. And this is given as one of the reasons for it’s “unusual” sound. However just because a scale has five notes doesn’t necessarily make it pentatonic as we understand it. The “true” pentatonic scale is just a subset of the Western/European diatonic (do, re, me) scale and has been used by all European cultures including the Scottish and Irish for tens of thousands of years. What makes the Native American scales sound so alien is that the pitches of the five notes are seemingly chosen at random. They vary from tribe to tribe, family to family, and person to person. > [Source](http://parlorsongs.com/insearch/amerindian/amerindian0.php) Also I’m not **Bad Astronomer**. If I’d known that was a well-known username on this board I would have picked a different one. ---
**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, 1:28am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/25 "2009-02-06T01:28:55Z")
> [@GorillaMan](#): > > Hexachord theories allowed for the transposition of the whole system, allowing B/B flat to become E/E flat, etc…and I’m certainly not talking about Greeks, but about 15th and 16th century guys! Also, I have to say that the idea of ‘big gaps’ and an ‘extra note’ does have a whiff of piano-centricity. Have you ever fingered a Violin, Guitar, etc? There are big and small gaps in the diatonic scale. Don’t be worrying 'bout my piano! ---
**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, 1:29am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/26 "2009-02-06T01:29:36Z")
> [@Bad\_Astronaut](#): > > Also I’m not **Bad Astronomer**. If I’d known that was a well-known username on this board I would have picked a different one. I just edited my post when I realized the error, but you beat me to it. ---
**Author:** ![Aspidistra](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aspidistra/32/3894_2.png) [@Aspidistra](https://boards.straightdope.com/u/Aspidistra)\ **Post date:** [February 6, 2009, 1:34am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/27 "2009-02-06T01:34:16Z")
We had a big thread on [a similar topic](http://boards.straightdope.com/sdmb/showthread.php?t=503007) just a couple of weeks ago. My gut reaction to that page is that it’s a big exaggeration to say there’s _no_ known reason for 12 notes in the octave. There’s plenty of reasons on his page alone (some of them ridiculous) - it’s just a matter of argument which one put the 12-note octave “over the line” as far as popularity is concerned. I think the “circle of fifths” argument provides a pretty good argument for the 12-note octave. If you take the simplest possible ratio of vibrations (3:2) and start stepping up, you get close to a power of two greater (ie, the “same note” as far as our brains process sounds) at steps 5, 7 and 12. And 12 is, of the three, by far the best fit. Or, to put it another way, if you construct a set of equal-temperament 12, 5 and 7 “octaves”, the 12-note one is far better at replicating the simple rations (3:2, 4:3, 5:3 etc) than either the 5-note or the 7-note (a fifth in the standard octave is only 0.1% off being an exact match to a 3:2 ratio, whereas the corresponding notes in a 5-note or 7-note scale are 1% off) Also, interestingly, if you look at a keyboard instrument, its 12 notes are split into a 5-note set and a 7-note set - obviously you don’t get an equal temperament scale out of either set exactly, but it’s interesting to see that if you go with a 12-note set you can get the 5 and 7 sort of “thrown in”. I can’t see that any other choice of base would give you so much flexibility. ---
**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, 1:36am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/28 "2009-02-06T01:36:07Z")
> [@Bad\_Astronaut](#): > > 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. But that I can’t tell you when a flat B becomes an A would indicate that to me, at least, there is not necessarily any “golden tone.” A golden interval, maybe. But these particular tones, are they anything really? ---
**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, 1:43am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/29 "2009-02-06T01:43:52Z")
> [@foolsguinea](#): > > But that I can’t tell you when a flat B becomes an A would indicate that to me, at least, there is not necessarily any “golden tone.” A golden interval, maybe. But these particular tones, are they anything really? The meaning of ‘tones’ in this discussion, at least my part of it, would be more accurately described as ‘intervals’ as you say. It seems pretty obvious to me that 440 Hz is a completely arbitrary basis, since a second is a rather arbitrary length of time (1/86400 of the time it takes the earth to rotate once on its axis). Our brains seem to only care about the intervals. ---
**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, 1:47am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/30 "2009-02-06T01:47:38Z")
> [@K364](#): > > Have you ever fingered a Violin, Guitar, etc? > > There are big and small gaps in the diatonic scale. Don’t be worrying 'bout my piano! I teach one of the above. (The reference to a viola pupil is a hint!) However, I’m not afraid to acknowledge that it’s a newcomer, embraced long after the issues of scales and intonation were already being debated. My point is that it’s easy to perceive scales _in relation to_ a piano keyboard, and by extension to perceive other systems in such a way. Far better to try singing along with them, to get a real feel for where the important differences are. (Guitars? Tuning? Intonation? Is that a joke? 😉 ) **Aspidistra** ’s description is very much a case of working from the present, that we have a system which functions well with keyboard instruments, and therefore this is where we inevitably arrived. The split in the keyboard directly corresponds to the transposition of hexachords I’ve mentioned earlier. ---
**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, 2:00am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/31 "2009-02-06T02:00:51Z")
So I guess if we make contact with extra-terrestrials we should not expect to find any common ground with music, contrary to the theories of Spielberg et al. We should still be ok on primes though! Cleaning up a few points I wanted to respond to: > [@jovan](#): > > 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. I didn’t mean you would perceive it as noise, just that you would know it was different. I know there is microtonal Western music, but it sounds microtonal and is clearly distinguishable from ‘regular’ or what I would consider ‘melodic’ music. It’s hard to describe the difference in meaningful terms. > [@jovan](#): > > 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. I think there are some things that can be said about this. A single note from a real instrument (including a singer) consists of a a fundamental plus various harmonics. If we perceived the harmonics as different notes there would be no such thing as a single note. Even with electronic systems you cannot produce a pure tone - all amplifiers and speakers produce some distortion (although with modern technology it can be made small enough not to matter). So you could theorize that our brains evolved to lump these harmonics together in order to reduce the number of distinct events that needed to be processed. ---
**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, 2:06am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/32 "2009-02-06T02:06:59Z")
> [@Bad\_Astronaut](#): > > I think there are some things that can be said about this. A single note from a real instrument (including a singer) consists of a a fundamental plus various harmonics. If we perceived the harmonics as different notes there would be no such thing as a single note. Even with electronic systems you cannot produce a pure tone - all amplifiers and speakers produce some distortion (although with modern technology it can be made small enough not to matter). It’s worth nothign that a major third, tuned to equal temperment, played by a signal generator, sounds BAD. On a piano, it sounds normal and natural (to western ears!) ---
**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, 2:11am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/33 "2009-02-06T02:11:42Z")
> [@Bad\_Astronaut](#): > > 440 Hz is a completely arbitrary basis, since a second is a rather arbitrary length of time (1/86400 of the time it takes the earth to rotate once on its axis). Our brains seem to only care about the intervals. Actually, that’s also mistaken. Your inner ear is tuned to respond to particular frequencies in such a way that a 440 Hz tone will always excite the same [hair cells](http://en.wikipedia.org/wiki/Hair_cell). People with [absolute pitch](http://en.wikipedia.org/wiki/Perfect_pitch) can tell pitches independently of others. Now, most people are much better at telling intervals apart, but the brain most definitely can perceive absolute frequency. After all, you’ll never mistake a 200 Hz tone for a 5000 Hz tone. So, while it’s true that the particular value of 440 Hz is arbitrary and far from universal, seconds aren’t really relevant to the discussion. ---
**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, 2:22am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/34 "2009-02-06T02:22:15Z")
> [@jovan](#): > > Actually, that’s also mistaken. Your inner ear is tuned to respond to particular frequencies in such a way that a 440 Hz tone will always excite the same [hair cells](http://en.wikipedia.org/wiki/Hair_cell). People with [absolute pitch](http://en.wikipedia.org/wiki/Perfect_pitch) can tell pitches independently of others. Now, most people are much better at telling intervals apart, but the brain most definitely can perceive absolute frequency. After all, you’ll never mistake a 200 Hz tone for a 5000 Hz tone. I knew someone would point this out. I know the ear/brain can detect the difference, but as far as judging the ‘musicality’ of notes everything is relative. Even people with perfect pitch can tell whether one note is a perfect third above the other, regardless of the absolute pitches. > [@jovan](#): > > So, while it’s true that the particular value of 440 Hz is arbitrary and far from universal, seconds aren’t really relevant to the discussion. They are relevant in that the standard is 440 Hz, and not 440.2612374 Hz. If the standard was non-arbitrary we would not expect it to be an even multiple of an arbitrary unit (A Hz is defined as 1/second if anyone is not following this). ---
**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, 2:24am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/35 "2009-02-06T02:24:49Z")
> [@Bad\_Astronaut](#): > > So you could theorize that our brains evolved to lump these harmonics together in order to reduce the number of distinct events that needed to be processed. It’s not so much a question of reducing the number of events as one of providing a likely interpretation. The brain receives low-level signals from the brain that correspond to amplitude levels of various frequency bands – much like a Fourier transform. From this data, the brain has to construct an _auditory scene_ that corresponds as much as possible to the real objects and events that caused those sounds if it is to survive. Since the harmonic series occurs naturally, grouping tones that belong to this series together will, in most cases, provide a “correct” interpretation of the data. > [@Bad\_Astronaut](#): > > They are relevant in that the standard is 440 Hz, and not 440.2612374 Hz. If the standard was non-arbitrary we would not expect it to be an even multiple of an arbitrary unit (A Hz is defined as 1/second if anyone is not following this). Okay, I see what you mean. (Perceptually, though, 440 Hz and 440.2612374 Hz are almost the same. I thought the question was why 440 and not 480, we do like round numbers.) ---
**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, 2:30am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/36 "2009-02-06T02:30:38Z")
> [@Bad\_Astronaut](#): > > They are relevant in that the standard is 440 Hz, and not 440.2612374 Hz. If the standard was non-arbitrary we would not expect it to be an even multiple of an arbitrary unit (A Hz is defined as 1/second if anyone is not following this). Huh? Cycles/second is certainly an arbitrary quantity, because its use in the measurement of the pitch of sounds has no connection with the origination of ‘second’. ---
**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, 2:32am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/37 "2009-02-06T02:32:18Z")
> [@jovan](#): > > Perceptually, though, 440 Hz and 440.2612374 Hz are almost the same. They’d be noticably different on violins, though 🙂 ---
**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, 2:33am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/38 "2009-02-06T02:33:53Z")
> [@jovan](#): > > It’s not so much a question of reducing the number of events as one of providing a likely interpretation. The brain receives low-level signals from the brain that correspond to amplitude levels of various frequency bands – much like a Fourier transform. From this data, the brain has to construct an _auditory scene_ that corresponds as much as possible to the real objects and events that caused those sounds if it is to survive. Since the harmonic series occurs naturally, grouping tones that belong to this series together will, in most cases, provide a “correct” interpretation of the data. Yes. I think this is equivalent to what I was getting at. Another thing that occurs to me is that since receptors respond to specific frequencies, notes an octave apart will trigger most of the same receptors. The fundamental receptors won’t be activated for the higher note, but the harmonic receptors will be activated in a very similar pattern for both. So it’s not surprising that we perceive them to be so similar. ---
**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, 2:39am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/39 "2009-02-06T02:39:37Z")
> [@GorillaMan](#): > > Huh? Cycles/second is certainly an arbitrary quantity, because its use in the measurement of the pitch of sounds has no connection with the origination of ‘second’. Nevermind. This point is of no importance. It was pretty much meant as a joke when I mentioned seconds in the first place. As long as we all agree that 440 Hz is an arbitrary choice, it’s not worth discussing further. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [February 6, 2009, 2:46am UTC](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645/40 "2009-02-06T02:46:35Z")
> [@Roadfood](#): > > 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. When I was in college, I worked out that 19 notes / octave would work well, and built a guitar with 19 frets/octave. It was made from free discard parts from a local guitar store, but it sounded good (well, in-tune). [Previous page](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645.md?page=1) [Next page](https://boards.straightdope.com/t/music-12-notes-octave-no-known-explanation/484645.md?page=3)