# Where did the 12 notes come from?



## millionrainbows

I said in another thread, and was soundly refuted, that the 12-note octave division was generated by the pythagoran practice of "stacking fifths."

Does anybody agree or disagree with this, or have any words on the origins of our 12-note octave division?

https://en.wikipedia.org/wiki/Pythagorean_tuning


----------



## Kjetil Heggelund

Don't know why or how I should disagree  The 12 notes seem to be very natural for many people. Would be interesting to hear a modern, advanced piece, based on 13 notes! Has that been done?


----------



## millionrainbows

Kjetil Heggelund said:


> Don't know why or how I should disagree  The 12 notes seem to be very natural for many people. Would be interesting to hear a modern, advanced piece, based on 13 notes! Has that been done?


This link should explain it: start with Che2007's post # 57. You will see that all of his points are academic and nit-picking, and are all disputed by the WIK definition of Pythagoran tuning.

Music is sound, and sound is harmonic, and harmony is instantaneous, and sound is bei

For some reason, this person was 'after' me with a vengeance. I can't be sure where he came from, or who sent him, but I commend myself highly for keeping a clear mind and refraining from ad hominems, as he obviously did not.

As far as octave division, the 12-division is based on preserving fifths.

A "13" division is not based on any sort of musical principle that I can see. Other usable divisions are possible, of course. The Thai scale is based on a 7-tone equal division of the octave. Others include 17, 19, 31, 43, and 54. There are reasons for this, but I don't feel like posting them, unless you are seriously interested.


----------



## Kjetil Heggelund

Wow! That's intense  I see I "accidentally stepped into" the music theory area. I'm more into listening to music than discussion/argument. So I would like some examples of music based on other divisions of the scale, if you're so kind. (Something tells me you're the man to explain Ferneyhough's "Kurtze Schatten" for guitar). I apologize for straying off topic


----------



## millionrainbows

The reason for most of these smaller divisions is not for effect, but to approximate the real "just" intervals.

That's why Harry Partch uses the 43-tone division, or 54: he can approximate very closely the sound of "just" intervals, such as 3:2 fifths, or better major thirds, as 5:4.

Thai music is strictly melodic; it uses no chords, so I'm not sure why they divide the octave into 7 equal parts. When you play music in this tuning, it sounds strangely familiar, because we also use a 7-note diatonic scale.

Remember, these are all equal divisions, so the octave can be closed and be a true 1:2 ratio. A=440, A=880, etc.

All ET divisions of the octave are strictly arbitrary, though, and are not based on harmonic phenomena, but on interval size. As long as all the intervals are the same, and the octave is closed, it is ET.

This is logarithmic, and can be tricky. As you go higher in pitch, the spaces get smaller physically (like guitar frets get smaller) but the pitches remain constant in relation to each other. That means a D is a D, no matter how high or low. So you can see by this that octave equivalence is maintained not only in the octave, but in whatever octave you choose between any two notes. This makes excellent melodic sense, for playing melodies, even if it does not make sense harmonically.


----------



## millionrainbows

To explore alternate and microtonal tunings, try these:























​


----------



## Barbebleu

The twelve notes came from Thetans!!


----------



## StephenBailey

My understanding is that they came from the overtone series (i.e. the partials we hear as harmonics above a particular fundamental note). 
This gets a little hairy when you include things like equal temperament, but I believe that was the inception.


----------



## Pugg

StephenBailey said:


> My understanding is that they came from the overtone series (i.e. the partials we hear as harmonics above a particular fundamental note).
> This gets a little hairy when you include things like equal temperament, but I believe that was the inception.


Nice first post StephenBailey, welcome to Talk Classical.


----------



## fluteman

millionrainbows said:


> I said in another thread, and was soundly refuted, that the 12-note octave division was generated by the pythagoran practice of "stacking fifths."
> 
> Does anybody agree or disagree with this, or have any words on the origins of our 12-note octave division?
> 
> https://en.wikipedia.org/wiki/Pythagorean_tuning


Yes, I would agree. It turns out that the octave divides into twelve roughly equal parts if the fifths are "stacked" and then collapsed into a single octave.


----------



## fluteman

Kjetil Heggelund said:


> Don't know why or how I should disagree  The 12 notes seem to be very natural for many people. Would be interesting to hear a modern, advanced piece, based on 13 notes! Has that been done?


It has indeed been done. For example, Easley Blackwood wrote some interesting microtonal music, including his 12 Microtonal Etudes for each equal tempered scale from 13 to 24.


----------



## millionrainbows

It should be noted that in most all discussions of equal temperaments, whether 15, 19, or other possibilities, that the intervals resulting from these tunings are nearly always compared to naturally occurring harmonics, and are compared with how accurate they are in achieving approximations of these "just" intervals.

Also, usually not all of the notes in an ET are used at once. The Thai scale, a 7-note ET, is that way because they use pentatonic (5-note) scales, and the two extra notes are used selectively, to create different pentatonic "modes."

Likewise, in the Arabic division of 17 ET (derived from the continuation of stacking fifths, at which we in the West stopped at 12 and adjusted for the comma), different scales and intervals are derived from the 17 possible notes, but there is no "17 note" scale that I am aware of that is used in practice.

The point I wish to make by all of this verbiage is that while Easley Blackwood's neat progress through each possible ET is interesting, it seems rather academic in a certain sense.

My further point is that ET systems like this usually have a practical agenda, so that musicians can make the sounds that they wish to hear, not just "Cool! 13 notes! So much for your 12!"


----------



## isorhythm

I wouldn't say they come only from stacked fifths. As you say yourself, they allow us to approximate lots of different just intervals (thirds, sevenths, etc). The tuning systems that preceded equal temperament made compromises between various intervals, not just fifths and the octave.


----------



## EdwardBast

millionrainbows said:


> I said in another thread, and was soundly refuted, that the 12-note octave division was generated by the pythagoran practice of "stacking fifths."
> 
> Does anybody agree or disagree with this, or have any words on the origins of our 12-note octave division?
> 
> https://en.wikipedia.org/wiki/Pythagorean_tuning


That is essentially correct. Stack twelve fifths and you end up a bit off of seven stacked octaves (like 23 cents high). The difference is the Pythagorean comma. It was close enough, however, that it seemed rational to use a twelve note system, closing the spiral by subtracting a bit off of each (or some) fifth(s). The history of western tuning systems was pretty much the history of adjusting for the comma.


----------



## millionrainbows

EdwardBast said:


> That is essentially correct. Stack twelve fifths and you end up a bit off of seven stacked octaves (like 23 cents high). The difference is the Pythagorean comma. It was close enough, however, that it seemed rational to use a twelve note system, closing the spiral by subtracting a bit off of each (or some) fifth(s). The history of western tuning systems was pretty much the history of adjusting for the comma.


That's the way I see it. Pythagoras is such an ancient figure anyway. The WIK definition seems to reinforce this general idea of fifths generating notes (interval projection).


----------



## fluteman

EdwardBast said:


> That is essentially correct. Stack twelve fifths and you end up a bit off of seven stacked octaves (like 23 cents high). The difference is the Pythagorean comma. It was close enough, however, that it seemed rational to use a twelve note system, closing the spiral by subtracting a bit off of each (or some) fifth(s). The history of western tuning systems was pretty much the history of adjusting for the comma.


Yes, well put, or in some cases, adjusting for it as little as possible, and attempting to maintain "pure" intervals as much as possible. But the German piano manufacturers in the mid-19th century seem to have been strong proponents of equal temperament, and of pitch based on a=440, though that didn't become the international standard until 1939. Of course, these days the dominance of the piano has begun to erode, and electronic, computer-programmed instruments are increasingly common. I wonder what the long-term impact will be on Western scales and harmony.


----------



## millionrainbows

Our 12-note equal divided octave is biased toward fifths. The interval that suffered the most damage was the major third. Our ET M3 is almost 14 cents sharp, at 400 cents, from a just major third, at 383.31 cents.

That's where all the tempered tuning came from, like mean-tone and Valloiti; they were attempts to get better M3s.


----------



## millionrainbows

On the subject of ET scales (of any division): what is best about them is that they a) preserve the octave, and b) since ET scales preserve the octave, they also preserve octaves of all the notes in the scale, so every note has its octave counterpart, above and below. This makes melodies which span octaves no problem, and would also preserve whatever harmonies result.

This might seem obvious, but consider the alternatives, and what happens when a scale or tuning does not "close" the octave: it will keep spiraling up and out, and each octave will be different. Maybe this would be good, maybe not.

Also, consider a scale which spans TWO octaves and closes.


----------

