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Thread: Where did the 12 notes come from?

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    Default Where did the 12 notes come from?

    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
    Last edited by millionrainbows; Oct-04-2016 at 18:02.

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    Senior Member Kjetil Heggelund's Avatar
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    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?

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    Quote Originally Posted by Kjetil Heggelund View Post
    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.

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    Senior Member Kjetil Heggelund's Avatar
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    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
    Last edited by Kjetil Heggelund; Oct-04-2016 at 20:31.

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    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.

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    To explore alternate and microtonal tunings, try these:








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    Senior Member Barbebleu's Avatar
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    The twelve notes came from Thetans!!
    "...it is said that first your heart sings, then you play. I think if it is not like that, then it is only just combination of notes, isn't it? " - Pandit Nikhil Banerjee, Master of the Sitar.

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    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.

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    Quote Originally Posted by StephenBailey View Post
    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.

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    Quote Originally Posted by millionrainbows View Post
    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.

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    Quote Originally Posted by Kjetil Heggelund View Post
    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.

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    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!"

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    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.
    Last edited by isorhythm; Oct-06-2016 at 20:17.

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    Quote Originally Posted by millionrainbows View Post
    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.
    Last edited by EdwardBast; Oct-06-2016 at 21:02.

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    Quote Originally Posted by EdwardBast View Post
    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).

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