Origin of the major scale

[CraigF]

To expound on Berstein's "nyah-nyah..." thing, these 3 tones are the first three non-octave harmonics (removing duplicate octaves). i.e. G E (Bb). The Bb is actually a microtone not in the chromatic scale, but it is the actual interval used in the nyah-nyah.

Also, the 12 step chromatic scale comes from the circle of fifths. The circle uses fifths because it is the dominant. It is the dominant because it is the first non-octave harmonic, thus the strongest.

[billkilpatrick]

is it possible that an international recitation of "nyah-nyah" might have been influenced by english language or american style television? i don't doubt that leonard bernstein heard it - it was certainly a subtle and very intelligent observation - but how could he or anyone else be sure where it came from?

it's not sung but the word "ok" is - i imagine - spoken almost everywhere on earth.

[Richard Polf]

Bernstein took this idea from the theory of the Hungarian composer Zoltan Koldaly (1882-1967), who used it as a basis for a system of musical education of children that bears his name. Along with those of the German composer, Karl Orff (1895-1982), the most influential of the 20th Century.

[billkilpatrick]

i knew orff was very influential as a teacher but the only thing i know about koldaly is his name.

do you know if either of them - or anyone else, for that matter - have speculated on the possibility of an "original tuning" - a primary relationship of notes which correspond to the basic sounds of human speech when sung?

[relux]

Here is a detailed discussion about the major scale: The Diatonic Scales

The diatonic scale is a very important scale. Out of all the possible seven note scales it has the highest number of consonant intervals, and the greatest number of major and minor triads. The diatonic scale has six major or minor triads, while all of the remaining prime scales (the harmonic minor, the harmonic major, the melodic and the double harmonic) have just four major or minor triads.

Etc...

[Lee]

Whenever the diatonic scale is discussed I always find it most illustrative to go to the piano for some hands-on explanation. The two theoretically perfect intervals for this discussion are the 2/1 Octave and the 3/2 Fifth. Beginning down low towards the left hand side of the keyboard find C, then play the fifth up from there, it being the G. Then play the next fifth up from there, it being the D. Then play the next fifth up from there, it being the A. Then keep on going in this fashion until you once again land on a C. (A fifth is seven half-steps, don't forget to count the black notes.) You'll find the sequence of notes looks like this:
C,G,D,A,E,B,F#,C#,G#,D#,A#,F,C (Piano tuners refer to all the black notes as sharps, there being no such thing as "flats" in our jargon) What we've done is to use the two ratios of the fifth and the octave to "discover" all twelve notes of the diatonic scale; more or less.
Note that we spanned seven octaves before landing on another C. Note that we spanned twelve fifths before landing on another C. Mathematically speaking seven spanned octaves are described as 2/1 to the seventh power, which equals 128. The twelve spanned fifths are described as 3/2 to the twelfth power, which equals a monstrous looking fraction 531441/4097, which equals 129.71467. The problem is; 129.71467 doesn't equal 128. The last step of the fifth's sequence takes us just a tad further than the C attained by doing the seven octaves. The difference between the 128 and 129.71467 is called "Pythagoras' comma" in honor of the discoverer. To compensate for this discrepency the piano tuner narrows all the fifths perceptably and widens the octaves almost imperceptably. This is what's called tempering the scale. The reknown "equal temperament" being when each half step is 1/12th of the octave, or the twelfth root of 2/1.
This same mathematical phenomenon can be seen with the major third, which is a 5/4 ratio. Start at C and play the third up from there, it being the F. Then play the next third up from there, it being the A#, then play the third up from there, it being the C one octave from whence we began. Mathematically the sequence of three contiguous major thirds which formed the octave is described as 5/4's to the third power, which equals 1-61/64's. This is just a tad short of the perfect 2/1 octave. Hence the piano tuner widens the thirds during the tempering process.
To see what's happening with the tempering process look at the fifth formed by the C-G, and beginning at that G look at the G-upperC interval which is a major third. If we keep both C's stable and "adjust" the G note slightly flat, we're simultaneously narrowing that C-G fifth while widening the G-C major third. What a lucky break, eh?!
It's really amazing how close the twelve note scale comes to adhering so closely to the perfect "just" intervals, yet not quite.

[Chip Booth]

Been gone for some days, thanks so much for all the fascinating information I have come back to. Now I just have to read it. But I think in the quick scan I just did that the circle of fifths comes closest to what I consider a logical explanation of where the twelve half steps come from. How obvious that was...

Chip