No-one knows who first adopted the letters A through G: that has been lost to antiquity. Someone at some stage arbitrarily gave the letter A to a frequency that it has more-or-less stayed at for thousands of years.

Then he gave the notes of the A minor scale the letters A B C D E F G. I say "minor" scale, but the concept of major and minor as we know it was not used that early on. The ancients referred to MODES. What we know now as major and minor scales were two of the modes.

To get the C major scale we take the same notes but start on the third of them, which makes C D E F G A B C. By starting the scale on any of the other notes we come up with a different mode. Nowadays two of the modes prodominate in Western music, but not everywhere.

Interestingly, about 20 years ago an Egyptian flute was discovered from about 5,000 years ago. They made an identical replica, since the original was too fragile. When they played it it was in the key or C major/A minor. That key has been prevalant for millenia. I imagine the Ancient Egyptians inherited it from early civilizations.

Early instruments were made to be played in the key of Amin/Cmaj. That's why there are black and white notes on the piano. The white notes create the Amin/Cmaj scale. (The black notes create the Eb scale, but that's another story !)

Filling in the half-notes we get

A A#/Bb B C C#/Db D D#/Eb E F F#Gb G G#Ab

Now here comes the problem. Those notes are okay in the key of C, but if you play in a different key, say D, the notes are at a different frequency. So the G, for instance, in the key of D is not the same note as the G in the key of C. Ancient instruments are made to be played in C or Amin, but they use a natural scale. This caused a problem for centuries.

Now enter JS Bach. He solved the problem by coming up with Equal Temperament. In Equal Temperament (tuning) every note except C is a little bit out, but not enough out to worry the average listener. The other notes are averaged out, giving equal space between the notes. To demonstrate this he wrote a piece known as the Well-Tempered Clavier (the well-tuned keyboard), which used all 24 major and minor keys in the same piece. Nowadays all organs, pianos, etc., are tuned to Equal Temperament.

Unfortunately Equal Temperament has never worked well on string instruments. Have you ever noticed that if you hold down a G chord on a guitar and tune it, when you play an E chord it's out of tune ? Early string instruments had moveable frets to compensate for this, but it never worked very well.

If anyone is interested I have an Excel spreadsheet where I demonstrate mathematically why it is impossible to tune a string instrument. The phenomenon was discovered by Pythagoras centuries ago. Basically, if you take a length of string and tune it to C, then you take two thirds of that length you end up with G. If you keep taking 2/3 you will work your way round all the notes, getting back to C a few octaves higher. But everyone knows that when you halve the length of string you move up an octave. The sounding length that you end up with deviates from the original length, but not by a power of 2. You eventually end up with the fraction 524288/531441.

I hope this simplifies the problem. Write to me if you want to see the Excel Spreadsheet.

[This message was edited by Alan F. Brookes on 12 December 2006 at 05:33 PM.]

That's as good an explanation as I have seen; it gets right to the heart of the frequency discrepancies without a lot of unnecessary verbiage.

Thanks

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Unfortunately Equal Temperament has never worked well on string instruments

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"The ancients referred to MODES"

And our understanding of modes was a misinterpretation of the original Greek modes, which, personally, I think worked out pretty good, if you're limited to 12-tone tuning systems.

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"The black notes create the Eb scale"

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if you take a length of string and tune it to C, then you take two thirds of that length you end up with G. If you keep taking 2/3 you will work your way round all the notes, getting back to C a few octaves higher.

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I wonder how horn players got so wierd & misguided, i.e. Bb, Eb and all. All that transposing seems so complicated, fortunately now we have machines to do it - soon, we'll not ever even have to think again!

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David, since you've mentioned it, the transposition of certain instruments has always been puzzeling to me.

I've been playing trumpet (a Bb instrument) for almost 35 years now. For those who don't know, for example, when a piano plays a Bb, I have to play my C in order to match the piano's note. Therefore, trumpet music is written one step higher then piano music. What has always puzzled me is why, way back when they invented the trumpet, didn't they just say that the note played on the trumpet that matched the piano, just carry the same name? In otherwords, when a piano plays a Bb, and the trumpet plays the same matching note, why didn't they just call it a Bb on trumpet as well? The same applies to any other transposed instrument. I have yet to have anyone give me an reasonable explanation for this.

As far as to what any of Alans' original post has to do with us becoming better steel players(?)...ANY extra musical knowledge, historic or theoretical, never hurts!

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Sho-Bud LDG, Gretsch Syncromatic Lap Steel, Fender Steel King amp, Bach Stradivarious 37 Trumpet, Getzen Eterna Flugelhorn, Fender Precision Bass (pre-CBS)

[This message was edited by Mark Trzepacz on 13 December 2006 at 10:25 AM.]

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"It's one louder"-

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Pat K

[This message was edited by Pat Kelly on 13 December 2006 at 08:00 PM.]

In another thread someone used the old saw = "a little knowledge is a dangerous thing"...I would add that less knowledge is more dangerous still...the more you know, the more you can do.

[This message was edited by ed packard on 14 December 2006 at 10:15 AM.]