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17 Tone Just Intonation Guitar

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#16 Tom M Culhane

Tom M Culhane

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Posted 20 August 2018 - 12:37 AM

I've claimed the 12 tone just intonation tuning I've posted here is THE original ancient 12 tone tuning and gives you the 12 real keys of music (24 if you want to call them major and minor keys).


I want to write out the numbers to help people see this. As I've said, I decoded all this by putting everything to whole numbers. I never would have figured it out otherwise. But people are used to putting just intonation musical notes to fractions, pitch ratios. The standard 7 just notes are said to be: 1/1 9/8 5/4 4/3 3/2 5/3 15/8 and the octave would start at 2/1. So if your first note, your 1/1, is 80 hertz, your second note would be 80 times 9/8 equals 90 hertz, and so on.


So I'm going to write out the tuning in fractions. The G key is the key that has these 7 pure tones. And as I've said, it should really be called the A key, and A should be called B, B should be C, etc. The piano keyboard should begin at the left end with an extra white and black key, and as I've said someone in Paris in 1877 knew this, see 1877 Erard Frederick Piano Collection and look at that beautiful 90 key piano. Now even though pianos are claimed to be fairly recent instruments, the keyboard pattern on them, seven white and five raised black keys per octave, goes back much further in time, with harpsichords, organs, and earlier instruments. Ok so if you look at that 1877 piano they show a close up of the left end. So if we place the 12 tone tuning onto that pattern, in fractions, starting at the first note of G (should be called A as I say), then this is how it looks (the 12 notes and then I've added the next 5 as well...):

  17/16   19/16             17/12  19/12               15/8    17/8    19/8

1/1      9/8      5/4      4/3      3/2      5/3      7/4      2/1      9/4      5/2 ...


So the lower numbers are white keys. 88 key pianos would not have keys for the 1/1 and 17/16 notes. 9/8 is on the key you would call A today, that normally starts piano, the 4/3 note is the modern C note, etc. Hope that's clear.


Ok so, who would ever have figured out that these are the right fractions to give you the real keys of music? (Everyone knows 7 of the notes, the pure tones, but the other 5 are where everybody screws up.) There seems to be no discernable pattern here. So let me write those same numbers in a different way. I'm going to write the 1/1 note as 16/16 and change others as well and this is what you get:

      17/16      19/16                                     17/12      19/12                                   15/8     17/8     19/8

16/16      18/16      20/16aka15/12      16/12      18/12      20/12      21/12aka14/8      16/8     18/8      20/8


So now you see the elegance of the math, how it flows along. It's this simple math that allows all the keys to be playable and beautiful and in harmony with the World of Form in which we live.

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