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17 Tone Just Intonation Guitar


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#16 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.



#17 Broomy

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Posted 10 November 2018 - 07:27 AM

Tom,

 

I find your theory interesting.

 

Do you have some links or sources for me to look further into it?

 

Hans


The Quintar Project:
- Popularizing an all fifths tuning for guitarlike instruments
- Youtube: Playing and Building
- Files: Sourceforge


#18 Broomy

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Posted 10 November 2018 - 08:32 AM

Do you know this study? It might interest you. The author also proposes a tuning similar as yours.

https://archive.org/...kAulos/page/n47


The Quintar Project:
- Popularizing an all fifths tuning for guitarlike instruments
- Youtube: Playing and Building
- Files: Sourceforge


#19 Tom M Culhane

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Posted 10 November 2018 - 09:27 PM

Hans,

 

The 4 just tunings (12 17 19 and 24 tone) that I believe were the basic tunings used in ancient Europe are given in this thread in my July 17, 2018 post here and more info follows it, with some more info also in my Removeable Fingerboards thread in this forum. If you read all that there's a thread called Why Is Just Intonation Impractical online. I posted info there showing why they are wrong. I also have info posted in an ancient history forum which links to posts of musical and other historical discoveries I have made. I always post under Tom M Culhane. I don't have one central place though or website.

 

12 tone instruments are of course found today and trace back into antiquity. 17 tone keyboards are found referred to in documents from centuries ago and reconstructed 19 tone keyboard images can be found online. 24 tone keyboards such as double register harpsichords can also be found.

 

Sources that compile all known tunings today don't show these four tunings. My explanation for this is they were disappeared, along with most books and records during the centuries preceding the Renaissance. They are based on the simplest, most logical math, the notes that naturally emerge on vibrating strings.

 

I don't plan to post more in this thread as it got so long.



#20 Broomy

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Posted 13 November 2018 - 08:19 AM

Thanks Tom for your reply, will look into it.


The Quintar Project:
- Popularizing an all fifths tuning for guitarlike instruments
- Youtube: Playing and Building
- Files: Sourceforge





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