The Mathematics of Music book

Hi all, John here,

I have worked out a formula for the strength values of musical intervals. If the interval is x/y (where x<=y and the interaval is simplified, e.g. 220/330 = 2/3) then the formula is...

(2 + 1/x + 1/y - diss)/2

If x/y <= 0.9375 then 'diss' = x/y
If x/y > 0.9375 then 'diss' = (1 - x/y)*15

If the result is 1.0 or higher then the interval is Major.
If the result is between 0.75 and 0.9999 then the interval is Minor.
If the result is less thsn 0.75 then the interval is no good.

How I worked it out is explained in my book, "The Mathematics of Music" which you can download from the "Files" link to the left or from my web site: www.johnsmusic7.com .

The formula is based on a few educated guesses. I have tested it extensively and it seems consistent with what my ears are telling me. My system does not use or depend on prime numbers.

A tune I wrote and recorded using my own peculiar "just" guitar can also be played or downloaded at this web site. It's not Stairway to Heaven, it's pretty basic but it demonstrates at least that my guitar works.

My tuning system, which seems to be new and unique and is based on my formula is...

1/1, 15/14, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 9/5, 15/8, 2/1.

It's identical to the Just Major with 7-limit tritone scale but the second note is 15/14 instead of 16/15. The 3/2 can also be used as a tonic with equal strength to 1/1.

Any and all comments/feedback are welcome.

John

Hi all, John here.

I have worked out a mathematical formula for the consonance value of a musical interval x/y (where x is less then or equal to y)...

(2 + 1/x + 1/y - diss)/2 where x<=y.

If x/y is between 0 and 0.9375 then 'diss' = x/y
if x/y is between 0.9375 and 1.0 then 'diss' = (1 - x/y)*15

If the result is 1.0 or higher then the interval is Major.
If the result is between 0.75 and 0.9999 then the interval is Minor.
If the reult is less than 0.75 then the interval is no good.

The formula is based on a few educated guesses but it seems to work consistently when tested.

How I worked it out is explained in my book "The Mathematics of Music" which you can download from the "Files" link on the left. Up until very recently I knew practically nothing about the various theories of Just Intonation, (I just plodded along for 14 years with simple ratios) and it seems to me now that the title of the book is a bit too grand and presumptuous. But, if my ideas are correct, then the title is perhaps justified.

You can hear a tune I wrote and recorded using a "Just" guitar that I built myself at my web site... www.johnsmusic7.com

The web site has a few other bells and whistles as well: you can download a chord and scale dictionary for my "Just" guitar and for luthiers, a spec for fret placement is also available.

My 12-key tuning system is...
1/1, 15/14, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 9/5, 15/8, 2/1.
It is identical to the Just scale but the second note is 15/14 instead of 16/15. 3/2 can also be used as a tonic with equal strength.

Check out the book, any and all comments/feedback welcome.

John.