Re: [LAU] retuning bristol

On Fri, Feb 27, 2015 at 09:24:50AM -0500, tom haddington wrote:
> Hey, Everybody--

Saluton

> i loaded bristol with a scala (.scl) file, this morning. That much worked
> fine. However, both my midi keyboard and the gui keyboard are nowhere near
> middle C. i've even tuned my midi keyboard up (a maximum) three octaves,
> and my middle C is still two octaves too low. Can this be prevented or
> adjusted in anyway?

The bad news is that Bristol uses only 440 Hz, 69 and 0 for reference
frequency, keynum and scale degree-index respectively. For example,
with the pitch values of a just intonation:

  16/15 9/8 6/5 5/4 4/3 7/5 3/2 8/5 5/3 9/5 15/8 2/1

the notes are:

  A (1) A# (16/15) B (9/8) C (6/5) C# (5/4) D (4/3)

  D# (7/5) E (3/2) F (8/5) F# (5/3) G (9/5) G# (15/8)

The middle C (keynum 60) is

    440 x 3/5 = 264 Hz

and probably it is not a big problem for you.

But what is the frequency related to the keynum 60 when the number of
the notes of a scale is not 12, and/or the interval between keynum 69
and keynum 72 is not a 3min ? I think it is your problem with Bristol.

For example, the pitch values of a golden pentatonic are

  5/4 21/16 3/2 13/8 2/1

and the keymap starting from keynum 60 (middle C) is

  60 5/16
  61 21/64
  62 3/8
  63 13/32
  64 1/2
  65 5/8
  66 21/32
  67 3/4
  68 13/16
  69 1
  70 5/4
  71 21/16
  72 3/2
  73 13/8
  74 2
  
If we press the key of the middle C, we hear the frequency

    440 * 5/16 = 137.5 Hz

and obviously it is not a middle C.

Without the possibility to define a keymap, the trick is to add other
notes to get a (not necessarily chromatic) scale with 12 notes. One
of the possible scales from the previous pentatonic is

     16/15 9/8 6/5 5/4 21/16 7/5 3/2 13/8 5/3 9/5 15/8 2/1

But what if we want play the ji-scale of the first example starting
from another note ? The trick is to write a scl file with the intervals
of a modal chromatic scale. If we want a ji in C, we write a modal
chromatic scale in A by translating the pitch values:

     9/5 / 5/3 = 27/25
    15/8 / 5/3 = 9/8
     2/1 / 5/3 = 6/5
    32/15 / 5/3 = 32/25
    [...]

and the result is

      27/25 9/8 6/5 32/25 27/20 36/25 3/2 8/5 42/25 9/5 48/25 2/1

In this example, the interval of a minor third is always 6/5, therefore
the frequency related to the middle C remains 264 Hz. Now we can play
the follow notes with Bristol:

  C (1) C# (16/15) D (9/8) D# (6/5) E (5/4) F (4/3)

  F# (7/5) G (3/2) G# (8/5) A (5/3) A# (9/5) B (15/8)

Just my 1200 cents :-)

Tito

P.S. I have written some utilities to create and manage musical tunings:

         http://incudine.sourceforge.net/tutorial_tuning.html
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Received on Sat Feb 28 16:15:01 2015