Re: extended reference?

>With the Beethoven fragment, I was consciously *not*
>seeking small-number ratios in many cases, which upon
>reflection seems to contradict the extended-reference
>idea. My method here was to tune the 'roots' of the
>chords to small-integer JI, then to tune other notes
>with commatic substitutions of small-integer JI wherever
>small-integer JI didn't sound right to me, and where
>I imagined Beethoven might want those commatic substitutions
>for harmonic or melodic reasons.
>
>So is that extended reference or not?

Extended reference is not rigorously defined, by me, Boomsliter & Creel, or
anyone else. It's just a term for something B. & C. observed. My
definition trys to put their observation in terms of what's been discussed
here over the last few years. Let's walk through it.

Say we agree that JI is important in melody. How should we apply JI in the
following example?

C D E D E F

The classical JI school would say [subscribers to this school please
forgive the color that follows], "The diatonic scale, eh? What intervals
does that involve?" They write...

1:1 9:8 5:4 4:3 3:2 5:3 15:8

Then they say, "C is the tonic of the above melody!" and write...

1/1 9/8 5/4 4/3 3/2 5/3 15/8
C D E F G A B

...and finally...

1/1 9/8 5/4 9/8 5/4 4/3

The extended reference version is more like, "Diatonic music, eh? What
basic set of intervals do we need?"

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

"Now, what's happening in our melody? The first note is always 1/1..."

1/1
C

"Let's make the 2nd above C a 9:8..."

1/1 9/8
C D

"And a cracking-good 3rd is 5:4..."

1/1 9/8 5/4
C D E

"And we see that the scale degree pattern 1 2 3 is now being repeated on D
[modal transposition]. So D is our new tonic, and the first note is always
a 1:1 [D stays 9/8]. Let's make the 2nd above D a 9:8. That gives..."

1/1 9/8 5/4 9/8 81/64
C D E D E

"And the third above D should be a 6:5..."

1/1 9/8 5/4 9/8 81/64 27/20
C D E D E F

There you have it. I've used the convention developed on this list -- /'s
for pitches, and :'s for intervals. Notice the main difference between the
classical JI school and the extended reference school is where the modal
transposition takes place -- on the pitches vs. on the intervals.

[It's important not to hang up on the details of my example. The "basic
set" actually chosen by the extended reference tuner, the particular just
"diatonic" scale chosen by the classical tuner, and the choice of tonics by
both parties may be entirely different than what I've given. The methods
themselves have nothing to say about these choices.]

So now maybe you can answer the question. I would guess that if you were
successful, the Robert Johnson transcription would be extended reference if
the performance was. The Beethovan?

[P.S. You can take out the "<--insert references...-->" part of my
definition. Thanks for inserting the references!!]

-Carl

>>With the Beethoven fragment, I was consciously *not*
>>seeking small-number ratios in many cases, which upon
>>reflection seems to contradict the extended-reference
>>idea. My method here was to tune the 'roots' of the
>>chords to small-integer JI, then to tune other notes
>>with commatic substitutions of small-integer JI wherever
>>small-integer JI didn't sound right to me, and where
>>I imagined Beethoven might want those commatic substitutions
>>for harmonic or melodic reasons.
>
>>So is that extended reference or not?
>
>No. Carl, care to back me up on this?

I can't get enough out of the top paragraph to make a determination. See
TD 502.7.

Raises the question if intent or content should determine extended
reference. One problem with content: If the basic set never leaves the
diamond of a certain scale, and you allow rapid tonic changes on the
current frequencies (not just the original ones), you can notate any
extended ref. interp. in classic JI using that scale. So should we define
classic JI as allowing modulation only on the original frequencies? Or
should we make a subjective judgement as to which notation is more concise
in a given case?

-Carl