Ratios in JI

Pieter Smit wrote:

>Would the 'natural' scale then be in the ratios
>1, 9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2
>for the scale CDEFGA(B-flat)Bc ? Do I get this right? What would
>this scale be called, and how would it sound ?

Your scale is constructed by taking the harmonic series from 8 to 16. You
could describe it as an Otonality scale to use Harry Partch's language. You
could say that it has a prime limit of 13. You could say using Kathleen
Schlesinger's term that it has a modal determinant of 8 (8 is the
denominator of all the ratios). Then you've just about described it. But it
certainly isn't THE natural scale. Dangerous word natural.

As to what it could sound like. I can only give my subjective response. OK
the second and the third are going to be what you expect from the Do Re Mi
major scale, the fourth is going to sound different from what you expect
because there's an 11 there, the eleventh harmonic. We are not used to
hearing that note in that place and so it will sound wrong, odd, difficult.
The next note the 3/2 is a perfect fifth. Great back to normality (in the
sense of what I'm used to) The sixth takes you to the thirteenth harmonic,
similar problem with 11, we're not used to it. After the 13 the 7/4 sounds
bearable. The 15/8 is familiar territory as well and then back to the
octave. In my listening experience, the higher the prime, the stranger the
note or as Lou Harrison puts it in his 1970 music primer "Each new prime
number is a new adventure."

But if you take the chord from your scale 1:5:3:7 (correcting for octaves
and ratio simplifications becomes 4:5:6:7), you've got something you can be
quite comfortable with even though it's got that unusual bluesy 7 there.
Most people I find can handle the newness of 7 but baulk at 11 and 13. In
the Arabic/Turkish/Persian musical tradition however, 11s and 13s are common
and any melody line that uses 11s or 13s as grace notes or part of a
melismatic figure will create the image in your western listener of the
Middle East. I can choose to support that image or to go against it.


>What would the scale be called
> 1, 9/8, 5/4, 4/3, 3/2, ......., where the fourth is tuned as a
>perfect fifth below ?

I'd like to know how you would continue your scale. Would you replace the 13
and 7 as well and go for a five limit scale or would you leave in the 7 as a
bit of spice?

>Would this be the JI scale?
No. You may be pointing to the scale that most people in the west would have
a go at singing if asked to sing the Do Re Mi scale without the
accompaniment of an ET instrument. But there is no one JI scale.

Brian Lee

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