Pinta Penta

Greetings,

It's been a while since I've posted anything to MMM. It is the first time
I've posted anything to non12comp. I guess I'll start by saying I hope
you're all doing well and feeling inspired. I've got something to share
today, so I'll get on with it.

There have been some excellent postings of pieces in 5tET, and some talk
about alternatives to 5tET. Some have suggested that some JI scale
approximating 5tET might be an interesting alternative to 5tET. An
intriguing suggestion. I've been waiting to hear examples, and then I got
tired of waiting.

I recorded a little improvisation in 5tET, and then I created a number of
retuned versions. I uploaded the whole set to my site:
http://www.soundclick.com/andrewheathwaite.

I will tell you all the scales I used (details below), but I'll leave my
opinions to myself for the time being.

� 5tET
� 7-limit JI approximation
� 17-limit JI approximation
� a MOS scale (13/10 generator, octave repeat)
� A segment of the overtone series
� 5th root of 3
� 5th root of 19/11

The first three sound the most like 5tET, then they start getting esoteric.
I had fun with it.

Share your thoughts!

-Andrew

===

Details of scales

=

5tET

cents from 1/1:
0, 240, 480, 720, 960

cents difference:
240, 240, 240, 240, 240

The original, equal steps and octave-repeating.

=

7-limit JI approximation

ratio from 1/1:
1/1, 8/7, 4/3, 3/2, 7/4

cents from 1/1:
0, 231, 498, 702, 969

cents difference:
231, 267, 204, 267, 231

A simple JI approximation, unequal, unbeating.

=

17-limit JI approximation

ratio from 1/1:
1/1, 15/13, 17/13, 26/17, 26/15

cents from 1/1:
0, 248, 464, 736, 952

cents difference:
248, 217, 271, 217, 248

A more complex JI approximation, further from 5tET, unequal, more
ear-bending.

=

MOS scale (13/10 generator, octave repeat)

cents from 1/1:
0, 292, 454, 746, 908

cents difference:
292, 163, 292, 163, 292

By definition, steps of two distinct sizes. Very unlike 5tET.

=

5 overtones

ratio from 1/1:
1/1, 6/5, 7/5, 8/5, 9/5

cents from 1/1:
0, 316, 583, 814, 1018

cents difference:
316, 267, 231, 204, 182

A section of the overtone series. Step sizes decrease continually. This
scale turns to piece into one big just chord.

=

5th root of 3

cents from 1/1
0, 380, 761, 1141, 1522, (1902)

cents difference:
380, 380, 380, 380, 380

Equal step sizes with the perfect twelfth (approx. 1902 cents) as repeat
interval.

=

5th root of 19/11

cents from 1/1:
0, 189, 378, 568, 757, (946)

cents difference:
189, 189, 189, 189, 189

Equal step sizes with 19/11 (approx. 946 cents) as repeat interval.

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