Non-Octave Self Similar Scales: Phi, E, Pi

Non-Octave Self Similar Scales: Phi, E, Pi

Hello Friends!

In today's installment of Non-Octave Scales, let's take a look at a
little variation on the Inversionally Symmetrical Self Similar theme,
with the below offerings. The difference here is there is no octave,
but only the constant proportions:

12 Tone Self Similar Phi, Non-Octave Mode with Inversional Symmetry
at the Ratio Phi

Cents Consecutive
0
75.120 75.120
121.546 46.427
196.666 75.120
318.212 121.546
514.878 196.666
833.090 318.212
1151.302 318.212
1347.968 196.666
1469.515 121.546
1544.634 75.120
1591.061 46.427
1666.181 75.120

You'll notice that the above Phi Mode, maps the Ratio Phi to what is
physically the Tritone, and what would be physically the Octave has
Phi*2. Not having the 2/1 really gives this an entirely different
feel. Basically, it is a mode of the other scales - not having the
clusters, or the octave though - only the constant proportions (very
nice for total Phi bliss). This invites a different stylistic
approach here, because there are larger scale gaps and less tones
than the versions with a 2/1. I think you'll like it and I seek your
opinion.

And now for something completely different!

12 Tone Self Similar E, Non-Octave Mode with Inversional Symmetry at
the Ratio E

Cents Consecutive
0
11.665 11.665
31.709 20.044
86.193 54.484
234.297 148.104
636.885 402.588
1731.234 1094.349
2825.583 1094.349
3228.171 402.588
3376.275 148.104
3430.759 54.484
3450.803 20.044
3462.468 11.665

The large scale degrees in the middle can be quite fun! I'll let you
be the judge.

And finally:

12 Tone Self Similar Pi, Non-Octave Mode with Inversional Symmetry at
Ratio Pi

Cents Consecutive
0.000
20.345 20.345
63.916 43.571
200.798 136.882
630.825 430.027
1981.795 1350.970
3332.766 1350.970
3762.793 430.027
3899.675 136.882
3943.246 43.571
3963.591 20.345

Thanks,

Jacky Ligon