Help with Just Intonation – ER-101

Hi all,

I’m looking to build: 1) a just-intonated major scale, 2) a just-intonated natural minor scale; 3) a just-intonated harmonic minor scale, all 7-notes, on the ER-101.

The idea is to fulfill one of the earliest ideas about the possibility of electronic music, as early as Busoni’s “Sketch of a New Musical Aesthetic” - in which he writes about the first oscillator ever made, and how its flexibility of tuning could open up new worlds for harmony. Since the voltages to oscillators can be transposed (with offsets or manually) it should be possible to allow movement between different just-intonated zones in a way not possible on X-TET tunings, or the compromises of 5-limit stuff - avoiding the problems of transposition of these tunings because oscillators don’t care.

Also, as subharmonic and additive synths prove, this stuff sounds great when it’s in tune!

I realize these voltages may be available with clever understanding of the 22 shrutis but I want to be able to quickly choose one of these scales without counting where we are in a 22-number space.

I know the ratios, (seen here) and collated into scales below. What I don’t know is how to convert them to ER-101 voltage tables! :slight_smile:

Can this excellent hive-brain help?

JUST MAJOR
1:1 - Unison
9:8 - Major second
5:4 - Major third
4:3 - Fourth
3:2 - Fifth
5:3 - Sixth
15:8 - Major Seventh
2: 1 - Octave

JUST NATURAL MINOR
1:1 - Unison
9:8 - Major second
6:5 - Minor third
4:3 - Fourth
3:2 - Fifth
8:5 - Minor Sixth
9:5 - Minor Seventh
2: 1 - Octave

JUST HARMONIC MINOR
1:1 - Unison
9:8 - Major second
6:5 - Minor third
4:3 - Fourth
3:2 - Fifth
8:5 - Minor Sixth
15:8 - Major Seventh
2: 1 - Octave

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To get the voltage, convert the ratio to cents and then divide by 1200.

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Omg, thanks Brian!
I’m a bit slow with maths…
What would an example be?
I’m not sure the numbers I get make any sense.

The page you linked has all the ratios that you want listed in cents, so you can just use those to check your calculations?

Here is a page that explains the ratio to cents conversion:
http://robertinventor.com/software/tunesmithy/help/cents_and_ratios.htm

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Thanks! Awesome. Thank goodness someone can think in numbers larger than 7.