I made some music in exotic just intonation tunings because why not
I'm currently exploring alternative tuning systems using MTS-ESP by Oddsound. I got it so I could try out some just intonation ideas for my music theory songs, but then, while I was at it, I started plugging in weird scales for the fun of it. I decided to just pick a denominator and systematically create every interval I could with it. For example, I made a scale tuned 5/5, 6/5, 7/5, 8/5, 9/5, 10/5. It turns out that this is a known approach to just intonation called primodality. It gets fascinating results!
I made a bunch of tracks this way in rapid succession:
https://soundcloud.com/ethanhein/sets/just-intonation
For each scale, I loaded up the tuning plugin, a synth or two, and a few beats. Then I recorded myself improvising, and edited the good parts together into what you're hearing. My goal was to make these scales sound, you know, good. I figured that your brain would be very busy keeping track of the unusual harmonies, so I kept the grooves and structures straightforward. I talk through the scales and tracks one at a time below.
First, here's quartal primodality, based on fractions of four.
4/4 (1/1) - unison
5/4 - major third
6/4 (3/2) - perfect fifth
7/4 - harmonic seventh
8/4 (2/1) - octave
This is not so much a "scale" as it is an arpeggiated just intonation dominant seventh chord. It sounds good, but it's not very interesting.
https://soundcloud.com/ethanhein/quartal-primodality-first-octave?in=ethanhein%2Fsets%2Fjust-intonation
You can take primodal scales into their "second octave," which means doubling the denominator and building all the possible fractions on it that way. (Or you can think of the second octave as splitting each interval in half, whichever makes more sense to you.) Here's the second octave of quartal primodality:
8/8 (1/1) - unison
9/8 - major second
10/8 (5/4) - major third
11/8 - undecimal superfourth
12/8 (3/2) - perfect fifth
14/8 (7/4) - harmonic seventh
15/8 - major seventh
16/8 (2/1) - octave
Now we're talking! We still have lots of familiar intervals from the basic diatonic scale, but they are spiced up with the 11/8 tritone and 13/8 minor sixth.
https://soundcloud.com/ethanhein/quartal-primodality-second?in=ethanhein/sets/just-intonation&si=5df9aa9393e24f22a222052ac3ee38fb
Quintal primodality is based on fractions of five.
5/5 (1/1) - unison
6/5 - minor third
7/5 - narrow tritone
8/5 - minor sixth
9/5 - minor seventh
10/5 (2/1) - octave
There's no fifth in here, but otherwise everything sounds pretty familiar. The 7/5 tritone is especially bluesy.
https://soundcloud.com/ethanhein/quintal-primodality-first?in=ethanhein/sets/just-intonation
The second octave of quintal primodality opens up lots of intriguing new possibilities:
10/10 (1/1) - unison
11/10 - undecimal submajor second
12/10 (6/5) - minor third
13/10 - tridecimal semisixth
14/10 (7/5) - narrow tritone
15/10 (3/2) - perfect fifth
16/10 (8/5) - minor sixth
17/10 - septendecimal major sixth
18/10 (9/5) - minor seventh
19/20 - undevicesimal diminished octave
20/10 (2/1) - octave
All those odd numbered intervals are seriously weird!
https://soundcloud.com/ethanhein/quintal-primodality-second?in=ethanhein/sets/just-intonation
Seximal primodality uses fractions of six. Most of this scale is warmly familiar. The subminor third is a great blue note. Taken together, it all feels like an asymmetrical whole tone scale.
6/6 (1/1) - unison
7/6 - subminor third
8/6 (4/3) - perfect fourth
9/6 (3/2) - perfect fifth
10/6 (5/3) - major sixth
11/6 - undecimal neutral seventh
12/6 (2/1) - octave
https://soundcloud.com/ethanhein/seximal-primodality-first-octave
The second octave has twelve pitches like the familiar chromatic scale, but they are distributed differently. It adds the familiar major third and harmonic seventh, but also a few spicy novelties.
12/12 (1/1) - unison
13/12 - neutral second
14/12 (7/6) - subminor third
15/12 (5/4) - major third
16/12 (4/3) - perfect fourth
17/12 - larger septendecimal tritone
18/12 (3/2) - perfect fifth
19/12 - large undevicesimal minor sixth
20/12 (5/3) - major sixth
21/12 (7/4) - harmonic seventh
22/12 - undecimal neutral seventh
23/12 - vicesimotertial major seventh
24/12 (2/1) - octave
https://soundcloud.com/ethanhein/seximal-primodality-second-octave
Septimal primodality uses fractions of seven.
7/7 (1/1) - unison
8/7 - supermajor second
9/7 - supermajor third
10/7 - high tritone
11/7 - undecimal minor sixth
12/7 - supermajor sixth
13/7 - tridecimal submajor seventh
14/7 (2/1) - octave
All of these intervals are exotic, but their clear harmonic relation to each other still gives them a folkloric integrity. The scale sounds like an mbira tuning to me.
https://soundcloud.com/ethanhein/septimal-primodality-first?in=ethanhein/sets/just-intonation
The second octave is even more exotic, but it does have a perfect fifth in there for your ear to hang onto. I love the 19/14 "Hendrix fourth."
14/14 (1/1) - unison
15/14 - septimal diatonic semitone
16/14 (8/7) - supermajor second
17/14 - septendecimal supraminor third
18/14 (9/7) - supermajor third
19/14 - Hendrix fourth
20/14 (10/7) - high tritone
21/14 (3/2) - perfect fifth
22/14 (11/7) - undecimal minor sixth
23/14 - unnamed
24/14 (12/7) - supermajor sixth
25/14 - middle minor seventh
26/14 (13/7) - tridecimal submajor seventh
27/14 - supermajor seventh
28/14 (2/1) - octave
https://soundcloud.com/ethanhein/septimal-primodality-second?in=ethanhein/sets/just-intonation
Nonary primodality is fractions of nine.
9/9 (1/1) - unison
10/9 - small whole tone
11/9 - neutral third
12/9 (4/3) - perfect fourth
13/9 - tridecimal diminished fifth
14/9 - subminor sixth
15/9 (5/3) - major sixth
16/9 - Pythagorean minor seventh
18/9 (2/1) - octave
This scale has several friendly and familiar intervals in it: perfect fourth, major sixth, flat seventh. That makes the weird intervals sound that much weirder by comparison.
https://soundcloud.com/ethanhein/nonary-primodality-first?in=ethanhein/sets/just-intonation
The second octave adds lots of extremely strange intervals.
18/18 (1/1) - unison
19/18 - large undevicesimal semitone
20/18 (10/9) - small whole tone
21/18 (7/6) - subminor third
22/18 (11/9) - neutral third
23/18 - unnamed
24/18 (4/3) - perfect fourth
25/18 - augmented fourth
26/18 (13/9) - tridecimal diminished fifth
27/18 (3/2) - perfect fifth
28/18 (14/9) - subminor sixth
29/18 - unnamed
30/18 (5/3) - major sixth
31/18 - unnamed
32/18 (16/9) - Pythagorean minor seventh
33/18 (11/6) - undecimal neutral seventh
34/18 (17/9) - large septendecimal major seventh
35/18 - septimal semidiminished octave
36/18 (2/1) - octave
https://soundcloud.com/ethanhein/nonary-primodality-second-octave?in=ethanhein/sets/just-intonation
Finally, here's undecimal primodality, fractions of eleven. The basic scale is uniformly weird.
11/11 (1/1) - unison
12/11 - neutral second
13/11 - neo-Gothic minor third
14/11 - undecimal major third
15/11 - undecimal augmented fourth
16/11 - minor fifth
17/11 - septendecimal subminor sixth
18/11 - undecimal neutral sixth
19/11 - undevicesimal semitwelfth
20/11 - small undecimal neutral seventh
22/11 (2/1) - octave
https://soundcloud.com/ethanhein/undecimal-primodality-first?in=ethanhein/sets/just-intonation
Undecimal primodality's second octave has 22 intervals to keep track of, and they are so fine that they start feeling like out-of-tune versions of each other rather than distinct notes. At least there's a perfect fifth to anchor yourself with.
22/22 (1/1) - unison
23/22 - greater vicesimotertial semitone
24/22 (12/11) - neutral second
25/22 - undecimal super-second
26/22 (13/11) - neo-Gothic minor third
27/22 - rastmic neutral third
28/22 (14/11) - undecimal major third
29/22 - unnamed
30/22 (15/11) - undecimal augmented fourth
31/22 - unnamed
32/22 (16/11) - minor fifth
33/22 (3/2) - perfect fifth
34/22 (17/11) - septendecimal subminor sixth
35/22 - unnamed
36/22 (18/11) - undecimal neutral sixth
37/22 - unnamed
38/22 (19/11) - undevicesimal semitwelfth
39/22 - unnamed
40/22 (20/11) - small undecimal neutral seventh
41/22 - unnamed
42/22 (21/11) - large undecimal diminished octave
43/22 - unnamed
44/22 (2/1) - octave
https://soundcloud.com/ethanhein/undecimal-primodality-second?in=ethanhein/sets/just-intonation
If you want to try these scales out for yourself, here are a couple of considerations:
Ableton's Wavetable synth, Simpler and Sampler are the only instruments native to Live that are fully compatible with MTS-ESP. (The other instruments work too, but only monophonically.) You will need the Max for Live MTS-ESP MIDI client plugin on each synth track.
If the scale has fewer than twelve notes in it, then it's easy to map it to the MIDI keyboard. Just pick a subset of the chromatic pitches that make sense to you and jam out. If the microtonal notes happen to fall on "normal" intervals like the perfect fifth, that makes for more obvious mapping choices.
If the scale has more than twelve notes in it, you will need to spread it across multiple octaves of the MIDI keyboard. I didn't do it in any systematic way, just piled them up on successive chromatic keys. This means that patterns won't repeat at octaves. On the other hand, if you're dealing with a very complex scale, one octave worth will probably be plenty.
I find that timbre makes a huge difference in how "out of tune" a given scale sounds. One synth preset will make the scale sound harsh and alienating, while another makes it intriguing and inviting. This is true of "normal" scales too, but we're just a lot more used to their affordances.
Am I going to turn into one of these weirdos who goes around muttering about how ugly 12-TET is, and who only listens to xenharmonic music? Stay tuned!
Update: I got some hilarious SoundCloud spam. "Do you like to sign a label deal??..Yo Ethan Hein, this record‘Quartal Primodality - First Octave’…Brilliantly!!!!!..Please send that demo for my team,and guys talk to you about further moves.." Yeah, exotic just intonation scales are burning up the charts.