Quartertone Harmony Chords

Quartertone Harmony is the youtube channel of a 24-EDO music theorist and composer. Curt's his name. He's so cute. He has a bunny named Poopy. I've wanted to do a deep dive into his methods for a long time. We're going to start with his first video.

He talks about a method for building 24-edo chords. Here are the rules.

Rule 1. Every chord has to have a chain of friends connecting every note in the chord. It's not totally clear to me if you can have three friends hanging off one one friend - the chain has branches - of if the chain is a straight line. It's also not clear to me if the chain has to form a circle, or if the ends can be disconnected. I went with a single-linked disconnected chain when generating chords in his style.

Curt says that friends are connected by a major third, minor third, neutral third, or "harmonic second", which is supposed the be the interval between G natural and A half sharp. He also says that the harmonic second is the inverse of the harmonic seventh. To me the inverse of an interval X is

    P1 - X

but he's talking abou the octave complement

    P8 - X

And that's fine. In my notation, the harmonic seventh is a sub-minor seventh, Sbm7, with a just tuning of 7/4, and its complement is a super major second, SpM2, with a just tuning of 8/7.

The intervals that can connect friends in Curt's system have these 24-EDO tunings:

    [SpM2, m3, n3, M3] -> [5, 6, 7, 8]

Unfortunately, Curt equivocates a little bit between EDO steps and intervals. For example, he says that the 11th harmonic and the 13th harmonic are separated by a minor third. In my notation, the interval between the 13th and 11th harmonics is a prominent descendent minor third, PrDem3, with a just frequency ratio of 13/11. It's true that this has "m3" at the end, so it's a kind of minor third, and they're both tuned by 24-EDO to 6\24 steps, but they're not the same. So when Curt says that two intervals can be friends if they're separated by a minor third, I don't interpret that intervallically: he just means they're friends if they're separated by 6 steps of 24-EDO.

Because of this, and because I like tertian chords spelled by thirds, I use Sbm3 instead of SpM2 for a 5\24-sized interval when I'm building up chords in Curt's style. Maybe I should use both, but I don't.

In fact, I use a bunch of third intervals that I think Curt wouldn't mind, since they have the right size in 24-EDO.

5\24 - Sbm3 # 7/6

6\24 - Grm3 # 32/27

6\24 - m3 # 6/5

6\24 - PrDem3 # 13/11

8\24 - ReAsM3 # 33/26

7\24 - AsGrm3 # 11/9

7\24 - DeAcM3 # 27/22

7\24 - Prm3 # 39/32

7\24 - ReM3 # 16/13

8\24 - M3 # 5/4

8\24 - AcM3 # 81/64 

It's really odd to me that Curt doesn't use a 9-step super-major third, SpM3, with a just tuning of 9/7. The sub-minor third and the super-major third are like the two core sounds of 7-limit just intonation, and I would never have thought to make a 13-limit interpretation of 24-EDO harmony that didn't include that sound. But this is Curt's method, mostly, and we shall continue in this vein.

Rule 2. No note can have an enemy. An enemy is a note separate from a target note by 1 quarter tone or (sometimes) 9 quarter tones or 15 quarter tones. I don't know what he means by "sometimes", so I just ruled out all chords that had notes separated by 9 or 15 quartone intervals. No two of my chain-of-friend intervals can sum to form 1 or 9, so that's not a problem. So really this just means that we can't have consecutive relative intervals of size (8, 7)\24 or (7, 8)\24. If I'd had a branching chain of friends, the 1\24 and 9\24 steps might have been a problem.

Rule 3. No crowding. No note can have more than one other (?note that is?) closer than a major second. This rule is another reason why I think Curt might be okay with a branched-chain of friends - if there's a single-linked chain of friends all connected by thirds of size 5\24 or more, you're never going to have crowding, so there wouldn't be a reason to mention this. Even if we use Curt's harmonic second, SpM2, that's not smaller than a major second, so you could in principle have a note with notes on either side surrounded by SpM2. I confess that I mishead this one when I first starded coding up Curt's method: I thought he considered 5\24-sized intervals on either side of a note to be crowded, so I was deleting any chord I generated with consecutive (5, 5)\24 sized intervals. Which is just more restricive, it's not really a problem.

Those are all the rules. Well, he also says that you should use a string timbre, but that's not a principle of chord construction. And I particularly like using clarinet, tuba, and oud for my microtonal works, so there. Let's see what we can make from these rules! When generating chords, I also remove any chord that has an interval with a just tuning with three digits or more in the numerator. I also remove any chords that only have even steps in their 24-EDO tuning, because I think they'll sound too much like 12-TET.

I came up with 161 chords. They *all* sound good. I must be really starved for microtones. How can they all sound so good? Some of them have the same 24-EDO tunings, but many of those still have very distinct sonic characteristics in their just tunings. I'm really pretty shocked about how good these sound. Like, I have tried to make 11-limit and 13-limit music using similar principles and totally failed to find anything this nice.

[0, 5, 11, 16] _ [P1, Sbm3, Sbd5, SbSbd7] - [1/1, 7/6, 7/5, 49/30]

[0, 5, 11, 17] _ [P1, Sbm3, PrDeSbd5, PrDeSbd7] - [1/1, 7/6, 91/66, 91/55]

[0, 5, 11, 17] _ [P1, Sbm3, Sbd5, PrDeSbd7] - [1/1, 7/6, 7/5, 91/55]

[0, 5, 11, 17] _ [P1, Sbm3, Sbd5, Sbd7] - [1/1, 7/6, 7/5, 42/25]

[0, 5, 11, 18] _ [P1, Sbm3, PrDeSbd5, DeSbm7] - [1/1, 7/6, 91/66, 56/33]

[0, 5, 11, 18] _ [P1, Sbm3, PrDeSbd5, PrSbGrd7] - [1/1, 7/6, 91/66, 91/54]

[0, 5, 11, 18] _ [P1, Sbm3, Sbd5, AsSbGrd7] - [1/1, 7/6, 7/5, 77/45]

[0, 5, 11, 19] _ [P1, Sbm3, PrDeSbd5, Sbm7] - [1/1, 7/6, 91/66, 7/4]

[0, 5, 11, 19] _ [P1, Sbm3, Sbd5, Sbm7] - [1/1, 7/6, 7/5, 7/4]

[0, 5, 12, 18] _ [P1, Sbm3, AsSbGrd5, AsSbGrd7] - [1/1, 7/6, 77/54, 77/45]

[0, 5, 12, 18] _ [P1, Sbm3, AsSbGrd5, PrSbGrd7] - [1/1, 7/6, 77/54, 91/54]

[0, 5, 12, 18] _ [P1, Sbm3, DeSbAc5, DeSbm7] - [1/1, 7/6, 63/44, 56/33]

[0, 5, 12, 18] _ [P1, Sbm3, PrSbd5, PrSbGrd7] - [1/1, 7/6, 91/64, 91/54]

[0, 5, 12, 18] _ [P1, Sbm3, ReSb5, DeSbm7] - [1/1, 7/6, 56/39, 56/33]

[0, 5, 12, 19] _ [P1, Sbm3, AsSbGrd5, Sbm7] - [1/1, 7/6, 77/54, 7/4]

[0, 5, 12, 19] _ [P1, Sbm3, DeSbAc5, Sbm7] - [1/1, 7/6, 63/44, 7/4]

[0, 5, 12, 19] _ [P1, Sbm3, PrSbd5, Sbm7] - [1/1, 7/6, 91/64, 7/4]

[0, 5, 12, 19] _ [P1, Sbm3, ReSb5, Sbm7] - [1/1, 7/6, 56/39, 7/4]

[0, 5, 13, 19] _ [P1, Sbm3, ReAsSb5, Sbm7] - [1/1, 7/6, 77/52, 7/4]

[0, 5, 13, 19] _ [P1, Sbm3, Sb5, Sbm7] - [1/1, 7/6, 35/24, 7/4]

[0, 6, 11, 17] _ [P1, PrDem3, PrDeSbd5, PrDeSbd7] - [1/1, 13/11, 91/66, 91/55]

[0, 6, 11, 17] _ [P1, m3, Sbd5, PrDeSbd7] - [1/1, 6/5, 7/5, 91/55]

[0, 6, 11, 17] _ [P1, m3, Sbd5, Sbd7] - [1/1, 6/5, 7/5, 42/25]

[0, 6, 11, 18] _ [P1, PrDem3, PrDeSbd5, DeSbm7] - [1/1, 13/11, 91/66, 56/33]

[0, 6, 11, 18] _ [P1, PrDem3, PrDeSbd5, PrSbGrd7] - [1/1, 13/11, 91/66, 91/54]

[0, 6, 11, 18] _ [P1, m3, Sbd5, AsSbGrd7] - [1/1, 6/5, 7/5, 77/45]

[0, 6, 11, 19] _ [P1, PrDem3, PrDeSbd5, Sbm7] - [1/1, 13/11, 91/66, 7/4]

[0, 6, 11, 19] _ [P1, m3, Sbd5, Sbm7] - [1/1, 6/5, 7/5, 7/4]

[0, 6, 12, 17] _ [P1, PrDem3, PrDed5, PrDeSbd7] - [1/1, 13/11, 78/55, 91/55]

[0, 6, 12, 17] _ [P1, m3, PrDed5, PrDeSbd7] - [1/1, 6/5, 78/55, 91/55]

[0, 6, 12, 17] _ [P1, m3, d5, Sbd7] - [1/1, 6/5, 36/25, 42/25]

[0, 6, 12, 19] _ [P1, Grm3, Grd5, Dem7] - [1/1, 32/27, 64/45, 96/55]

[0, 6, 12, 19] _ [P1, Grm3, Grd5, PrGrd7] - [1/1, 32/27, 64/45, 26/15]

[0, 6, 12, 19] _ [P1, PrDem3, PrDed5, Dem7] - [1/1, 13/11, 78/55, 96/55]

[0, 6, 12, 19] _ [P1, PrDem3, PrDed5, PrGrd7] - [1/1, 13/11, 78/55, 26/15]

[0, 6, 12, 19] _ [P1, m3, Grd5, Dem7] - [1/1, 6/5, 64/45, 96/55]

[0, 6, 12, 19] _ [P1, m3, Grd5, PrGrd7] - [1/1, 6/5, 64/45, 26/15]

[0, 6, 12, 19] _ [P1, m3, PrDed5, Dem7] - [1/1, 6/5, 78/55, 96/55]

[0, 6, 12, 19] _ [P1, m3, PrDed5, PrGrd7] - [1/1, 6/5, 78/55, 26/15]

[0, 6, 12, 19] _ [P1, m3, d5, AsGrd7] - [1/1, 6/5, 36/25, 44/25]

[0, 6, 13, 18] _ [P1, Grm3, De5, DeSbm7] - [1/1, 32/27, 16/11, 56/33]

[0, 6, 13, 18] _ [P1, Grm3, PrGrd5, PrSbGrd7] - [1/1, 32/27, 13/9, 91/54]

[0, 6, 13, 18] _ [P1, PrDem3, De5, DeSbm7] - [1/1, 13/11, 16/11, 56/33]

[0, 6, 13, 18] _ [P1, PrDem3, PrGrd5, PrSbGrd7] - [1/1, 13/11, 13/9, 91/54]

[0, 6, 13, 18] _ [P1, m3, AsGrd5, AsSbGrd7] - [1/1, 6/5, 22/15, 77/45]

[0, 6, 13, 19] _ [P1, Grm3, De5, Dem7] - [1/1, 32/27, 16/11, 96/55]

[0, 6, 13, 19] _ [P1, Grm3, PrGrd5, PrGrd7] - [1/1, 32/27, 13/9, 26/15]

[0, 6, 13, 19] _ [P1, PrDem3, De5, Dem7] - [1/1, 13/11, 16/11, 96/55]

[0, 6, 13, 19] _ [P1, PrDem3, PrGrd5, PrGrd7] - [1/1, 13/11, 13/9, 26/15]

[0, 6, 13, 19] _ [P1, m3, AsGrd5, AsGrd7] - [1/1, 6/5, 22/15, 44/25]

[0, 6, 13, 19] _ [P1, m3, AsGrd5, PrGrd7] - [1/1, 6/5, 22/15, 26/15]

[0, 6, 13, 19] _ [P1, m3, DeAc5, Dem7] - [1/1, 6/5, 81/55, 96/55]

[0, 6, 13, 19] _ [P1, m3, Re5, Dem7] - [1/1, 6/5, 96/65, 96/55]

[0, 6, 13, 20] _ [P1, Grm3, De5, Grm7] - [1/1, 32/27, 16/11, 16/9]

[0, 6, 13, 20] _ [P1, Grm3, De5, PrDem7] - [1/1, 32/27, 16/11, 39/22]

[0, 6, 13, 20] _ [P1, Grm3, PrGrd5, Grm7] - [1/1, 32/27, 13/9, 16/9]

[0, 6, 13, 20] _ [P1, Grm3, PrGrd5, PrDem7] - [1/1, 32/27, 13/9, 39/22]

[0, 6, 13, 20] _ [P1, PrDem3, De5, Grm7] - [1/1, 13/11, 16/11, 16/9]

[0, 6, 13, 20] _ [P1, PrDem3, De5, PrDem7] - [1/1, 13/11, 16/11, 39/22]

[0, 6, 13, 20] _ [P1, PrDem3, PrGrd5, Grm7] - [1/1, 13/11, 13/9, 16/9]

[0, 6, 13, 20] _ [P1, PrDem3, PrGrd5, PrDem7] - [1/1, 13/11, 13/9, 39/22]

[0, 6, 13, 20] _ [P1, m3, AsGrd5, m7] - [1/1, 6/5, 22/15, 9/5]

[0, 6, 13, 20] _ [P1, m3, DeAc5, m7] - [1/1, 6/5, 81/55, 9/5]

[0, 6, 13, 20] _ [P1, m3, Re5, m7] - [1/1, 6/5, 96/65, 9/5]

[0, 6, 14, 19] _ [P1, Grm3, P5, Sbm7] - [1/1, 32/27, 3/2, 7/4]

[0, 6, 14, 19] _ [P1, PrDem3, P5, Sbm7] - [1/1, 13/11, 3/2, 7/4]

[0, 6, 14, 19] _ [P1, m3, P5, Sbm7] - [1/1, 6/5, 3/2, 7/4]

[0, 7, 12, 18] _ [P1, AsGrm3, AsSbGrd5, AsSbGrd7] - [1/1, 11/9, 77/54, 77/45]

[0, 7, 12, 18] _ [P1, AsGrm3, AsSbGrd5, PrSbGrd7] - [1/1, 11/9, 77/54, 91/54]

[0, 7, 12, 18] _ [P1, DeAcM3, DeSbAc5, DeSbm7] - [1/1, 27/22, 63/44, 56/33]

[0, 7, 12, 18] _ [P1, Prm3, PrSbd5, PrSbGrd7] - [1/1, 39/32, 91/64, 91/54]

[0, 7, 12, 18] _ [P1, ReM3, ReSb5, DeSbm7] - [1/1, 16/13, 56/39, 56/33]

[0, 7, 12, 19] _ [P1, AsGrm3, AsSbGrd5, Sbm7] - [1/1, 11/9, 77/54, 7/4]

[0, 7, 12, 19] _ [P1, DeAcM3, DeSbAc5, Sbm7] - [1/1, 27/22, 63/44, 7/4]

[0, 7, 12, 19] _ [P1, Prm3, PrSbd5, Sbm7] - [1/1, 39/32, 91/64, 7/4]

[0, 7, 12, 19] _ [P1, ReM3, ReSb5, Sbm7] - [1/1, 16/13, 56/39, 7/4]

[0, 7, 12, 20] _ [P1, ReM3, ReSb5, ReSbM7] - [1/1, 16/13, 56/39, 70/39]

[0, 7, 13, 18] _ [P1, AsGrm3, AsGrd5, AsSbGrd7] - [1/1, 11/9, 22/15, 77/45]

[0, 7, 13, 18] _ [P1, AsGrm3, PrGrd5, PrSbGrd7] - [1/1, 11/9, 13/9, 91/54]

[0, 7, 13, 18] _ [P1, DeAcM3, De5, DeSbm7] - [1/1, 27/22, 16/11, 56/33]

[0, 7, 13, 18] _ [P1, Prm3, PrGrd5, PrSbGrd7] - [1/1, 39/32, 13/9, 91/54]

[0, 7, 13, 18] _ [P1, ReM3, De5, DeSbm7] - [1/1, 16/13, 16/11, 56/33]

[0, 7, 13, 19] _ [P1, AsGrm3, AsGrd5, AsGrd7] - [1/1, 11/9, 22/15, 44/25]

[0, 7, 13, 19] _ [P1, AsGrm3, AsGrd5, PrGrd7] - [1/1, 11/9, 22/15, 26/15]

[0, 7, 13, 19] _ [P1, AsGrm3, PrGrd5, PrGrd7] - [1/1, 11/9, 13/9, 26/15]

[0, 7, 13, 19] _ [P1, DeAcM3, De5, Dem7] - [1/1, 27/22, 16/11, 96/55]

[0, 7, 13, 19] _ [P1, DeAcM3, DeAc5, Dem7] - [1/1, 27/22, 81/55, 96/55]

[0, 7, 13, 19] _ [P1, Prm3, PrGrd5, PrGrd7] - [1/1, 39/32, 13/9, 26/15]

[0, 7, 13, 19] _ [P1, ReM3, De5, Dem7] - [1/1, 16/13, 16/11, 96/55]

[0, 7, 13, 19] _ [P1, ReM3, Re5, Dem7] - [1/1, 16/13, 96/65, 96/55]

[0, 7, 13, 20] _ [P1, AsGrm3, AsGrd5, m7] - [1/1, 11/9, 22/15, 9/5]

[0, 7, 13, 20] _ [P1, AsGrm3, PrGrd5, Grm7] - [1/1, 11/9, 13/9, 16/9]

[0, 7, 13, 20] _ [P1, AsGrm3, PrGrd5, PrDem7] - [1/1, 11/9, 13/9, 39/22]

[0, 7, 13, 20] _ [P1, DeAcM3, De5, Grm7] - [1/1, 27/22, 16/11, 16/9]

[0, 7, 13, 20] _ [P1, DeAcM3, De5, PrDem7] - [1/1, 27/22, 16/11, 39/22]

[0, 7, 13, 20] _ [P1, DeAcM3, DeAc5, m7] - [1/1, 27/22, 81/55, 9/5]

[0, 7, 13, 20] _ [P1, Prm3, PrGrd5, Grm7] - [1/1, 39/32, 13/9, 16/9]

[0, 7, 13, 20] _ [P1, Prm3, PrGrd5, PrDem7] - [1/1, 39/32, 13/9, 39/22]

[0, 7, 13, 20] _ [P1, ReM3, De5, Grm7] - [1/1, 16/13, 16/11, 16/9]

[0, 7, 13, 20] _ [P1, ReM3, De5, PrDem7] - [1/1, 16/13, 16/11, 39/22]

[0, 7, 13, 20] _ [P1, ReM3, Re5, m7] - [1/1, 16/13, 96/65, 9/5]

[0, 7, 13, 21] _ [P1, AsGrm3, AsGrd5, AsGrm7] - [1/1, 11/9, 22/15, 11/6]

[0, 7, 13, 21] _ [P1, AsGrm3, PrGrd5, AsGrm7] - [1/1, 11/9, 13/9, 11/6]

[0, 7, 13, 21] _ [P1, AsGrm3, PrGrd5, PrGrm7] - [1/1, 11/9, 13/9, 65/36]

[0, 7, 13, 21] _ [P1, DeAcM3, De5, DeAcM7] - [1/1, 27/22, 16/11, 81/44]

[0, 7, 13, 21] _ [P1, DeAcM3, De5, DeM7] - [1/1, 27/22, 16/11, 20/11]

[0, 7, 13, 21] _ [P1, DeAcM3, De5, ReM7] - [1/1, 27/22, 16/11, 24/13]

[0, 7, 13, 21] _ [P1, DeAcM3, DeAc5, DeAcM7] - [1/1, 27/22, 81/55, 81/44]

[0, 7, 13, 21] _ [P1, Prm3, PrGrd5, AsGrm7] - [1/1, 39/32, 13/9, 11/6]

[0, 7, 13, 21] _ [P1, Prm3, PrGrd5, PrGrm7] - [1/1, 39/32, 13/9, 65/36]

[0, 7, 13, 21] _ [P1, ReM3, De5, DeAcM7] - [1/1, 16/13, 16/11, 81/44]

[0, 7, 13, 21] _ [P1, ReM3, De5, DeM7] - [1/1, 16/13, 16/11, 20/11]

[0, 7, 13, 21] _ [P1, ReM3, De5, ReM7] - [1/1, 16/13, 16/11, 24/13]

[0, 7, 13, 21] _ [P1, ReM3, Re5, ReM7] - [1/1, 16/13, 96/65, 24/13]

[0, 7, 14, 19] _ [P1, AsGrm3, P5, Sbm7] - [1/1, 11/9, 3/2, 7/4]

[0, 7, 14, 19] _ [P1, DeAcM3, P5, Sbm7] - [1/1, 27/22, 3/2, 7/4]

[0, 7, 14, 19] _ [P1, Prm3, P5, Sbm7] - [1/1, 39/32, 3/2, 7/4]

[0, 7, 14, 19] _ [P1, ReM3, P5, Sbm7] - [1/1, 16/13, 3/2, 7/4]

[0, 7, 14, 20] _ [P1, AsGrm3, P5, Grm7] - [1/1, 11/9, 3/2, 16/9]

[0, 7, 14, 20] _ [P1, AsGrm3, P5, PrDem7] - [1/1, 11/9, 3/2, 39/22]

[0, 7, 14, 20] _ [P1, AsGrm3, P5, m7] - [1/1, 11/9, 3/2, 9/5]

[0, 7, 14, 20] _ [P1, DeAcM3, P5, Grm7] - [1/1, 27/22, 3/2, 16/9]

[0, 7, 14, 20] _ [P1, DeAcM3, P5, PrDem7] - [1/1, 27/22, 3/2, 39/22]

[0, 7, 14, 20] _ [P1, DeAcM3, P5, m7] - [1/1, 27/22, 3/2, 9/5]

[0, 7, 14, 20] _ [P1, Prm3, P5, Grm7] - [1/1, 39/32, 3/2, 16/9]

[0, 7, 14, 20] _ [P1, Prm3, P5, PrDem7] - [1/1, 39/32, 3/2, 39/22]

[0, 7, 14, 20] _ [P1, Prm3, P5, m7] - [1/1, 39/32, 3/2, 9/5]

[0, 7, 14, 20] _ [P1, ReM3, P5, Grm7] - [1/1, 16/13, 3/2, 16/9]

[0, 7, 14, 20] _ [P1, ReM3, P5, PrDem7] - [1/1, 16/13, 3/2, 39/22]

[0, 7, 14, 20] _ [P1, ReM3, P5, m7] - [1/1, 16/13, 3/2, 9/5]

[0, 7, 14, 21] _ [P1, AsGrm3, P5, AsGrm7] - [1/1, 11/9, 3/2, 11/6]

[0, 7, 14, 21] _ [P1, AsGrm3, P5, DeAcM7] - [1/1, 11/9, 3/2, 81/44]

[0, 7, 14, 21] _ [P1, AsGrm3, P5, ReM7] - [1/1, 11/9, 3/2, 24/13]

[0, 7, 14, 21] _ [P1, DeAcM3, P5, AsGrm7] - [1/1, 27/22, 3/2, 11/6]

[0, 7, 14, 21] _ [P1, DeAcM3, P5, DeAcM7] - [1/1, 27/22, 3/2, 81/44]

[0, 7, 14, 21] _ [P1, DeAcM3, P5, ReM7] - [1/1, 27/22, 3/2, 24/13]

[0, 7, 14, 21] _ [P1, Prm3, P5, AsGrm7] - [1/1, 39/32, 3/2, 11/6]

[0, 7, 14, 21] _ [P1, Prm3, P5, DeAcM7] - [1/1, 39/32, 3/2, 81/44]

[0, 7, 14, 21] _ [P1, Prm3, P5, ReM7] - [1/1, 39/32, 3/2, 24/13]

[0, 7, 14, 21] _ [P1, ReM3, P5, AsGrm7] - [1/1, 16/13, 3/2, 11/6]

[0, 7, 14, 21] _ [P1, ReM3, P5, DeAcM7] - [1/1, 16/13, 3/2, 81/44]

[0, 7, 14, 21] _ [P1, ReM3, P5, ReM7] - [1/1, 16/13, 3/2, 24/13]

[0, 8, 13, 19] _ [P1, M3, Sb5, Sbm7] - [1/1, 5/4, 35/24, 7/4]

[0, 8, 13, 19] _ [P1, ReAsM3, ReAsSb5, Sbm7] - [1/1, 33/26, 77/52, 7/4]

[0, 8, 13, 20] _ [P1, M3, Sb5, ReSbM7] - [1/1, 5/4, 35/24, 70/39]

[0, 8, 14, 19] _ [P1, AcM3, P5, Sbm7] - [1/1, 81/64, 3/2, 7/4]

[0, 8, 14, 19] _ [P1, M3, P5, Sbm7] - [1/1, 5/4, 3/2, 7/4]

[0, 8, 14, 19] _ [P1, ReAsM3, P5, Sbm7] - [1/1, 33/26, 3/2, 7/4]

[0, 8, 14, 21] _ [P1, AcM3, P5, AsGrm7] - [1/1, 81/64, 3/2, 11/6]

[0, 8, 14, 21] _ [P1, AcM3, P5, DeAcM7] - [1/1, 81/64, 3/2, 81/44]

[0, 8, 14, 21] _ [P1, AcM3, P5, ReM7] - [1/1, 81/64, 3/2, 24/13]

[0, 8, 14, 21] _ [P1, M3, Gr5, DeM7] - [1/1, 5/4, 40/27, 20/11]

[0, 8, 14, 21] _ [P1, M3, Gr5, PrGrm7] - [1/1, 5/4, 40/27, 65/36]

[0, 8, 14, 21] _ [P1, M3, P5, AsGrm7] - [1/1, 5/4, 3/2, 11/6]

[0, 8, 14, 21] _ [P1, M3, P5, DeAcM7] - [1/1, 5/4, 3/2, 81/44]

[0, 8, 14, 21] _ [P1, M3, P5, ReM7] - [1/1, 5/4, 3/2, 24/13]

[0, 8, 14, 21] _ [P1, M3, PrDe5, DeM7] - [1/1, 5/4, 65/44, 20/11]

[0, 8, 14, 21] _ [P1, M3, PrDe5, PrGrm7] - [1/1, 5/4, 65/44, 65/36]

[0, 8, 14, 21] _ [P1, ReAsM3, P5, AsGrm7] - [1/1, 33/26, 3/2, 11/6]

[0, 8, 14, 21] _ [P1, ReAsM3, P5, DeAcM7] - [1/1, 33/26, 3/2, 81/44]

[0, 8, 14, 21] _ [P1, ReAsM3, P5, ReM7] - [1/1, 33/26, 3/2, 24/13]

Hats off to Curt, I guess. I hope you like my chords, Curt. I made them for you. Okay, time to look at more of his videos and see what I did wrong. His next step is to describe some chords that follow his rules.

Here is the chord Curt describes the "minor harmonic seventh" chord, with pitches [G, Bb, D, Fb_up]. I don't know his notation - it's probably just HEJI, but I refuse to learn HEJI. It seems odd to call a subminor seventh F flat_up when it's lower than Fb. Maybe it's a typo, or maybe it's odd notation. Either way, presumably he's talking about this:

[0, 6, 14, 19] _ [P1, m3, P5, Sbm7] - [1/1, 6/5, 3/2, 7/4]

which was among my 161 chords. Nice.

Curt next plays the "neutral 13th chord", which is [G, Bb, Ct, Ed]. Ct is C half sharp, Ed is E half flat. I think in 24-EDO steps that would be [0, 6, 11, 17]. This isn't spelled by thirds - though it could be if it were inverted / cyclically permuted to be rooted on C. But let's continue anyway. The octave reduced 13th harmonic is a prominent minor sixth in my naming system, Prm6, with just tuning of 13/8, and a 24-edo tuning of 17\24. So clearly when Curt calls this chord "neutral 13th", part of what he means is that it includes the 13th harmonic, which is a half-flat / neutral tone. The octave-reduced 11th harmonic is the ascendant fourth, As4, with a just frequency ratio of 11/8 and a 24-EDO tuning of 11\24 steps. I'm pretty sure Curt is thinking of this chord as

    [0, 6, 11, 17] _ [P1, m3, As4, Prm6] # [1/1, 6/5, 11/8, 13/8]

If we move the bottom two notes up by an octave, and then subtract As4 from everything (or divide all the frequency ratios by 11/8), then we get this chord from my set of 161 chords:

    [0, 6, 13, 19] _ [P1, PrDem3, De5, Dem7] - [1/1, 13/11, 16/11, 96/55]

That's the rooted tertian spelling of Curt's neutral 13th chord. Great! I'm very pleased that our chords are alignable so far, if not identical. If you're curious, De5 in its just tuning is flat of P5 by about 53 cents,

    (3/2) / (16/11)  = 33/32

    1200 * log_2(33/32) ~ 53.2 cents

The next chord Curt presents is the "19th to 15th" chord. Is he going to use the 19th harmonic? He had only mentioned 13-limit ratios up to this point. If so, this guy's on another level. The pitches given are [F#, A, Ct, Eb_up]. In 24-EDO steps, I think that would be [0, 6, 11, 19].

My set of 161 chords had two intervallic chords with that same 24-EDO tuning, namely

[0, 6, 11, 19] _ [P1, PrDem3, PrDeSbd5, Sbm7] - [1/1, 13/11, 91/66, 7/4],

[0, 6, 11, 19] _ [P1, m3, Sbd5, Sbm7] - [1/1, 6/5, 7/5, 7/4],

But I don't know any reason you'd call either of those a "19th to 15th" chord. I don't think "19th to 15th" is referring to a sequence of prime harmonics - this chord is a long way from the utonal 19:17:16:15, for example. And for otonal chords, 15:16:17:18:19 would be 

    [1/1, 16/15, 17/15, 6/5, 19/15]

which is also way off from the 24-EDO tuning of Curt's chord. A 19th interval, octave reduced, is a fifth, and a 15th interval, octave reduced, is a unison. That's probably not what he means either. I just don't know what the name means. But I've got a chord that matches his chord, so that's something.

After listening again, I think he's saying, "The 19th, the 15th chord". I still don't know what that means.

He talks about "9-15" chords in a later video called "The Magic Chord". So maybe I misheard him every time? But I just relistened, and it really sounds like "the 19th to 15th" or "the 19th, the 15th". Anyway, in "The Magic Chord", Curt gives [A, C, Ed, Gd] as a 9-15 chord on A, which would be

    [0, 6, 13, 19]\24

I think. But that's the rooted tertian spelling of Curt's neutral 13th chord. So confused. Ah, but then he says that he goofed, the chord spelled that way is not a 9-15 chord, it is instead "nine fifteen fo(u)r flat seven(th)". So lost.

If this Ct is the same one that was 11/4 over G, then Curt might be thinking of this chord as

    [P1, m3, AsGrd5, Sbm7] # [1/1, 6/5, 22/15, 7/4]

i.e. we're widening the 11/4 by a 5-limit minor second to represent the gap (Ct - F#) instead of (Ct - G).

My program didn't find that chord because between the chord degrees ^5 and ^7 there's an unusual interval of DeSbAcM3 with a just tuning of 105/88. On the other hand, DeSbAcM3 is tuned to 6 steps of 24-EDO, so maybe Curt just thinks of it as a minor third.

The next chord Curt gives is the "added 13th minor", with pitches of [G, Bb, D, Eb_up]. Curt's probably thinking of this as

    [P1, m3, P5, Prm6]

which we can invert to get a tertian chord. Move the top three notes up an octave and reduce/rebase/re-root. That gives us

    [0, 7, 13, 21] _ [P1, ReM3, Re5, ReM7] # [1/1, 16/13, 96/65, 24/13]

which was one of my 161 tertian intervallic chords. Nice.

He also plays the minor harmonic 11th chord, for which the accidentals look a little weird. It looks like [G, Bbt, C, Fb_up], but most people wouldn't use both flat "b" and half-sharp "t" on one note unless they were thinking intervallically, and I ... didn't think that Curt was? I thought he would just write Bd for "half flat" instead of "flatten by one comma and raise by another". Anyway, in steps of 24-EDO, if Fb_up is supposed to be F three quarters flat, then this is

    [0, 7, 14, 19]

in 24-EDO steps. I had four chords with this tuning in my set of 161 intervallic chords, namely

[0, 7, 14, 19] _ [P1, AsGrm3, P5, Sbm7] - [1/1, 11/9, 3/2, 7/4]

[0, 7, 14, 19] _ [P1, DeAcM3, P5, Sbm7] - [1/1, 27/22, 3/2, 7/4]

[0, 7, 14, 19] _ [P1, Prm3, P5, Sbm7] - [1/1, 39/32, 3/2, 7/4]

[0, 7, 14, 19] _ [P1, ReM3, P5, Sbm7] - [1/1, 16/13, 3/2, 7/4]

And I think either of the first two (11-limit) chords is a fine just intonation for Curt's neutral 11 chord. 

He also shares chords called the neutral 11th, the major harmonic 11th, the neutral triad, the neutral harmonic seventh, the neutral dominant seventh, the harmonic diminished seventh, and "two stacked harmonic seconds".

He also plays some nice sounding chords that break his rule about not allowing 9-step and 15-step intervals. These are the subminor triad, the sub-minor harmonic seventh, the sub-minor dominant seventh, and three stacked harmonic seconds.  

I might write those out and analyze them eventually, but in the meantime, I think we're doing fine. We've mostly found the same chords as him. Good job, us.

I started writing about his content in other videos, but it sounded kind of judgey, so I'll stop here. Thanks for your chord construction technique, Curt. Good guy, Curt.

Here is a rendering of all 161 chords in order. I won't pretend that 4 minutes of microtonal chords on the same tonic is easy listening, but I hope you'll agree that the chords individually aren't too dissonant.

A Grammar Of Diminished Chords

 :: Intro

In my crash course on jazz piano, I described the grammatical/functional use of diatonic chords, modal chords, and augmented chords. I also talked at good length about diminished chords, but I didn't present a grammar for using them in relation to diatonic tetrads. I'm going to do that here and now.

:: Dim7 Chords In The Barry Harris System

In the Barry Harris jazz piano system, there's a diminished seventh chord that you can play before or after almost any other chord. 

Here are our main diatonic tetrads in C major for concreteness:

[C.maj6, C.maj7, D.m7, E.m7, F.maj7, G.7, A.m7, B.m7b5]

We'll target each of those with a .dim7 chord. In lots of jazz, C.maj6 and C.maj7 are played fairly interchangeably, but my understanding is that they're quite distinct in the Harris system, so we'll treat them separately in this section.

Let's write out the .dim7 options that alternate against diatonic tetrads in the key of C major.

C.maj6 ↔ B.dim7

C.maj7 ↔ F#.dim7

D.m7 ↔ E.dim7

E.m7 ↔ F#.dim7

F.maj7 ↔ B.dim7

G.7 ↔ C#.dim7 or B.dim7.

A.m7 ↔ B.dim7

B.m7b5 ↔ C#.dim7

If you've already learned about the Barry Harris system, here's a refresher on where these come from:

C.maj6 and B.dim7 are the two chords that alternate in the C major-diminished scale at the heart of the method.

Since A.m7 is an inversion of C.maj6, you play B.dim7, which comes from the C maj6-dim scale. 

Since D.m7 is an inversion of F.maj6, you play C#.dim7, which comes from the F maj6-dim scale.

Since E.m7 is an inversion of G.maj6, you play F#.dim7, which comes from the G maj6-dim scale.

Since F.maj9 is A.m7 over F, and we play B.dim7 against A.m7, we also play B.dim7 against F.maj7.

Since C.maj9 is E.m7 over C, and we play F#.dim7 against E.m7, we also play F#.dim7 against C.maj7.

Since B.m7b5 is an inversion of D.m6, you play C#.dim7, which comes from the D m6-dim scale.

G.7 is treated in the Barry Harris system as G.9 or G.7b9.

G.9 is B.m7b5 over G, and we play C#.dim7 against B.m7b5, so we also play C#.dim7 against G.9.

G.7b9 is B.dim7 over G, and B.dim7, so when you want a .dim7 chord that sounds good with G.7b9, obviously you can play B.dim7. But actually, since G.7b9 and B.dim7 have very similar sounds, you'd probably actually play C.maj6 against G.7b9. I haven't written that above because this post is just about diminished chords.

:: Dim7 Chords As Chromatic Approach Chords

Let's get away from the Barry Harris method now. Much like the idiom of approaching a note chromatically from below, there is an often used idiom of preceding a chord with a .dim7 chord whose root is a m2 below the root of the target chord. In the key of C major, that looks like

1. B.dim7 → [C.maj6 or C.maj7]

2. C#.dim7 → D.m7

3. D#.dim7 → E.m7

4. E.dim7 → F.maj7

5. F#.dim7 → G.7

6. G#.dim7 → A.m7

7. A#.dim7 → B.m7b5

Rule 7 here sounds a little worse than the others, but you can make it work. Rule 1 is partly familiar from Barry Harris (B.dim7 → C.maj6) and partly new (B.dim7 →  C.maj7). Rule 6 is also accounted for by the Harris system if you're working in a tuning such as 12-TET where G#.dim7 is enharmonic with B.dim7. The dim7 chords from rules 2, 4, and 7, namely (C#.dim7, E.dim7, and A#.dim7) are also enharmonic with each other. G.dim7 is also enharmonic with those three, so if you see a G.dim7 chord in a piece in C.maj, and you're struggling to analyze it, you might check if one of its enharmonic re-spellings makes more sense.

:: Half Diminished Chords As Secondary Dominants

Next let's talk about half diminished chords as secondary dominants. Since V.7 and VII.m7b5 both have dominant functions, we can talk about secondary VII.m7b5 chords just as much as secondary V.7 chords. In the key of C major, this gives us the following relations:

B.m7b5 → C.maj

C#.m7b5 → D.m7

D#.m7b5 → E.m7

E.m7b5 → F.maj7

F#.m7b5 → G.7

G#.m7b5 → A.m7

A#.m7b5 → B.m7b5

You'll notice these are all just half-diminished versions of the full diminished chord rules in the previous section. Easy. No sweat. Actually, we could also consider these chords to be rootless V.9 secondary dominants.

:: Dim7 Chords As Descending Chromatic Line Cliches

In addition to preceding a diatonic chord with a .dim7 approach from below, you can often follow a minor chord on a root with a .dim7 chord that has the same root, for a sound that is something like a descending chromatic line cliche. Here are some examples:

D.m7 → D.dim7 → C.maj7

F.maj7 → F.m7 → F.dim7 → ?(G.7) → C.maj7

A.m7 → A.dim7 → ?

E.m7 → E.dim7 → ?

The question marks are there as placeholders until I sit down at a piano and verify what my memory is telling me about these.

:: Dim7 Chords On Flat Three

Another pretty common use for .dim7 chords that you see in jazz is the [I → bIII] transition. Here's a common way to continue that:

C.maj7 → Eb.dim7 → D.m7

From all our previous experience with diminished chords, we'd expect that here, before D.m7, that we'd see an E.dim7 in the Harris system or C#.dim7 in the chromatic approach idiom, or C#.m7b5 as a half-diminished secondary dominant. But Eb.dim7 isn't any of those. Eb.dim7 happens to be enharmonic in 12-TET with chords such as D#.dim7, Gb.dim7, F#.dim7, A.dim7, and C.dim7. No match, no cigar.

Maybe the bIII dim7 chord is a rootless secondary dominant! You can add one of these notes [B, D, F, G#] to Eb.dim7 and get one of these dominant chords, [B.7b9, D.7b9, F.7b9, or G#.7b9], respectively, which means that Eb.dim7 can act like a rootless version of any of those. But none of those are secondary dominants to D.m7.

You could analyze this progression by calling the first transition a chromatic mediant relation between C and Eb, but those usually have chromatic mediant motion usually involves major and minor chord sonorities, not diminished.

Here's what I think is going on. My key insight was that this also sounds good:

    C.maj7 → Eb.dim7 → G.7

Here Eb.dim7, with notes [Eb, Gb, A, C], is a acting as an alteration of D.7, with notes [D, F#, A, C], which is a secondary dominant of G.7. You could also call it rootless D.7b9. And then

    C.maj7 → D.7 → D.m7

is like a chromatically descending like cliche, maybe.

There are probably other uses of .dim7 chords as alterations of secondary dominants or descending line cliches like these, but I haven't put in the leg work to find them yet.

...

I guess .dim7 chords as rootless V.7b9 chords would look like this:

Ab.dim7 → C.maj7

Bb.dim7 → D.m7

C.dim7 → E.m7

Db.dim7 → F.maj7

Eb.dim7 → G.7

F.dim7 → A.m7

...

The last transition, F.dim7 → A.m7, sounds a little weak, but the rest are very good.

We already saw .m7b5 as rootless secondary V.9 dominants of target chords. These .dim7 transitions are rootless secondary V.7b9 dominants of target chords. 

If the secondary V.7 of a chord has a root a perfect fifth up from the original chord, then this .dim7 chord, that arises as a rootless .7b9, has a tonic P5 + m2 = m6 above the original chord (or a major third below).

:: Outro

If you know any other uses of .dim7 or .m7b5 chords that aren't accounted for by the above rules, or if you have a different analysis of I.maj7 → bIII.dim7, please do let me know.

Canaan

I want a pixel art video game with a simulated economy set in ancient Canaan, featuring quests and story lines based on the lore of the Canaanite pantheon (which is primarily attested in the Ugaritic texts). I'm going to share some development progress here. Partly I think this will keep me organized. Partly, I'm worried that I won't every finish it, but at least this way people can see some of what almost was.

One of the first things I did was come up with a Canaanite video game ontology, i.e. a sorted list of things I might want in the video game that are probably all historically appropriate, I'm not sure, I'm not a historian. Here it is:

: Canaanite Video Game Ontology

 

* domestic animal: ox, horse, goat, sheep, cow, sheep, camel, rock dove.

* wild animal: lion, wild dog, crocodile, snake, lizard, deer, gazelle.

* wild insect: ant, beetle, bee, fly, wasp, butterfly, dragonfly.

* wild bird: eagle, vulture, falcon, goose, duck, pigeon, sparrow, bulbul, bunting, grebe, gull, heron, kite, lark, owl, pipit, sandpiper, serin, shrike, sparrow, swift, vulture, warbler, wheatear.

* wild fish: sea bream, grouper, mullet, perch, sea bass, tilapia, string ray, shark, shrimp.

* plant: grass, seaweed, wheat plant, reed, barley plant, flax plant, fig tree, grape vine, olive tree, almond tree, date palm tree, pomegranate tree, oak tree, cedar tree, pine tree, sycamore tree.

* character class: god, king, servant, handmaid, merchant, beggar, child, farmer, bee keeper, fisherman, herdsman, pigeon fancier, butcher, sheep shearer, spinner, weaver, scutcher, brick mason, stone mason, brick maker, carpenter, potter, miner, smelter, copper smith, flint knapper, shipwright, fletcher, miller, baker, vintner, candler, sailor, guard, soldier, wet nurse.

* food: honey, pigeon meat, fish meat, fish roe, goat meat, cow meat, goat milk, cow milk, barley, wheat berry, millet seed, flour, bread, fava bean, chickpea, pea, lentil, almond, flax seed, date, fig, olive, olive oil, grape, grape juice, wine, pomegranate, drinking water, salt.

* textile: string, rope, linen fiber, linen cloth, wool yarn, wool cloth, animal skin, leather, fur.

* tool: adze, mattock, scythe, pick, billhook, flint blade, sickle, spear, oar, paddle, net, sharpened stick, club, bronze axe, bronze sword, bronze dagger, bow, arrow, shield, helmet, walking stick, crook.

* furniture: wicker chair, wicker table, oven, fireplace, door, gate, fence.

* furnishing: waterskin, candle, linen sack, linen blanket, bronze platter, reed mat, wool blanket, woven basket, clay amphora, clay jar, clay pot, clay cup, clay vase, stone plate, stone bowl, clay plate, clay bowl, stone pot, incense, lyre, horn, flute, drum, flint knife, shell spoon, bone spoon, brass spoon, wood spoon.

* valuable: silver piece, ruby, emerald, sapphire, diamond, carnelian, agate, bronze ring, bronze earring, bronze bead, bronze necklace, bronze bracelet, bronze hair pin, bronze collar, silver ring, silver earring, silver bead, silver necklace, silver bracelet, silver hair pin, silver collar, gold ring, gold earring, gold bead, gold necklace, gold bracelet, gold hair pin, gold collar.

* clothing: linen dress, linen robe, linen tunic, linen cloak, wool dress, wool robe, wool tunic, wool cloak, linen shawl, wool kilt, headband, arm band, hat, turban, hair tie.

* vehicle: boat, ship, cart, chariot.

* raw material: water, beeswax, clay, copper, tin, bronze, dung, flax fiber, papyrus, reed, wood, ivory, brick, silver, gold, malachite, chalcopyrite, cassiterite, emery.

* map region: palace, garden, lodge, house, stream, temple, country, field, lake, large rock, mine, city, hill, plain, shrine, marsh, village, river, tomb, dovecote, mountain, market, dock, sacred grove, grotto, waterfall, cliff, cave.

* human activity: sleeping, bathing, eating, drinking, working, farming, hoeing, weeding, harvesting, sowing, rowing, celebrating, binding flax, mining, collecting reeds, collecting dung, cleaning, cooking, washing laundry, childcare, praying, singing, dancing, selling goods, cutting wood, making bricks, building, guarding, butchering, making wine, bronze working, making a religious offering, harvesting fruit, harvesting grain, harvesting legumes, talking, walking, running, fishing, counting money, thinking, begging, haggling, cutting wood, smelting tin, hammering bronze, making candles, tending livestock, firing bricks, laying bricks, grinding flour, shearing sheep, spinning yarn, weaving fabric, fetching water, boiling water, cooking meat, throwing clay, firing clay.

Nice. Next, here is my initial pixel art: 

These thigns don't look good in isolation, don't look good together, and the objects certainly don't look good superimprosed over the terrain, but they show the vibe I'm going for. I think the brick walls need to be replaced entirely, but most of the rest of it just needs heavy clean up.

I started by cleaning up the terrain tiles. That got me a three material dual grid tileset (water, grass, sand/stone):

These are 16x16 tiles, and they're offset from by half a tile from the world map as the players see it, because there are only 3^4 = 81 distinct corners where materials meet, whereas there are 3^8 = 6561 neighbors for a tile in three materials, and I didn't want to draw a different central tile for each of those options. In short, by drawing the corners instead of the centers, you can draw many fewer tiles. This is called a dual grid system.

Levels generated with that dual grid tileset let me test my path finding algorithms, but they felt very flat, so I started working on a mountainous tileset. Actually, I started with rivers and a waterfall, and it didn't look right with the land tiles that I already had - they didn't seem adequate to surround a waterfall in a natural looking way. So I drew a lot of terraced land spaces trying to figure out what looked right. 

I don't have my mountain tiles organized very well; I think some of these might need to be offset by half a tile in one or both directions for consistency, but first I'm just trying to cut down duplicate tiles to see what I've got.

 Eventually I want tiles for a biome progression like:

    [sea and shore → town → fields and forest and desert → mountains and waterfalls → caves and mines]

I also want a lot of sprites for crops, but I might just have a few generic crop sprites, and you'll have to look in the textual user interface to tell if a grain growing on a square is barley or wheat or millet.

Let's talk a little about NPC activities.

I originally wrote a scheduling function that put all the NPCs on a 24 hour schedule like [sleep, bathe, eat breakfast, walk to work, work, eat lunch, work, walk home, eat supper, relax, sleep]. They were all offset from each other by different wake times, but otherwise they had identical schedules. Then I wrote a path planning algorithm, and instead of just automatically telling an NPC to dp a verb at a given time, it made sense for them to e.g. only work once they finished walking to their own work area. Preconditions for verbs. Nice.

I also wrote verbs for different tasks. These took the form of economic production functions, describing what a person could produce in a work day, given different inputs - tools, time worked, material inputs that are consumed in production, material inputs like land that aren't consumed in production.

For example, a hunter could produce certain amounts of [meat, hide, bone, sinew, horn, and antler] in a given day, with a certain amount of inherent randomness, and different gains to these products based on whether they possess, for example, a [javelin, bow and arrow, knife, or snare trap]. Fun side note: my code estimates/calculates the amount of hide obtained from an animal by assuming a spherical cow of unit density (1 gm/cm^3).

For most jobs, you do a specific verb for a few hours a day, and once your time card tally says you've done 8 hours of work, then the production functions is called and drops some items into your inventory.

The production function for fishermen checks if the player or NPC has a cast net, a fishing pole, or a shore trap. Fishermen produce both fish meat and fish meal (heads, viscera, bones, skin, scales, and fins) which can be used to feed livestock.

My production functions for farmers are much more involved and I'm not done writing them. The basic calculation for different crops is just

    total yield = yield per hectare * workable area

with workable area depending on whether you have a family and/or a draught animal, and yield having some inherent variability and also depending on seasonal factors like rain and growing degree days. But then you also have a smaller net yield for many crops, like grains and legumes, and this is found by subtracting off how much of the crop is saved for planting-seed, i.e. 

    planting seeds saved = planting rate * workable area

    net yield = total yield - planting seeds saved

I'm also planning to model seasonality of work that's done on different crops (when you plant, when you weed, when you harvest) based on what you farm, with the work differing by season for every crop, but with work functions being broadly divisible into categories of: grain, legumes, or fruit. Fruit farmers will also mostly have side gigs as goat farmers, which I think is realistic.

Farmers don't get a portion of crops in their inventory every 8 hours - they harvest once a year and either sell their crop throughout the year at market, or maybe they sell to a food merchant who sells the crop at market and then the farmer doesn't have to spend time in the market. So when the game starts, the code makes up numbers for last year's harvest and how much the farmer has probably sold up to the current date to figure out their inventory.

Here's a thing I made when working on crop seasonality code that I wouldn't want to lose. Maybe you'll have a use for it also:

date_ranges = {

"January": [1, 31],

"February": [32, 59],

"March": [60, 90],

"April": [91, 120],

"May": [121, 151],

"June": [152, 181],

"July": [182, 212],

"August": [213, 243],

"September": [244, 273],

"October": [274, 304],

"November": [305, 334],

"December": [335, 365],

}

I won't use those modern names for months in the game, but it's convenient to be able to look up when a crop is harvested in the modern era, like late May to early July, in order to say what days of the year the crop was probably harvested in the past.

When a player or NPC does a verb, I want there to be some visual indication of the fact, even if you can't e.g. see their fingers weaving reeds into mats. So I've been working on animations for bending over and moving hands.

At some point I might also have sleeping animations or animations for moving hands while sitting at a chair.

Let's talk about simulating the economy. I think at some point I'm going to change the NPC scheduling function so that everyone goes to market for a while each day, both to buy and sell. A person walks around, inquires about prices from the people they bump into, and then makes some purchases. The market will have booths for a realistic appearance, but the selling and buying will probably happen virtually following this bump-encounter price-sharing.

I don't know much economics and I'm sure I will have to do a lot of debugging to get an economy that is both somewhat stable and somewhat realistic.

For this time period, a daily wage for most labor was 0.07 to 0.10 troy ounces of hacksilver, which is 2.07 to 3.11 grams. I'd be really pleased if I got my economy to reproduce a typical wage like that, but I'm also just considering enforcing that wage and seeing what happens to the rest of the economy as a consequence, or enforcing it for a few physically demanding jobs.

Sellers are going to set one price for each good that they sell in a day. There will be no daily haggling, and no adjusting of prices when a seller sees other sellers' prices that day (though maybe they can base today's price on prices seen yesterday).

Sellers are going to try to maximize profit, in the sense of

    profit = items sold * price per item

or

    profit = quantity sold * unit price for quantity

I don't think the sellers need to include [cost of production] in their profit calculations. Like, that does influence the final number, but it doesn't influence the optimization problem, right? The right price to maximize [price weighted number of sales] doesn't depend on whether you go into debt afterward because the cost of production was too high. But I don't know much econ. Maybe I'm wrong and my Canaanite economy won't work without that term in the mental calculus of the merchants. We'll see.

Wait, it's realistic for the price to go up if the cost of production goes up, right? Right. But maybe that's not due to the mental calculus of sellers. Maybe it's due to there being less of the produced thing on the market, combined with some purchasers being willing and able to buy at a higher price in order to get some share of what is still on the market. That might be way off, but it's how I'm going to code things up for a first pass. The sellers don't consider cost of production when price setting.

Whether an item is net profitable for a seller after the cost of production is still important of course - it influences whether you decide to keep producing that particular thing at all, and more broadly whether you decide to keep or change your profession. I might include a mechanism for NPCs to change their jobs like this. I've also considered that if an NPC goes too long without food, they could, um, reincarnate as a new healthy NPC with a randomly chosen job. This way I wouldn't have to model everyone choosing the optimal job given their expectations about the economy, but the economy would still move toward a workforce that was doing profitable things, in case fig farming or linen scutching turns out to not be in such high demand in my virtual world. Also I don't have to worry about everyone switching to fig farming if that suddenly looks like a very profitable career. Reincarnation with random jobs hopefully means that there is both job diversity and individual wealth (due to non-wealthy generating jobs being replaced after a few days), without everyone having to calculate Hamilton–Jacobi–Bellman equations or POMDPs or other life-history optimal decision process math.

Like in real life, sellers won't have access to demand functions (either demand functions for individual purchasers or aggregate market demand functions) for use in setting their prices to maximize profit. They'll just do little experiments from day to day and see how their profit changes as a consequence.

For there to be a market for expensive non-consumable goods, like houses and boats, I think the purchasers will have to periodically have a need to replace them, i.e. the items need to wear out or break or maybe get lost sometimes - otherwise the boat makers would makes a boat for everyone and then no one would ever need a boat again unless the population increased. So I'll probably end up putting an age or usage counter on lots of material artifacts in the game, and I'll cause items to break based on age or usage, simply so that there can be a realistic economy on durable goods.

So that's a sketch of how sellers do things. How do the NPCs choose what to buy? This sounds a lot harder to model. I said before that the sellers don't have access to demand functions of the market, for the sake of realism. Also for realism, the NPCs don't have demand functions at all, full stop, regardless of access. I just don't think demand functions are good models of economic choice. If you think otherwise, please show me your demand function for apples or window panes or '95 ford crown victorias.

So I'm not writing demand functions for NPCs. What else can we do? We could say that NPCs have daily needs for calories, and they have finite budgets, and maybe finite storage, and they try to minimize days when they go hungry over some small time horizon? I think this would produce a really weird market that cared mainly for producing the food with the cheapest-to-produce calories, and then cared about producing tools used in producing that food, and then cared about inputs to the production of those tools if any. But it's not going to create a rich human world where people cook for their families and rest on their funiture and play musical instruments and wear colorful clothes or precious stone jewelry or burn incense or bring wine to a festival or other acts of human flourishing that are aided by material goods.

Here's a slight increase in the mental complexity of the NPCs that can support a much richer economy: an NPC wants to buy something they don't have. People who aren't starving will have some discretionary funds, and use this to buy a trinket randomly.

In the long run, I think this results in all the impulse purchases having the same price (unless that price isn't enough to offset the cost of production, and then the profession that makes the impulse item disappears from the market (unless the impulse item is a byproduct of labour that the market directly values - like maybe there's a market for sinew because there's a market for meat, even though a hunter couldn't live by only selling sinew)). I'll say that again: I expect that impulse purchases will all have the same price eventually roughly or disappear from the market. And in this economy, there still won't be any purchases of things that are more expensive than the normal discresionary fund value.

So that's a slight improvement, but only slight. Let's make the NPCs a little more mentally complex to improve the maket realism more.

Suppose that people make somewhat strategic purchases for their professions. A wine maker buys grapes from the grape farmer and maybe ?(buys yeast from a miller or a brewer)? and buys amphorae from the potter. Then in addition to grape farmers being supported by food purchasers and impulse buyers, they're also supported by the occasional reincarnation of a person into a wine maker.

Let me say that again. Wine makers exist and try to maximize personal profits by doing their jobs. This supports other jobs. Hopefully the economy is productive enough that NPCs can support each other in making nice things, instead of everyone starving because they're not making food - the main things that the market necessarily values - and so gradually everyone reincarnates into an X that reincarnates into a Y, and the cycle of rebirth always ends in you being a barley farmer or a barley farmer tool supplier.

I'm not sure that this is enough purchaser preference to act as the foundation for a world that looks human, but it's a start. I'm also not sure how complicated I should make the mental calculation for the NPCs trying to maximize profit within their profession by purchasing instrumental goods.

I could also tie food purchasing into instrumental preference - people work better when fed, so profit maximizing is a reason to buy food. But I absolutely refuse to do that. That's a move away from humanity. If anything, I should add more preferences for direct social and sensory experience - preference for food variety, preference for caring for people and pets, preference for making beautiful things, et cetera. And then instead of just trying to buy one of every cheap thing in the market, people would save up to buy a piece of pretty jewelry or a food they'd never tried before or a nice collar for their dog, who is a good girl. I'm not sure if I can code all that up, but it would be nice.

I already mentioned that for there to be a market in durable goods, I think that durable goods have to become useless at some point - e.g. worn away, broken down, or maybe lost. I'd like for NPCs to model this a little bit - they have an expectation of when a thing they own will break and save up in advance to replace it. Alternatively, they just don't think about it till it breaks, and if it's useful for their job, then they stop making random impulse purchases until they've saved up enough to clear their shopping list of profession-specific capital.

So I'm not sure how much NPCs should think about purchases in order to maximize personal producitivty, but maybe just having to clear your shopping lists before doing impulse purchases is enough. I guess we have 1) a home grocery list, and 2) a shopping list for materials consumed in production at their job, and 3) a shopping list for job tools, and then I have to figure out how a player makes purchases with those lists looming over their head.

I might have different purchasing functions for each profession. That doesn't sound too hard. And, uh, maybe some fixed percent of daily pay check goes into savings for purchasing capital. And .... I think "diverse professions buying instrumental goods" should make for a fairly diverse economy on its own, and impulse purchasing can fill in some of the gaps.

Another idea is that I could give each NPC a preference for doing a particular leisure activity, like playing music or home decorating or religious worship, and they devote some resources to their hobby weekly.

Having a bunch of shopping lists in the mind of each NPC isn't so difficult, but I'll need a mechanism that goes from lists of items that could be purchased to actual decisions about how much the NPC is willing to spend on each given item given the need for other objects on the shopping list.

I don't want the NPCs to be so detailed as to have experiential preferences or beliefs about their causal contingencies, so we're not doing expected utility calculations. But there will need to be some kind of preference ordering.

Here's a first stab at it:

An agent first makes sure they have enough food for three days. Three meals a day, and a meal is measured as a set number of kilocalories, which are known for each unit quantity of food type, and must also include foods from two food groups, e.g. [grain, legumes, fruit]. They purchase the cheapest food they can that day to satisfy those dietary requirement. No preference for variety or quality of food. I'm not sure if NPCs will have households and make purchases for the whole house. We'll see.

I tried doing a more realistic diet calculation. Suppose our food options are these: [Almond, Barley, Bread, Chickpea, Cow Meat, Cow Milk, Dried Date, Dried Fig, Fava Bean, Fish Meat, Fresh Fig, Goat Meat, Goat Milk, Grape, Honey, Lentil, Millet, Olive Oil, Olive, Pea, Pigeon Meat, Wheat Berry, Wine]. I looked at total kilocalories per 100 grams and kilocalorie from protein per 100 grams. I assumed a diet of 2500 kcal/day, of which at least 224 kcal should be protein. I found how much of each food you'd need to reach that many kilocalories, then checked if that quantity met the daily protein requirements (many did), and then estimated a historic price to see which foods you can live on most cheaply. The cheapest ones were [Bread, Millet, Wheat Berry, Chickpea], and it's a little odd that bread is cheaper than wheat, but maybe that's because flour has more protein per gram than wheat berries with their bran. The quantity of bread to reach 2500 kcal is like 2.5 loaves, which doesn't actually sound like a healthy daily diet, even ignoring the missing vitamins and other nutrients. Even if I bump up the daily required protein to 500 kcal, then [Chickpea, Lentil, Fava Bean] still clock in as adequate mono-food diets and almost as cheap as bread. Milk and meat are 3 to 10 times more expenive than grains and legumes, and I'm not sure that anyone in this fictional economy has an incentive to buy them besides as an impulse purchase. Unless crops fail maybe. Yeah, that's not a crazy possibility, between occaional bad weather and spiteful gods. And then it makes total sense that fruit growers might supplement by raising goats: goat milk and goat meat aren't just supplementary income, they're income precisely for when the crops fail. Diversifying with anti-correlated risk, might be the term? And people might also buy meat or milk if they need food and haven't found anyone in the market selling cheaper foods on that day. Or if they already own lots high calorie foods but not lots of protein, then a little high quality protein might let you make good use of what you already have. Ooh! Let's see what *pairs* of foods from the list above lets you hit your total calorie and protein calorie requirements in a day most cheaply.

For a given pair of foods, we want to find quantity_a and quantity_b that minimize 

total_price = food_a.unit_price * quantity_a + food_b.unit_price * quantity_b 

subject to

food_a.calories * quantity_a + food_b.calories * quantity_b >= total_calories_needed

food_a.protein * quantity_a + food_b.protein * quantity_b >= total_protein_needed

...

I just sampled possible pairs instead of working out the optimization, but a diet of [almost entirely bread plus a tiny amount of something else] wins every sampling run. If we don't let bread into the running, then Barley with Millet or Barley with Chickpea wins.

If we get rid of all the diets where both elements are (grains or legumes) and we get rid of all the diets where less than 100 g of one of the items is used, then Goat Milk with Millet or Barley wins, and also there are some fairly cheap diets involving Fresh Fig, Cow Milk, Grape, Olive, Almond.

Having seen this, and wishing to promote diversity in diets and in the market, I propose that a daily diet has to include an item that isn't a grain or legume, and non-grain/legume items consumed in a day have to come to at least 100 grams (which is just a scant half cup for a material with a density like water). Not too expensive a contraint, not too weird a constraint, and it will make the markets and the diets more human. Nice.

...

Lol, my sysem for food preferences doesn't work. It might work if I constrain the number of grams of food you eat in a day. Suppose a bee keeper has a lot of honey in their inventory. And honey has ~1 protein kilocalorie per 100 grams, and a person needs 244 protein kilocalories per day. In the current system, the beekeper is going to eat 22.4 kilograms of honey from their own inventory, per day, and only start buying other foods when they have less than a three-day stock of honey, i.e. less than 67.2 kilograms. For those of you who only do clown units, this person is eating 50 lb of honey a day. Not super realistic. This scenario isn't even ignoring the requirement to get 100 grams of diverse calories from non-grain/non-legume food, because honey is such a food.

Possible fixes: 

    Solution 1: A player can't eat from their sellable inventory. This would probably work, but it's unrealistic. A wheat farmer should be allowed to eat their own wheat.

    Solution 2: Have the player consider the market value of their food when choosing what to eat. The value of a few grams of fish is less than the value of 22.4 kilograms of honey, so maybe they should buy some fish instead of losing all their valuable honey. One problem with this is that I don't think that my markets necessarily have a value for items though - sellers can experiment with their prices any time they want, there isn't always going to be one price for millet. Another problem with this is that... I don't want players to act like they can sell everything they own. I want bee keepers to sell honey and not millet. So a beekeeper shouldn't think too much about the market value of millet when deciding to eat it; they already have it, time to enjoy it, there's nothing else to do with it, except maybe save it for another meal in order to maintain a balance of macronutrients. But maybe they should think about the value of their honey before eating it all? How about this: instead of considering the "market value", they consider their current price information for that day: how much they charge for honey, versus how much the farmer overe there is charging for goat milk. And then.... I'm not sure what happens after that. I guess it breaks down a little bit of you own millet but you didn't see anyone selling it today. I'll keeping thinking. But let's look at solution number 3 first in case that solves everything with no thinking required.

    * Solution 3: A player can only eat so many grams of food in a day. If you need 2500 daily kcalories, and caloric food has an average calorie density something like 2 kcal/gram, then we eat about 1500 grams (2.76 lbs). By averaging over the caloric foods in my game, I actually got 1.98 kcal/gram, but I'm going to stick with 2 kcal/g for these example calculations.

If I just ask the internet about the typical mass of food that humans ingest daily,  instead of trying to make a ballpark estimate of the answer, then supposedly people eat more like 3 to 5 pounds of food per day. Maybe that includes the weight of very low calorie beverages, like water, coffee, and tea? Or my number for calorie density is a little off. It's hard to generalize over all caloric foods. And really, to figure out the weight of  your diet, you should weight the calorie densities by how much of each food you eat, but I can't do that because I'm in the process of figuring out how the players select their diets.

Anyway, based on the input of the internet, let's bump up the mass a little and say that 1657 grams of food per day (3.65 lbs) is an average for a Canaanite diet, and we'll cap the daily maximum at 1.25 times that, or 2071 grams (4.67 lbs). Now, even if they bee keeper tries to eat only honey, they would only get 21 protein kcal per day, out of a required 224. So they have to buy another food. Doing this means I have to solve a small optimization problem for each player: instead of just checking if the player has enough protein kcalories in their inventory, and buying a cheap protein source if not, now I have to figure out which combination of foods from their inventory might satisfy their daily food needs while not exceeding 2071 grams. I can do this, it's not crazy hard, but I didn't want to. And I can satisfice instead of optimizing too: find a reasonable diet given these constraints instead of finding the perfect diet.

Here's an algorithm, which is very similar to the food purchasing algorithm: 

    3a) Set aside 100 grams of any random food that isn't grain or legume.

    3b) Find the most protein dense food in your inventory, and set aside enough to meet daily protein calorie needs (and any protein from the diverse food in the previous step goes toward that goal also). If you don't have enough for that, then set it all aside and grab some of the next most protein dense food in your inventory. If you've exceeded 2071 grams at this point, you have to go buy some more protein rich food. Which food though? If you just buy the food with the chepeast (protein calories per 100 grams), you'll probably satisfy the constraints, because these foods aren't actually that nutrient poor, but theoretically, this purchase should also consider the weight of the protein calories and not just their price. So....buy the cheapest protein calories per gram? That seems kind of reasonable. Keep going till you've satisfied your protein requirements

   3c) Find your most calorie dense food (kcal / gram), find how much of it you need to meet your daily calorie needs (and any calories from the previous two steps also contribute toward reaching that goal), and set aside that much food aside. If you've exceeded 2071 grams at this point, then you have to go and buy some more calorie rich foods. And you don't just buy the cheapest kcalories, you also have to consider kcalories per ounce. So....buy the cheapest kcalories per gram. Why not. How much do you buy? You buy... enough to meat your kcalorie needs without exceeding a 2071 gram diet, I guess?

...

Before thinking of buying the cheapest kcalories per gram, I thought of having the NPCs make food purchases based on cheapest kcalories (kcal/grams of silver), but constructing their diets based on calorie density (kcal / grams of food). I really like that for its .... psychological realism, maybe. Like, you go to the store and mostly buy foods that are healthy and cheap per gram, like frozen vegetables, and then you go home and eat the junkiest things you got right away, like potato chips, soda, snack cakes. 

I wrote the following when I still thought I'd buy based on cheap nutrients and make diets based on dense nutrients: "But if your diet calculation says you don't have enough protein kcal/gram, and then your shopping algorithm buys the cheapest protein kcal, ....is that going to work? Probably. I mean, the price system is going to be variable, so who knows which foods will be available at affordable rates, but there are lots of foods that are cheap and have good macros. The foods with the lowest protein kcal per total calorie for 100 grams are fruits (fig, grape, date, olive) and honey. If those become the only thing on the market somehow, then maybe people wouldn't be able to buy protein.

Anyway, the diet calculation says buy more protein dense food, but how much needs to be bought? My shopping function had been looking at total protein calories in the player's inventory to see if it should get more of (cheapest protein calories item), but that doesn't work to keep sellers from gorging on their own supply."

...

    * Solution 5. I could say that a food can't account for more than a 1/3 of your total calories in a day. That would be pretty easy. You find statistics for how much general kcal, protein kcal, and grams of diverse food, and try to construct a diet from that. If one food is represented too much in the diet, then you clamp it to 1/3 of that number of calories, consider those macros accounted for, and then redo the diet calculation ignoring that food and trying to meet the smaller dietary requirements.

* Solution 6: Suppose one food can't account for more than a third of your grams of food eaten in a day! Then when I check the player's inventory to see if they need to purchase more diverse food, more protein, or more calories, each food will only count up to 2071/3 = 690 grams. That could work.

...

Anyway, if a purchaser doesn't have enough food stocked up in their inventory to last for three days and they don't have enough silver to buy food for three days, then ... I mean, in real life, if you had a little money and no income stream, you could consider buying something to help you do a job, but I think in this world, people will just save their money if they don't have enough money to buy food. They might make some money the next day, or they might go hungry for a few days and then reincarnate with a new character class. Things will work out either way, and we don't have to do expected utility calculations (and don't have to make minds detailed enough to do EU calculations).

After securing food, we run a profession-specific purchasing function. Let's try to sketch out the broad outline of such a function. Many jobs have consumed inputs to the job-specific production function, like reeds for a reed weaver. Many jobs with consumed inputs will have labour-based and capital-based limits to how much of an input like this can be processed in a day. People will try to keep three-days-worth of these consumed resources in stock - the amount that they can process in three days with their current setup of labour and capital resources. They don't buy more reeds because they're about to get an apprentice labourer or because they're about to get a reed weaving machine. 

If the production function can use multiple consumed inputs independently, like a metal smith can make a candle stick from silver or from bronze, ... that sounds hard, and maybe I won't do that. Silver smiths are different from coppersmiths. But then, what, do I need a wheat miller as a separate job from a millet miller? That sounds dumb.

...

Suppose, as an NPC, you see a piece of durable equipment that would make you more productive at your job, and you have food and consumable inputs stockpiled for three days, and you have money to purchase it. Then ... go ahead and purchase the tool, I think. Expand your enterprise.

What if you're short of food or consumable resources of production but no one is selling them right then when you're buying, or not selling them at a price you can afford? Like the market is out of food that day or it's out of reeds for your reed weaving. In that case, you save your pennies and go home for the day, I think.

If you're not short of food or production resources, and you haven't seen any useful capital at the end of you're shopping trip, but you do see something useful for your assigend leisure activity, you can buy that, if you don't already have it. Maybe you can only buy one leisure item per week. I don't know, man.

I think there's probably some decision tree like this that makes for a fairly realistic looking economy. You may have noticed that the NPCs give almost no consideration to price of items when purchasing. (This may not remain true as I work out more details of NPC purchasing functions. It may already not be true when you're reading this.) Perhaps naively, I don't expect that will be a problem. If prices are too high, then most NPCs won't be able to buy things and sellers may adjust their prices down if they want to sell to more people. I say "may" because, like, consider if there were someone very rich in the economy who is e.g. buying all the food and not re-selling it. Then food sellers get decent money, but no one has food beside Ritchie Rich, and everyone else goes hungry, reincarnates, goes hungry? I think my economy could be destroyed by an agent like that, but my agents aren't like that. If prices are too low, then sellers won't make enough to meet costs of production and ... go hungry and reincarnate? Or raise prices maybe. I'm not so sure about that one.

But I think I can keep prices in a reasonable range with seller-side price setting mechanisms, even if buyers have no consideration of prices and their mental model is basically just asking if

    1. I can or can't afford this.

    2. I do or don't need this.

    3. I can or can't get this cheaper from that guy over there.

You might wonder why I want to have a simulated economy. If the goal is a fairly realistic and fairly stable economy, then the obvious solution is to fix the prices of goods to be realistic and perfectly stable. Why bother with dynamic price setting? Well, the stories of Canaanite gods are a little interesting, but they're not that rich in detail. Most ancient religious texts, in fact, are like "oh you who created everything and you who are wise and you who are the moon and sun", and neglect to mention that the locals use cast nets with stone weights and wood floats for fishing, or that kept rock doves for meat and goats for milk, or that they had dressed stone masonry, or whatever else. But what if we combined the factual historic richness of the ancient Levant with the lore of the gods? What if we let the gods interact with the people, and we could see how semi-rationally motivated agents would respond to the wordly consequences of the actions of the gods. Wouldn't that make the stories so much richer?

Maybe not that much richer. Maybe a god makes a famine and then there's a famine, the end. But that's the idea that motivated this project and I'm going to try it out. 

...

Okay, so now you have some idea of how little I know about economics. Hopefully I haven't embarrased myself too much. Let's switch to talking about the Canaanite Pantheon.

Gods will have their own abodes. Towns and divine abodes will have fixed map designs, and the wilderness between them will be procedurally generated. Maybe there will be some other landmarks with fixed map designs as well. Travelling through the wilderness might be taxing. Like you need to store up resources before going on a trip and you use up your food while you walk or sail. Or maybe there are theives or wild animals that attack you. I'm not sure. I don't want to discourage exploration too much, but I do want some challenge.

When you find a god after a journey through the wilderness, they'll give you a quest. I might also let each town have a shrine to a god, and the god can act through the shrine in some way. But when you find a god, they have a quest for you. And gods have quests for every economic specialty, and they'll give you a specific quest for a specialty that you possess.

I don't know that I'll enumerate the possible quests of every god here, but here's a coarse categorization of quest types based on which activities can be done with which entities.

Go to place. Explore/investigate place.

Receive [message, prophecy, riddle, information] at place.

Take [material, item, plant] from place.

Bring [material, item, plant] to place.

Guide [animal, person] from place to place.

Find [material, item, plant, animal, person, monster, god].

Find all things on a list.

Fight [animal, person, monster, god].

Fight all [animals, persons, monsters, gods] trying to enter place or harm target.

Give [message] to [person, god].

Give [material] to [plant, animal, person, monster, god].

Give [item, plant, animal] to [person, monster, god].

Build structure.

Start fire. Tend fire.

Burn incense at place.

Extinguish fire.

Plant seed or cutting.

Identify special [item, material, plant] among similar items.

Process special [item, material] into special product.

? Cause damage to [plant, vehicle, structure, sign].

These will be much more specific things in practice, like 

Bring tribute to head of city state to establish diplomatic relations.

Build a temple for Astarte.

Protect a village by fighting a monster that emerges from a cave in that mountain.

Move a herd to high ground before a storm.

Collect a rare plant to cure the miller of her disease.

Find shipwreck treasure on the beach.

Bring lamp oil to a shrine.

Gather ingredients for a grand temple feast.

Bake bread using special grain harvested under moonlight.

Clear trees and plant a new field.

But I wanted to establish for myself what sort of general verbs/activities I would want to have available to the player in order for them to do quests like those. And e.g. animals don't go in your inventory, so they have to be guided to places, while small plants do go into inventories and can be directly transported.

Not all of these quests would have to come from gods; they could also come from other NPCs or come from nothing as game achievements to check off an ever looming list.

In addition to Gods giving quests, Gods will also sometimes cause miracles in the world. These will be noticeable events like droughts, storms, sacred light and fire and darkness and cold and wind and lightning, monster appearances, calls and songs and whispers of disembodied voices, maybe plagues, all sorts of things. Blood seeping out of statues. Tons of options.

Gods will also sometimes have conflicting goals about the state of the world, and there will be events showing the contrary interplay of their miracles.

Gods also sometimes cooperate about the state of the world, so there can be cooperative interplay of miracles.

: Music

Finally I want a microtonal soundtrack. I've been playing with middle eastern modal music, but I don't have any finished pieces I want to include in the score just yet.

Summary: In this game, you can do jobs in the Canaanite economy, and hopefully some of those will be fun, like a farm or fishing simulator. You can acquire resources doing these jobs to go on journeys. On journeys, you can meet gods, who will give you quests. You might learn a little bit about the personality of the gods this way. You'll learn what they can influence and who their enemeis and allies are at least. And maybe the status quo of the gods will change throughout the game, and you'll live through the whole Baal cycle or something, I don't know. That feels harder to tell without narration, but it might be doable. I sure hate narration in video games.

What do you think? A pixel art video game with a middle eastern microtonal soundtrack set in ancient Canaan, with a rich set of productive actions that can be used by players and NPCs to produce material goods in a simulated economy with a dynamic price system, and also there might be quests through a dangerous wilderness to meet gods, for further quests that tie into Canaanite pantheon lore, and also the gods might just mess with the world occasionally. That has the potential to be a good game, right?

This is absolutely not the right way to make my first game. My first game should be something like asteroids or dinosaur cactus jump, where you have one or two simple actions available, and it's fun from the get-go. All of these layers, I know, are not adding fun. But it's the game I want to make, so it's the game I'm going to occasionally work on when I'm too sad to do anything else.