#100daysofpractice days 81-83. The Pythagorean Tetractys, or how multiplying by 2 & 3 gets you all the notes you need, w/ stops at the Pythagorean Comma & Equal Temperament along the way. I love how chance encounters can lead you down rabbit holes like this.

Cc @mannfishh

@FHaruspex @FHaruspex I tagged you on this, then noticed you’d retweeted it 😀

We’re hearing a symbolic reference of the structure of our existence … this was a bit too deep for my 8AM brain. Thanks for your experimentation and exploration man what a trip! 🙌

Thanks for this fascinating and very clear analysis, most enjoyable too!

Great dive! Wonder if it has some nice chords shapes in the tetractys 👀

Thank you!

Wow, that was a trip.

best presentation of this material i've seen. great work

🙏🏻

Fantastic, Dan! Two questions: what about the overtone series of...natural machines, lower case – musical instruments/objects? How does that relate to Pythagorean math? Also, when played in an ascending scale, your first F sounds quite sharp to me, perhaps as sharp as the B#. ,?

Hey David! Great question. Pythagorean tuning is a “3-limit” tuning system in which we only use 2 and 3 as multipliers. So we only build things in 5ths. But other tuning systems are “5-limit”, meaning you can also use just thirds to build, and others go higher than that.