Pythagorean Tetractys: Build All of Music With Only the Numbers 2 & 3

Fascinating! 🔥🔥🔥

thank you! this also gives some hints about how multiples of 2 and 3 somehow defines most rythmic configurations, even hidden in the milisecond inconsistencies of seemingly even spaced grooves

1.Commendable! The Blessings of the Spheres upon You! The Pythagorean Comma explained practically☆

I knew about the Pythagorean comma from theory books but never grasped how it was derived. Until now. This unpacks it incredibly clearly and does indeed uncover the ultimate simplicity underlying our tonal system. Thanks, Dan!

Thank you, Dan, for building this program for demonstration. It really helps a lot. Now I understand what it means "shrinking the fifths".

Yay! This make total sense. Thank you for sharing your findings on the Pythagorean Tetractys! I'm going to share this with my piano technician. Have you already done thirds?

gotta love how y led to the comma! Good stuff) Would like to learn coding myself for sorts of stuff like that

Thank you Dan. I came across your work from your blog post converting pulse into pitch. I have been looking at this stuff for a while and your computer programming of these harmonic experiments and sharing them are wonderful and greatly appreciated. I'm looking that the harmonic system with to relation to pulse, rhythm and movement. Polyrhythmic expression. Your work helps me out greatly. Well done!

Wow. At once the clearest and the most detailed explanation I've heard of just vs. equal temperament. That's a real accomplishment! Thanks!

2. Now, what has the West done with the Pythagorean comma? They spread it evenly... but the Comma is a Microtone. A whole Tone is made of Nine commas in Byzantine music, in Ottoman music and even in Arabic music. In Ottoman music, between C and D there are 9 commas and at 1 comma above C there is a small sharp. At 4 commas above C is the large sharp. Symmetrically, at 1 comma below D there is a little flat and at 4 commas below D is the large flat. So there are 4 accidentals beteen C and D. Hence there are no chords played because of extra beats of frequency but there is an enormous amount of tetrachords and pentachords possible that gave rise to 400plus modes or Makams at the apex of development of Ottoman music still studied, performed and used for composition.

When most of teachers brushed Pythagoras off as mostly just having to do with music, my brain discounted it. It is the music of the universe. Those doubling patterns are powers of 2.

This is an excellent explanation! +1

Is surely connected with the Kaballah and the sephirot analysis

Amazing video! I subscribed.

12:13 The twist in my head feels better now, thanks .

Outstanding. ❤

Fascinating!

3.The accidentals of Ottoman music do not match at all any of the Western accidentals. A kanun[ lap zither like]has a system of levers under each course of 3 strings tuned in unison for each pitch. There are 9 or 10 levers raising or lowering the tension by a minute amount related to the comma. The octave division can be seen on an Ottoman tanbur. The higher octave is shorter on the neck of the instrument so not all divisiins of the first Octave are reproduced.

The adventure starts when you emancipate the comma and keep going from there 🌿

Thanks!