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

[@alexgabriel5423]

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

[@sebastianchand8392]

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

[@RickBeato]

Fascinating! 🔥🔥🔥

[@DanTepferMusic]

Thank you Rick!

[@goosopolis]

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!

[@DanTepferMusic]

🙏🏻🙏🏻

[@the.mystic.techie]

Finally! a very sensible video about 432 Hz tuning system!

[@JackSeefeldt]

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

[@DanTepferMusic]

🙏🏻

[@alexgabriel5423]

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.

[@DanTepferMusic]

Thank you for this. Amazing what different cultures have made of this basic mathematical property of music.

[@alexgabriel5423]

@@DanTepferMusic I went to Istanbul a few years ago and I saw how the vocalists for Classical Ottoman music train...the trainer plays the tanbur [34 frets/ first octave] or the kanun. The vocalist must reproduce each musical phrase with laser mark pitch accuracy. This gives them such precision that the irregularities of the speaking timbre are no longer there. When they pronounce the syllables in pitch one thinks it s an instrument that pronounces words and not a human trying to imitate instrument pitch. Portamento is not used.

[@TravisTellsTruths]

Super, super, super cool.

[@lenablochmusic]

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

[@DanTepferMusic]

🙏🏻🙏🏻

[@TravisTellsTruths]

Fifths up is 4ths down!

[@alistairlethlean9804]

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!

[@victork8708]

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

[@Worldahurt]

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

[@excitinguniverseofmusictheory]

This is an excellent explanation! +1

[@kenzeller6518]

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?

[@ilovetech8341]

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.

[@alexgabriel5423]

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.

[@newblueentertainment]

Brilliant!

[@AnnoyedBuffalo-rx1dy]

Is surely connected with the Kaballah and the sephirot analysis

[@TravisTellsTruths]

The entire major scale is all derived mostly all from the first 9 harmonics but the Major 7th is derived fron the 15th harmonic. Mostly all in the first 6 (5 notes within first 6 harmonics!)

[@DanTepferMusic]

In this video we derive the entire chromatic scale using only the first 3 harmonics (i.e. a doubling and a tripling of frequency). Also, the first 6 harmonics only contain the major triad, so that's not going to help you get the major scale.

[@TravisTellsTruths]

I wrote you a big thing but I'm going to save it to one day make a video about it. There's other ways to understand the Tetractys.

[@TravisTellsTruths]

Incredibly great video, by the way. I love it tremendously 👏

[@maandalen]

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

[@maandalen]

What I mean by that is that you could just as easily view the chromatic scale as a subset of a larger commatic(?) scale.

[@DanTepferMusic]

@@maandalen Yes!

[@karenbartholomew200]

Fascinating!

[@mysticalmusicmythology9918]

Amazing video! I subscribed.

[@666pinkster]

Outstanding. ❤

[@taunado]

Thanks!

[@algorhythm_3177]

First this is amazing. I love it. Do you know of any references to numbers being applied to the Tetractys in this way. Other than this video I have never seen this example.

[@josephduke5186]

“Obviously you’re not a golfer.” Pythagoras

[@DanTepferMusic]

lol

[@rosshoyt2030]

This is awesome from so many angles! Amazing video Dan. Out of curiosity, what programming language are you building this app with? To me it looks like OpenFrameworks or Processing if I had to guess!

[@DanTepferMusic]

Good guess! It’s all in Processing :-)

[@oscarvelay]

You will get so many more subscribers

[@kitstamat9356]

Excellent! But it seems you are not aware that this order of numbers is also included in the Pythagorean Tetractys. Wikipedia didn't mention this, but you can see how Plato used it in Timaeus (36a) - it was certainly known to the Pythagoreans.

[@DanTepferMusic]

Definitely did not know that! Do you have a link to something online on this subject?

[@kitstamat9356]

@@DanTepferMusic It's called "Plato's Lambda" and I'm familiar with it mostly through books... what I see online useful for a quick review? One page is under the title "More about the Tetractys" and another one "Plato's Lambda - historical background". I hope it helps.

[@DanTepferMusic]

@@kitstamat9356 Indeed, lots of information about Plato's Lambda online. Will investigate. Thanks much!

[@johanneskepler873]

….mmmmm no. We don’t get…those This would be mean tone just intonation, using the 2nd and 3rd harmonic relationships. It’s why you get the pythagorean comma. You can get different-sized commas using the interval ratios of other harmonics. What would be more true to say is we get all of our musical structure from the harmonic series, which was first approximated using mean tone tuning. The topic of musical tuning is so vast just by itself And the math is so damn cool.

[@gnenian]

You've found Pythagoras's Hill Of Beans (the Tetractys). BUT are you prepared to DIE on it yet? No? Wait. Think about it some more.

[@mysticalmusicmythology9918]

What program are you using to produce just intonation?

[@DanTepferMusic]

this is all custom code i wrote :-)

[@MatthewSuffidy]

All that relies on the definition of a second in time to describe as 1 hz. But yes the original system was based on some low fraction relations.

[@DanTepferMusic]

No, it doesn’t. This is entirely about fractional relationships between frequencies, not about absolute numbers. If our measurement unit for frequency were different, it would simply shift the names of the notes; it wouldn’t change the underlying relationships at all.

[@MatthewSuffidy]

@@DanTepferMusic I meant the values of the notes being a certain hz. The same sound would be different hz if people chose a different duration for a second. So A does not need to always be 432hz as a value. It is in my view more appropriate to start with a tone you think should be A because it sounds a certain way and divide backwards.

[@DanTepferMusic]

Well yes, of course. But that’s not really relevant. If whales heard music as we do, but with their range of hearing, all the above would just be shifted downwards by a number of octaves. These ideas even apply to the much much slower orbital ratios of planets in planetary systems. It’s not about the absolute numbers, it’s about their relationship to each other.

[@DanTepferMusic]

@@MatthewSuffidy I think I finally understand your point: you are saying that 432hz is an arbitrary value. I happen to agree with you, but my video here has really nothing to do with the 432Hz topic. It has to do with how to build a scale of frequencies from whatever your starting frequency happens to be. Could be 440Hz, could be 432, could be 0.5Hz - it just doesn't matter.

[@MatthewSuffidy]

@@DanTepferMusic Well it also means that a note you call for example 'A' is a certain pitch due to what someone called a second in duration. But yes I think it mostly does not matter.

[@franciscoajanel]

We can find your app to make music?

[@DanTepferMusic]

not available publicly at this point...

[@exoclient]

This is 2 real

[@frankjamesbonarrigo7162]

Is this app available? Was it down in supercollider?

[@DanTepferMusic]

Not available, just some custom code I wrote in Processing

[@mandanglelow1442]

This is excellent and fascinating...now...how can we use this knowkedge to Create compelling music? Is this all Whys but no hows?

[@DanTepferMusic]

knowledge is power! you decide how to use it :-)

[@ryanmurtha2392]

666=2/3 mind and body without heart

[@AnnoyedBuffalo-rx1dy]

IS RA EL