RockofStrength

My former piano student, u/physicsstudent137, has created a brilliant and simple method for identifying the tonic of a given key signature:

Step 1: Count the number of sharps or flats in the key signature.

Step 2: If an even number of sharps or flats, start on C. If an odd number, start on F♯ (F♯ is the 'odder' note, after all). Step 3: For flats you go left from there that many half-steps. For sharps you go right from there that many half-steps.

Step 4: (If necessary) disambiguate between enharmonic equivalent note labels (e.g., F♯/G♭). For sharps, the note is the sharp note name. For flats, the note is the flat note name.

Whatever note you land on is the major tonic of the key signature.

Try it yourself!: https://editor.p5js.org/remote-files/full/-n651WXmu

Here is his description below:

I numbered the notes of the octave 0-11 and found that the key signatures can be identified based on whether the note number is even or odd. It's as if there are two sub-cycles within the circle of fifths: one for even key signatures, and one for the odd key signatures. Also, the number of accidentals in a key signature has the same parity as the tonic note. That is, if the note number is odd, then the number of sharps/flats in that key signature is also odd. Same for evens.

The even notes start at the index of 0 accidentals on the circle of fifths and go clockwise in the order 0, 2, 4, 6, 8, 10.

The odd notes start at the index of -5 (aka +7) accidentals and go clockwise in the order 1, 3, 5, 7, 9, 11.

Assuming sharps to be positive numbers and flats to be negative numbers, I found that the tonic note of a given (major) key signature can be determined by adding the number of accidentals in the key signature to either the note 0 (note C) for even key signatures or to the note 6 (note F♯/G♭) for odd key signatures. I sometimes call these two "landmark notes" in this context since they are fixed reference points.

I made a visualizer to hopefully make the pattern clearer (see link at bottom of post). I suggest trying the following: Step 1: Set the note labels to "Numbers" Step 2: Click on all of the odd-numbered notes in the circle of fifths in ascending order and observe the pattern. Step 3: Click on all of the even-numbered notes in the circle of fifths in ascending order and observe the pattern. (I used G♭ instead of F♯ for the key signature of note number 6 for simplicity, but the pattern still holds for F♯ and can be extended to enharmonic and theoretical key signatures.)

To go the in the reverse direction and answer the question "how many accidentals are in the key signature of this tonic note" is a little trickier, but I just visually reverse the procedure above, either while looking at a keyboard or by visualizing a keyboard in my mind. After a long time of staring at the numbered circle of fifths, I ended up memorizing the note numbers and whether each note is even or odd, so I just ask myself "how many semitones away is this note from its corresponding landmark note?"

For those who are curious, pedantic, or masochistic, I wrote a much lengthier and more detailed write up, see the link below. Derivation write-up: https://drive.google.com/file/d/1Oyi2s9HowefMtI3-I5A7z10VlDj... Visualizer: https://editor.p5js.org/remote-files/full/-n651WXmu

All credit goes to u/physicsstudent137.

TL;DR: Given a number of flats or sharps in a key signature... start on C for even and F# for odd... go left that many half-steps for flats and right for sharps... you land on major tonic. For any mode, start with the mode's prototype on the white notes (eg D for dorian) plus its respective tritone and do the same. At first glance you might hate, at second you will love.

If nothing changes the market will drop 20% next week.

Since the first color was right between blue and green, I refused to choose one or the other. I'm not gonna play that game.

Another lens is ii7-II♭7-IM7 = ii7-V7♭5♭9-IM7, viewing the II♭7 as an altered V7. This would retain the same 3-7 (just flips them).

Here're a couple links for you:

https://www.reddit.com/r/math/comments/cbd0a7/found_e_in_the...

https://www.reddit.com/r/math/comments/ikwn03/e_in_the_prime...

https://www.reddit.com/r/math/comments/n0mw3r/deriving_e_fro...

(2,3,5) because 2 to 3 = 1 and 3 to 5 = 2. 5 to 7 is also 2 so the gap does not grow, so 7 starts the next set.

You get e from the primes by averaging the set size of only growing gaps (2,3,5)(7,11)(13,17)... or only non-shrinking gaps (2,3,5,7,11)(13,17)(19,23,29)...

Not a property of primes per se, just a property of growth. It works better with a set of randoms.

This is already incorporated to some extent. Keeping in mind sets vary,

Knight's profile is the L-shape.

Rook has four parapets (and four gaps).

Bishop has a diagonal slit.

King has 8 stubby protrusions in his crown.

Queen has 8 pointy protrusions in her crown.

Pawns are most basic (ironic considering their qualities are most byzantine). I guess it's nice to have a baseline piece for aesthetics.

Chess.com seems to have excellent opening instruction. It actually tells you the opening name as you play. After you play, it gives you more. It shows where you screwed up, gives you a chance to find a better move, etc. If I was starting over (I'm over 2k now) I'd start with chess.com's interactive organic approach. Chessable is just rote memorization which is in essence trash.

After reading the complete Shakespeare, it is a natural continuation to go on to read the complete Milton. Outside the core of Paradise Lost/Regained, Samson Agonistes is another gem, and Lycidas is of course a classic poem.

The way Milton uses English the language exalts it into the profundity of Latin. One feels Milton's words are of sanctified origins; it feels as though they are coming from a higher power.

One random connection: In the same way Milton dictated his writing, Debussy dictated his music. To some extent this method may free the mind's work from the tedium of transcribing thought, and allow for more free-flowing expression in creation.

CAPTCHAs are used as a literal Turing test; that's their whole purpose. From the get-go their usefulness window had a looming expiration date.

How about to hold the female in place during mating?

Robert Wilson theorizes that each character in Sideways symbolizes a type of wine. Miles = Pinot noir (thin-skinned, great potential). Jack = Cabernet Sauvignon (adaptable, survivor). Maya = 1961 Cheval Blanc (Miles' prized bottle, actress born 1961). Stephanie = Cabernet Franc (hollow, flabby, overripe, shallow). https://www.youtube.com/watch?v=L0mO0UhBim4&ab_channel=Rober...

It was a divine move in the sense that he created a surprise tsumego that crashed AG. Lee Sedol called it his 'trick move' in the post game interview I believe. Move 78 shouldn't have damaged AlphaGo's moyo if it had responded correctly. See diagram 9 here for an explanation: chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/viewer.html?pdfurl=https%3A%2F%2Fdeepmind-media.storage.googleapis.com%2Falphago%2Fpdf-files%2Fenglish%2Fls-vs-ag4%2FLS%2520vs%2520AG%2520-%2520G4%2520-%2520English.pdf&clen=4258493&chunk=true

Move 78 was humanity's last great stand against AI in a board game. Lee Sedol, tired and inspired, reddens AlphaGo's ears with a move plucked from a higher dimension.

It now seems humorous that Kasparov once accused people of helping computers behind the scenes. Now chess masters have been caught huddled in bathroom stalls with their smart phones. Chess commentators choose to willfully ignore chess engines in their presentations, in order to enable our understanding of the analysis. The torch has been passed.

The Recife (Brazil) logo is just brilliant. https://mapa-metro.com/en/brazil/recife/recife-metro-map.htm

The OEIS can also be considered a sort of number encyclopedia, especially for large numbers.

It can also be interesting to link geometric observations with unrelated OEIS sequences. For example, the number of rectangles on a square grid turned out to be the octagonal pyramidal numbers.

Also 3^3 + 4^3 + 5^3 = 6^3

If they don't cap the apm at 300 or so, this means nothing. I am not impressed with super speed, only decision making matters. Deepmind, you can do better.

Reminds me of meta-algebra. For example, a^n - b^n = (a - b)(a^(n-1) + (a^(n-2))ab + ... b^(n-1)) .

http://oeis.org/A257479 Maximal kissing number in n dimensions: maximal number of unit spheres that can touch another unit sphere.

One idea is Bongard problems, because they are purely creative categorization, so it's interesting for AI. http://www.foundalis.com/res/bps/bpidx.htm

Brave New World

If a copy is allowed to live on, the ego will no longer fear oblivion, as nothing is lost in death.

"If the piano fundamentally outlines anything, it is the A minor (aeolian) scale" Are you saying this because the D note is the symmetrical white note, and it lies in the center of the A minor scale? A similar argument could be made for Eb minor, because the Ab note is symmetrical.

An interesting phenomenon is that C Ionian harmony can be 'flipped' to A Aeolian by mirroring all the notes around the central D. The C chord becomes A minor, G7 becomes Dm6, F6 becomes Em7. The melody can switch as well; the contour is reversed yet the tune retains its essence.

Anything that changes behavior can eventually lead to speciation.

This reminds me of the silly tight melee formations in Myth 2 that were necessary to compete online.