9
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It's my birthday today, 5/13! Below are some of my role models. Can you tell me when their birthdays are?

$0,9,8,9,8,5,0,9$

$0,-7,0,8,0,8,12,-7,0,8,0,8,12$

$0,7,7,7,-8,-5,7,4,7,12,7,7,7$

$0,5,9,5,4,5,7,5$

$$\_\_,\_\_,\_\_,\_\_,\_\_,\_\_,\_\_,\_\_$$

You know what I really want for my birthday? Probably a pair of

Women’s UA PIP® Micro G® Pulse Running Shoes!

****Not part of the puzzle: Let me know if the shoes don't exist in your region of the world. ****

I hope they're not sold out! Could you check for me? nudge wink


Meta:

The answer to the puzzle is a single word. EDIT: the word may have nothing whatsoever to do with the context of the puzzle.

Sorry if the puzzle is too hard. Certain types of people will be extremely advantaged in this puzzle. This is my first puzzle of this kind; I was unsure what to tag it.

Clarifications:

The length of the sequences is irrelevant. They could have gone on much longer, but I arbitrarily ended them when I thought there was enough information.

Google is allowed and most likely extremely necessary.

Hint 1 (edited, no spoilers):

Look at the title. Also, the order the sequences appear in is important.

Hint 2 (no spoilers):

The first sequence is (subjectively) the easiest. If you solve that one, you will have a clear path to solving the others. Again, a very specific certain set of people will find this much easier.

Hint 3 (spoilers but probably necessary):

If $c=0$, then the numbers $10,1,3,1$ respectively, could be useful. You might want to become friends with a certain device that can't unlock anything despite its many keys.

Hint 4 (edited, spoilers):

The shoes give an seven digit number to manipulate the eight letter sequence you just found.

Extra Credit:

Wow, the answer is a really cool word! It's the __.

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  • $\begingroup$ 'Composition' and the device with keys - something to do with music/a piano? $\endgroup$ – LogicianWithAHat May 13 '15 at 10:32
  • $\begingroup$ Spoiler alert! But yes :) $\endgroup$ – ant11 May 13 '15 at 10:33
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    $\begingroup$ Given the final spoiler, could the answer be hemidemisemiquaver? $\endgroup$ – Rand al'Thor May 13 '15 at 14:53
  • $\begingroup$ @rand al'thor Sadly, no. How did you arrive at such a bizarre answer? $\endgroup$ – ant11 May 13 '15 at 15:51
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    $\begingroup$ @ant11 That's the only "really cool word" I know related to music ;-) $\endgroup$ – Rand al'Thor May 13 '15 at 18:49
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Final answer! The sequences are:

the starting notes of these music compositions:

1) Nocturne In E Flat Major Op.9 No.2 - Frederic Chopin

2) Allegretto tranquillo in F-sharp minor Book 2, Op.30, No.6 - Felix Mendelssohn

3) Prelude in G minor, Op. 23, No. 5 - Sergei Rachmaninoff

4) Hungarian dance No. 5 in F# minor - Johannes Brahms

Their birthdays are:

1) March 1 (3/1)
2) February 3 (2/3)
3) April 1 (4/1)
4) May 7 (5/7)

The seven digit number is:

1244687 which is the style number of this running shoe.

The seven letter word could then be:

CABBAGE which is derived by using the 7 digit substitution key followed by letter substitution.
This is a cool word because it is the longest common word that can be made from the music notes A-G.
Table

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  • $\begingroup$ I am not sure what you are doing in the penultimate spoiler. Just apply the seven letter code to the numbers, to get a seven letter word. Also I believe the second composer is still incorrect. Here is a hint: GONDOLA. $\endgroup$ – ant11 May 22 '15 at 3:16
  • $\begingroup$ It is never said that the answer itself is eight letters. The answer is only seven letters, and is obtained from the seven digit number in the simplest way. $\endgroup$ – ant11 May 22 '15 at 7:28
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    $\begingroup$ This is the correct answer! Why is it a cool word though... $\endgroup$ – ant11 May 22 '15 at 18:43
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    $\begingroup$ @ant11 - haha. Thanks. I have added the explanation and here is a silly video. $\endgroup$ – Len May 22 '15 at 19:16
  • $\begingroup$ Again, perfect solution! I look forward to your input on further puzzles. $\endgroup$ – ant11 May 22 '15 at 19:23
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This converted to notes becomes:

c,e+,d+,e+,d+,a,c,e+,c,c,c,d+,c,d+,d,e,c,c,d+,c,d+,d,e,c,c,c,c,b,e,c,g,c,d,e,c,c,c,c,a,e+,a,g,a,c,a,

where

+ for next octave and - for previous octave.

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