Every rhythmic pattern up to 16 counts

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SrinathK
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#1 Every rhythmic pattern up to 16 counts

Post by SrinathK »

I've just found a very simple way to derive EACH AND EVERY ONE of the 65536 rhythmic patterns up to 16 counts in MS Excel in a matter of 5 mins in 3 steps. The result is 1395 pages long and it has 'em all! :twisted:

Technology marches on...!

msakella
Posts: 1930
Joined: 30 Sep 2006, 21:16

#2 Re: Every rhythmic pattern up to 16 counts

Post by msakella »

As per Talaprastara, only 32,768 rhythmic patterns derive from 16-units’ permutation but not 65536 patterns.

Nowadays, it is very easy to find the details of any one of these rhythmic patterns through the modern technology of the computer. But, prior to the invention of the computer, there was a traditional method to get this. But, unfortunately, the details of it have never been furnished in any of our treatises. Starting from around 1960s, in the absence of either the calculator or computer, I had to struggle for four decades to find this traditional method of it. However, I shall be thankful to you if you kindly furnish the details of the treatise in which this method is furnished clearly. amsharma

SrinathK
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#3 Re: Every rhythmic pattern up to 16 counts

Post by SrinathK »

Sir, this is a modern algorithm. These include all the patterns from 1-16 counts, therefore the actual number will be twice the number of 16-unit patterns alone -- hence I said "up to 16 counts" and not "of 16 counts". It is in fact derived like this:

1) Let us take 5 dashes - _ _ _ _ _

2) Each dash can be filled up with either a beat (t) or a pause (,). Hence this is entirely based on binary logic = sollu + karvai

3) We know that a 5 count pattern can be decomposed into 16 patterns. However, in order to have a 5-unit pattern, the first _ must be "t". Therefore patterns of 5 will be "t _ _ _ _"

If the first dash is a comma however, then we will get only 4-unit patterns -- such as , t , , , since all commas to the left of the 1st beat are useless.

If the first 2 dashes are filled with commas, then we will get only 3-unit patterns, starting with , , t , ,. The 1st 2 commas will not contribute.

In a same manner, we can get patterns of 2 and 1 count also. The total number of patterns is = Mahapatala, which in this case will be 32.

4) Another way of explaining it is that each dash can be either marked as "t" or as ",". Therefore each box has 2 possibilites, so the total number of possibilities will be 2 x 2 x 2 x 2 x 2 = 2^5 = 32 patterns.

At this point I was also not sure how I had got 32 patterns. Earlier I have manually sat down and derived all the patterns up to 9 counts based on the algorithm you had given me, and I have it all in a notebook. I was expecting 16 patterns, but I had ended up with 32.

Then I realized that this binary method gave me not just the 5 patterns, but also the 4, 3, 2, 1 and 0 patterns as well. Therefore the total number is actually double the value of only 5 patterns alone.

5) I then realized, that if I converted the numbers from 1-32 into their binary forms, I would get 32 binary numbers. If I replaced each 1 with a "t" and each 0 with "," -- then automatically all the 32 patterns of 1,2,3,4 and 5 units would be derived. This is exactly how computer memory also works.

6) There is a simple function in MS excel called dec2bin () that will convert any number into it's binary form.

7) For 16 counts, we get 32768 counts of 16 patterns, 16384 counts of 15 patterns, etc... -- the total is 65536.

The rest was simple. I will share the sheet here.
Last edited by SrinathK on 06 May 2015, 22:07, edited 1 time in total.

SrinathK
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#4 Re: Every rhythmic pattern up to 16 counts

Post by SrinathK »

To keep the explanation simple, here's what I did.

1) Ok? So you want up to 5 counts. 2^5 = 32. Write down all the numbers from 0 to 31 in column A.
2) Use dec2bin() function to convert each number into it's binary form in column B.
3) Copy the whole column B and paste only the values in column C.
4) In Column C, Use Ctrl + H, replace all 0 with , and replace all 1 with t. For better presentation I say add 2 spaces like ", " and "t " at the time of replacing.
5) You have obtained every rhythm from 0 counts to 5 counts.

Here's the sheet for up to 5 counts. https://www.dropbox.com/s/fpqv3lgrtlz0v ... .xlsx?dl=0

Let me know if the link is bad.

I have included a simplified form to make reading easier, which I can do for smaller numbers. But for 16 counts, I have to go with the original form.

When everyone's ok with this sheet, I'll share the big one.

msakella
Posts: 1930
Joined: 30 Sep 2006, 21:16

#5 Re: Every rhythmic pattern up to 16 counts

Post by msakella »

I am a very old Matriculate. I can understand the traditional method of Talaprastara only which doesn’t need either calculator or computer but cannot understand any modern methodologies even in respect of Talaparastara.

However, I shall be thankful if you kindly bring out the respective Sankhya and Mahapatala, apply the Nashta, Uddishta and Kalita and write all the relevant tables of the concerned in the traditional method. amsharma

SrinathK
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Joined: 13 Jan 2013, 16:10
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#6 Re: Every rhythmic pattern up to 16 counts

Post by SrinathK »

@msakella, Dear Sir, I am awed by the achievements of our previous mathematicians in their ability to decompose a number into all possible permutations and do it in a way where they can tell you the exact order in which the patterns will appear and then apply it to talas as well. But for your reference, here are the 32 patterns from 0-5 counts given by the binary method. I have your book and have followed all the thread postings.

First, here are the numbers converted into binary form :

No. Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111
16 10000
17 10001
18 10010
19 10011
20 10100
21 10101
22 10110
23 10111
24 11000
25 11001
26 11010
27 11011
28 11100
29 11101
30 11110
31 11111

After converting it into rhythmic patterns, this is the final result :

0 ,
1 t
2 t ,
3 t t
4 t , ,
5 t , t
6 t t ,
7 t t t
8 t , , ,
9 t , , t
10 t , t ,
11 t , t t
12 t t , ,
13 t t , t
14 t t t ,
15 t t t t
16 t , , , ,
17 t , , , t
18 t , , t ,
19 t , , t t
20 t , t , ,
21 t , t , t
22 t , t t ,
23 t , t t t
24 t t , , ,
25 t t , , t
26 t t , t ,
27 t t , t t
28 t t t , ,
29 t t t , t
30 t t t t ,
31 t t t t t

This is the simplified form. Now I request rasikas to kindly examine and tell me if this is the same as the traditional method's result.

SrinathK
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Joined: 13 Jan 2013, 16:10
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#7 Re: Every rhythmic pattern up to 16 counts

Post by SrinathK »

Ok, then. Here's the link to the full file. It has been upgraded a bit, with an additional sheet going up to 18 counts. I mean, almost nobody could toss anything harder than a double speed sankeerna nadai (18 units per beat at you), would they? :lol: . Word of warning, it is HUGE. The 18 unit sheet runs to 5200+ pages!

https://www.dropbox.com/s/s6ew9t2fyy845 ... .xlsx?dl=1

Also practically, once you go beyond 9 units, most of the patterns you will ever see will be some combination of smaller unit patterns. Chances of seeing a 13 beat pattern like t , , , , , , , , , , t t are rather unlikely. It will usually be a 7+6 or an 8+5 or some other.

msakella
Posts: 1930
Joined: 30 Sep 2006, 21:16

#8 Re: Every rhythmic pattern up to 16 counts

Post by msakella »

You did not answer my question at all. By all this it became clear that you did not understand the topic of my books even though you have them all. While there is each and every scope to answer any of your questions in this respect with the help of some tables but without the help of either calculator or computer do you have any method to do so?

I very sincerely and honestly feel that the teacher’s duty always is to make the matters easier to learn quickly and efficiently. I do not understand in which way your version makes it easier to learn them to a common man.

More over, to tell the fact, like you, I was not awed by the way our previous mathematicians like Sharngadeva defined the Prastara in his Sangita Ratnakara. Even though his Sangita Ratnakara is the only source to get more information than any other treatise in the history of our music I feel ashamed to call him ‘Nisshanka’. He may have brought out a monumental work on our music but the lacunae in the chapter of Tala he furnished are far more than enough to call him ‘Kusshanka’. I can certainly prove it at any time and place if needed. amsharma

SrinathK
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Joined: 13 Jan 2013, 16:10
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#9 Re: Every rhythmic pattern up to 16 counts

Post by SrinathK »

Sir, to clarify, my only goal of this exercise was to demonstrate how the computer could generate the rhythmic patterns here.

msakella
Posts: 1930
Joined: 30 Sep 2006, 21:16

#10 Re: Every rhythmic pattern up to 16 counts

Post by msakella »

Dear brother-member, SrinathK, I heartily appreciate you in honestly helping the society in the way you can. This is the criteria.

Having been a victim of the present un-standardised, illogical and irrational system of teaching our music I had to struggle all my life to standardize and make it fully logical by which I could un-believably minimize the duration of learning independently within a couple of years. This is the criteria.

If each and every musician thinks on these lines and try to contribute his/her might in honestly giving our music to our kids the entire scenario of our music would have entirely been different. amsharma

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