Here are two four-finger tapping patterns.  I show two cycles of each
pattern.  Try tapping them.  Use right hand, index finger is 1, little
finger is 4.  What are the analogous three-finger patterns?  The analogous
thumb-and-four-finger patterns, if the thumb has index 0?

   2 2 3 $ 1 2 3 4 3 2  NB. pattern one
1 2 3
4 3 2

1 2 3
4 3 2
   2 3 4 $ 1 2 3 4 3 2  NB. pattern two
1 2 3 4
3 2 1 2
3 4 3 2

1 2 3 4
3 2 1 2
3 4 3 2

--Kip

On Friday, June 27, 2014, Mike Day <[email protected]> wrote:

> And for "hands" with an arbitrary number of fingers:
>
> NB. eg Homer Simpson plays a three-fingered scale twice
>    ($(,|.@}:@}. )@:>:@i.@}.) 5 3
> 1 2 3
>
> 2 1 2
>
> 3 2 1
>
>
>  NB. If Paul the Octopus doesn't omit any limbshe can manage a whole octave
> <:($(,|.@}:@}. )@:>:@i.@}.) 4 8
>
> 0 1 2 3 4 5 6 7
>
> 6 5 4 3 2 1 0 1
>
> 2 3 4 5 6 7 6 5
>
> 4 3 2 1 0 1 2 3
>
>
> It's interesting that this representation can show certain numbers of
> complete scales for Homer or Paul (eg 12321 for Homer) but not for Mike:
>
>     |:($(,|.@}:@}. )@:>:@i.@}.) 20 3  NB. transpose to save space
>
> 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2
>
> 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3
>
> 3 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2
>
> So this can show 2 full scales, in 3 rows (columns here),or 5 in 7, or 8
> in 11 etc....
>
>
>     |:($(,|.@}:@}. )@:>:@i.@}.) 20 4  NB. eg Mike can only "finish" on 2
> or 4
>
> 1 3 3 1 3 3 1 3 3 1 3 3 1 3 3 1 3 3 1 3
>
> 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2
>
> 3 1 3 3 1 3 3 1 3 3 1 3 3 1 3 3 1 3 3 1
>
> 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 2
>
>
> Thanks, Kip!
>
> Mike
>
> On 27/06/2014 07:50, Kip Murray wrote:
>
>> That's what I was thinking of.  Quick work!  --Kip
>>
>> On Friday, June 27, 2014, robert therriault <[email protected]>
>> wrote:
>>
>>  Hi Kip,
>>>
>>> I came up with
>>>
>>>     6 4 $ 1 2 3 4 3 2
>>> 1 2 3 4
>>> 3 2 1 2
>>> 3 4 3 2
>>> 1 2 3 4
>>> 3 2 1 2
>>> 3 4 3 2
>>>
>>> Are you looking for a deeper pattern?
>>>
>>> Cheers, bob
>>>
>>> On Jun 26, 2014, at 10:18 PM, Kip Murray <[email protected]
>>> <javascript:;>> wrote:
>>>
>>>  Hold up your right hand with its back toward you and number the
>>>>
>>> forefinger
>>>
>>>> through little finger 1 through 4.  (I suppose the thumb has index 0.)
>>>>
>>>   Now
>>>
>>>> try finger tapping this pattern:
>>>>
>>>> 1 2 3 4
>>>> 3 2 1 2
>>>> 3 4 3 2
>>>> 1 2 3 4
>>>> 3 2 1 2
>>>> 3 4 3 2
>>>>
>>>> Write a J expression to produce this pattern.
>>>>
>>>> --Kip Murray
>>>>
>>>>
>>>> --
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>>>
>>>
>>
>
>
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