> CM13 has the natural
> maj seventh and the 6th (or thirteenth, 9th optional, 11th omitted) <c e g
> b
> d a'> and <c e g b a'> are both CM13 chords with one omitting the ninth. 
> C13 again is a dominant flatted seventh with 11th omitted, 9th optional,
> and
> 13th (or sixth) present depending on how your instrument is able to finger
> it.

yes, but a 13th is always a 13th, regardless in which ocatve played. 

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