AHNENTAFEL --An explanation and  an example
Ahnentafel :  A German word.  "Ahnen" meaning "ancestor" + "tafel" meaning "table'.
The starting person, can be anyone,  they are given the number 1.    Their father is number 2 and mother number 3.   The father of number 2 is 4 and his father is 8 and his father is 16, etc. The father of number 3 is 6 and his father is 12 and his father is 24, etc.  To find the father of any person, double that number.  To find the mother, double the number and add one. Other than the starting person, males always have even numbers and women have odd numbers.
 
Using myself as an example, my ahnentafel,  through my great-grandparents is:
1.   Henry Joseph Muller, Jr. (me) #1- start
      2.   Henry Joseph Muller, Sr. (my father) 1 doubled = 2
      3.   Jennie Evelyn Gates (my mother) 1 doubled + 1= 3
      4.   Henry Adolph Muller  (my father's father, my grandfather) 2 doubled = 4
      5.   Mary Emma Bauer (my father's mother, my grandmother) 2 doubled + 1=5
      6.   Joseph Ainslie Gates(my mother's father, my grandfather) 3 doubled = 6
      7.   Anna Judson Cheesman (my mother's mother) 3 doubled + 1= 7
      8.   Frederick Adolph Muller (my paternal grandfather's father) 4 doubled =  8
      9.   Mary Stanislaus Higgenbottom (my paternal grandfather's mother) 4 doubled +1= 9
     10.  John Michael Bauer (my paternal grandmother's father) 5 doubled = 10
     11.  Katherine Cantwell (my paternal grandmother's mother) 5 doubled + 1 = 11
     12.  George Washington Gates (my maternal grandfather's father) 6 doubled = 12
     13.  Jennie Elizabeth Blake (my maternal grandfather's mother) 6 doubled + 1 =13
     14.   Charles Edward Cheesman (my maternal grandmother's father) 7 doubled + 14
     15.  Esther Evelyn Colman (my maternal grandmother's mother) 7 doubled + 1 = 15

 
The same information that is shown as an Ancestor Chart would look like this:

                                       8. Frederick Adolph Muller
                                       |
                        4. Henry Adolph Muller
                                       |
                        |              9. Mary Stanislaus Higgenbottom

                        |

           2. Henry Joseph Muller, Sr.
           |            |              10. John Michael Bauer
                                        |
           |            5. Mary Emma Bauer
                                        |
           |                           11. Katherine Cantwell

1. Henry Joseph Muller, Jr.

           |                           12. George Washington Gates
                                        |
           |            6.  Joseph Ainslie Gates
                                        |
           |            |              13. Jennie Elizabeth Blake

           3. Jennie Evelyn Gates

                        |

                        |              14. Charles Edward Cheesman
                                        |
                        7. Anna Judson Cheesman
                                        |
                                       15. Esther Evelyn Colman
 

The numbers on the Ahnentafel  are the same numbers that are assigned to my ancestors on my actual Ancestor Chart. The Ancestor Chart shows you the easy way to see relationships but the Ahnentafel Chart allows for more information in less space and it's up to you to determine how much, or how little, information you wish to include.


 
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