A heterogram (from hetero-, meaning "different", + -gram, meaning "written") is a word, phrase, or sentence in which no letter of the alphabet occurs more than once.
- The term isogram has been used to mean the same thing as a heterogram. However, isogram has also been used to mean a string where each letter present is used the same number of times.
- A perfect pangram is an example of a heterogram, with the added restriction that it uses all the letters of the alphabet.
An isogram (also known as a "nonpattern word") is a term in recreational linguistics. It has been used with two different definitions:
- Equivalent to heterogram; or
- A word or phrase where every letter appears the same number of times.
Multiple terms have been used to describe isograms where each letter used appears a certain number of times. For example, a word where every featured letter appears twice, like APPEASES, might be called a pair isogram, a second-order isogram, or a 2-isogram. The word isogram is itself an isogram (under either definition), making it autological.
Origin of the term
The term appears in Dmitri Borgmann's 1965 book, Language on Vacation: An Olio of Orthographical Oddities, and in a 1985 article, Borgmann claims to have "launched" the term then. In the 1985 article, he suggests an alternative term, asogram, to avoid confusion with lines of constant value such as contour lines, but continues to use the term "isogram" in the article itself.
Uses in ciphers
Heterograms can be useful as keys in ciphers, since isogram sequences of the same length make for simple one-to-one mapping between the symbols. Ten-letter isograms like PATHFINDER, DUMBWAITER, and BLACKHORSE are commonly used by salespeople of products where the retail price is typically negotiated, such as used cars, jewelry, or antiques.
For example, using the PATHFINDER cipher, P represents 1, A represents 2 and so on. The price tag for an item selling for $1200 may also bear the cryptic letters FRR, written on the back or bottom of the tag. A salesman familiar with the PATHFINDER cipher will know that the original cost of the item was $500, so that if the price is negotiated he will not accidentally eliminate all of the 140% margin in the $1200 price shown to prospective buyers.
A twelve-letter cipher could be used to indicate months of the year.
In the book Language on Vacation: An Olio of Orthographical Oddities, Dmitri Borgmann tries to find the longest such word (though he uses the terms "nonpattern word" and "isogram" instead of "heterogram"). The longest one he found was "dermatoglyphics" at 15 letters. He coins several longer hypothetical words, such as "thumbscrew-japingly" (18 letters, defined as "as if mocking a thumbscrew") and, with the "uttermost limit in the way of verbal creativeness", "pubvexingfjord-schmaltzy" (23 letters, defined as "as if in the manner of the extreme sentimentalism generated in some individuals by the sight of a majestic fjord, which sentimentalism is annoying to the clientele of an English inn").
In the book Making the Alphabet Dance, Ross Eckler reports the word "subdermatoglyphic" (17 letters) can be found in Lowell Goldmith's article Chaos: To See a World in a Grain of Sand and a Heaven in a Wild Flower. He also found the name "Melvin Schwarzkopf" (17 letters), a man living in Alton, Illinois, and proposed the name "Emily Jung Schwartzkopf" (21 letters). In an elaborate story, Eckler talked about a group of scientists who name the unavoidable urge to speak in pangrams the "Hjelmqvist-Gryb-Zock-Pfund-Wax syndrome".
The longest German heterogram is "Heizölrückstoßabdämpfung" (heating oil recoil dampening) which uses 24 of the 30 letters in the German alphabet. It is closely followed by "Boxkampfjuryschützlinge" (box fight jury fosterlings) and "Zwölftonmusikbücherjagd" (twelve-tone music book chase) with 23 letters. The longest Dutch heterogram is "Exvakbondsjuryzwijgplicht" (former union jury oath of secrecy) with 24 of the 27 Dutch letters.
There are hundreds of eleven-letter isograms, over one thousand ten-letter isograms and thousands of such nine-letter words. Heterograms are not particularly useful in the game of Hangman but could make a particularly difficult puzzle on the game show Wheel of Fortune.
- Nymphs beg for quick waltz (Angus Walker) (22)
- The big dwarf only jumps. (Alain Brobecker) (20)
- Lampez un fort whisky! (Alain Brobecker) (18)
- Plombez vingt fuyards! (Alain Brobecker) (19)
- "Fix, Schwyz!", quäkt Jürgen blöd vom Paß. (30)
- Malitzschkendorf (16): German city
- Høj bly gom vandt fræk sexquiz på wc. (29, perfect pangram)
- Velho traduz, sim! (14)
- Centrifugadlos (14, longest heterogramatic word in Spanish)
- "Do You Know the Meaning of These Words With No Repeating Letters?". play.howstuffworks.com. 8 May 2019. Retrieved 3 February 2020.
- Nordquist, Richard (9 January 2020). "What Is an Isogram (Or Word Play)?". ThoughtCo. Retrieved 3 February 2020.
- Francis, Darryl (November 2015). "Now My Fifty ++ Great New Isograms". Word Ways – via Digital Commons @ Butler University.
- "Isogram". www.dcode.fr. Retrieved 3 February 2020.
- Gooch, Rex (February 1998). "Isograms: the Sequel". Word Ways – via Digital Commons @ Butler University.
- Francis, Darryl (February 2012). "New Pair Isograms". Word Ways – via Digital Commons @ Butler University.
- Borgmann, Dmitri (1965). Language on vacation: an olio of orthographical oddities. Scribner. OCLC 8478220.
- Borgmann, Dmitri (May 1985). "Long Isograms (Part 1)". Word Ways.
- Eckler, Ross (2001). Making the Alphabet Dance. Macmillan. ISBN 9780333903346.
- Goldsmith, Lowell (September 1990). "Chaos: To See a World in a Grain of Sand and a Heaven in a Wild Flower". Arch Dermatol. 126(9): 1159–60.
- Berry, Nick (2012). "Distinct letters". datagenetics.com. Retrieved 28 September 2012.
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- Eric Chaikin (1 February 2004), "Renaming the Schwar(t)zkopf baby.", Word Ways, retrieved 30 September 2010
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