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I'm peculiar about typefaces. I choose the one that best suits my mood at the time, and often change machines while, say, typing a long letter. This results, sometimes, in a letter that resembles a ransom note. That said, I lean toward Pica and machines with inkier imprints, such at that on my Royal Quiet Deluxe.
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I feel that the typeface needs to reflect the content of the typing. The principles of desktop publishing apply to typewriters, too. IMO. While I could use Courier in pica for a letter to a friend, I would rather use the Olympia script #75. I wouldn't go for senatorial, much as it reminds me of the older OCR daisy wheels of yesteryear.
Writing to a business or a stranger or just banging out fiction, I go with tradition: Courier pica.
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Senatorial elite and Senatorial pica are examples of Senatorial fonts.
I think we get confused in the digital world with typewriter typeface vs word processor fonts.
Typeface is the character style, be it Gothic, SansSerif, Senatorial, Roman, etc. which includes the character's traits of thinness or thickness, cursive, and so on. Pica or Elite were always defined as characters per line or per inch and is referred to as monotype as the spacing is not proportional as can be in fonts. Pica is 10 cpi or 85 characters per line where Elite is 12 cpi or 102 characters per line. This is important to know as to figure where your center point is for headers and setting margins.