In the second measure here (source) two notes marked with stacatto dots are also tied. Aren't these two things incompatible? How is this to be understood?

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It's a red herring! It's not a tie, and they're not staccato, per se. It's a separate sign called 'portato',or more accurately and easily understood 'articulated legato', and if it was applied to notes that were not the same, obviously it couldn't be a tie. A slur it would be. Now, you can see that two slurred notes separated because they need to be shortened is how it's played. Usually for strings, as in the same bow stroke, with a small gap between the playing of each note. Brass players also find portato, and they would probably tongue the second note gently, to produce separation without much attack on the second note. I guess that the second 'staccato' sign actually has no effect on the second note - it's just part of the potato sign that needs to be there.

  • Another indicator that these are slur/phrase markings rather than ties is that tie markings usually start from beside the note heads, while slur/phrase markings are usually over (or under) the note heads, so that they can, if necessary, cover more than two notes.
    – Wilson F
    Apr 13 '18 at 23:19
  • ... or at least, that's what I've seen in the engraving software I've used. I've seen examples on this site that counter that, so I guess it isn't that clear-cut, though it would be helpful if it were.
    – Wilson F
    Apr 13 '18 at 23:34
  • @WilsonF - tie markings only join notes of the same pitch/name/place on the piano.
    – Tim
    Apr 14 '18 at 7:04
  • Yes. || However, what if you want to notate two notes that are the same not to be tied, but played smoothly, as you might mark them with a slur? || My point is that in the 2 pieces of engraving software that I've used (Noteworthy Composer and Lilypond), the ties and slurs are positioned differently (though drawn the same), so that you can actually tell the difference between them visually. || For what it's worth, my intent was not to disagree with your point, but simply supplement it with information from my own experience.
    – Wilson F
    Apr 16 '18 at 16:05

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