\version "2.19.45"

\markup "1) Four note cluster, space at the top"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{<c d e f>2._\markup{dots limit 0: FAIL (need dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{<c d e f>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{<c d e f>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{<c d e f>2._\markup{dots limit 3: OK (unnecessary dot on A space)} }
}


\markup "2) Four note cluster, space at the bottom"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d e f g>2._\markup{dots limit 0: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d e f g>2._\markup{dots limit 1: FAIL (need dot on A space, not on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d e f g>2._\markup{dots limit 2: FAIL (need dot on A space, not on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d e f g>2._\markup{dots limit 3: OK (unnecessary dot on B space)} }
}


\markup "3) Triad with sixth, triad on lines"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c e g a>2._\markup{dots limit 0: FAIL (need dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c e g a>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c e g a>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c e g a>2._\markup{dots limit 3: OK} }
}


\markup "4) Triad with seventh, triad on lines"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <b c e g>2._\markup{dots limit 0: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <b c e g>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <b c e g>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <b c e g>2._\markup{dots limit 3: OK} }
}


\markup "5) Triad with ninth, triad on lines"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d e g>2._\markup{dots limit 0: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d e g>2._\markup{dots limit 1: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d e g>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d e g>2._\markup{dots limit 3: OK} }
}


\markup "6) Triad with fourth, triad on lines"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c e f g>2._\markup{dots limit 0: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c e f g>2._\markup{dots limit 1: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c e f g>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c e f g>2._\markup{dots limit 3: OK} }
}


\markup "7) Triad with sixth, triad on spaces"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d f a b>2._\markup{dots limit 0: FAIL (need dot on C space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d f a b>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d f a b>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d f a b>2._\markup{dots limit 3: OK} }
}


\markup "8) Triad with seventh, triad on spaces"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d f a>2._\markup{dots limit 0: FAIL (need dot on the A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d f a>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d f a>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d f a>2._\markup{dots limit 3: OK} }
}


\markup "9) Triad with ninth, triad on spaces"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d f a e>2._\markup{dots limit 0: FAIL (need dot on A space, not on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d f a e>2._\markup{dots limit 1: FAIL (need dot on A space, not on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d f a e>2._\markup{dots limit 2: OK (unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d f a e>2._\markup{dots limit 3: OK (unnecessary dot on B space)} }
}


\markup "10) Triad with fourth, triad on spaces"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d f a g>2._\markup{dots limit 0: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d f a g>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d f a g>2._\markup{dots limit 2: OK (unnecessary dot on C space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d f a g>2._\markup{dots limit 3: OK (unnecessary dot on C space)} }
}

\markup "11) 5-note line-top cluster"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d e f g>2._\markup{dots limit 0: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d e f g>2._\markup{dots limit 1: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d e f g>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d e f g>2._\markup{dots limit 3: OK} }
}


\markup "12) 5-note space-top cluster"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d e f g a>2._\markup{dots limit 0: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d e f g a>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d e f g a>2._\markup{dots limit 2: OK (unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d e f g a>2._\markup{dots limit 3: OK (unnecessary dot on B space)} }
}


\markup "13) Extension above 4-note space-top cluster with a 3rd"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d e f a>2._\markup{dots limit 0: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d e f a>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d e f a>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d e f a>2._\markup{dots limit 3: OK (unnecessary dot on G space below staff)} }
}


\markup "14) Extension above 4-note space-top cluster with a 4th"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d e f b>2._\markup{dots limit 0: FAIL (need dot on C space, not on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d e f b>2._\markup{dots limit 1: FAIL (need dot on C space, not on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d e f b>2._\markup{dots limit 2: OK (unnecessary dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d e f b>2._\markup{dots limit 3: OK (unnecessary dot on A space)} }
}


\markup "15) Extension above 4-note space-top cluster with a 5th"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d e f c'>2._\markup{dots limit 0: FAIL (need dot on C space, not on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d e f c'>2._\markup{dots limit 1: OK (unnecessary dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d e f c'>2._\markup{dots limit 2: OK (unnecessary dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d e f c'>2._\markup{dots limit 3: OK (unnecessary dot on A space)} }
}


\markup "16) Extension above 4-note line-top cluster with a 3rd"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d e f g b>2._\markup{dots limit 0: FAIL (need dot on C space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d e f g b>2._\markup{dots limit 1: FAIL (need dot on C space, unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d e f g b>2._\markup{dots limit 2: FAIL (need dot on C space, unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d e f g b>2._\markup{dots limit 3: OK (unnecessary dot on B space)} }
}


\markup "17) Extension above 4-note line-top cluster with a 4th"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d e f g c>2._\markup{dots limit 0: FAIL (need dot on C space; not on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d e f g c>2._\markup{dots limit 1: FAIL (need dot on C space; not on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d e f g c>2._\markup{dots limit 2: OK (unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d e f g c>2._\markup{dots limit 3: OK (unnecessary dot on B space)} }
}


\markup "19) Extension above 4-note line-top cluster with a 5th"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d e f g d'>2._\markup{dots limit 0: FAIL (need dot on E space; none on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d e f g d'>2._\markup{dots limit 1: OK (unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d e f g d'>2._\markup{dots limit 2: OK (unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d e f g d'>2._\markup{dots limit 3: OK (unnecessary dot on B space)} }
}





\markup "20) Extension below 4-note space-top cluster with a 3rd"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d e f a,>2._\markup{dots limit 0: FAIL (need dot on G space below staff)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d e f a,>2._\markup{dots limit 1: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d e f a,>2._\markup{dots limit 2: OK} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d e f a,>2._\markup{dots limit 3: OK (unnecessary dot on A space)} }
}


\markup "21) Extension below 4-note space-top cluster with a 4th"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d e f g,>2._\markup{dots limit 0: OK } }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d e f g,>2._\markup{dots limit 1: OK } }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d e f g,>2._\markup{dots limit 2: OK (unnecessary dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d e f g,>2._\markup{dots limit 3: OK (unnecessary dot on A space)} }
}


\markup "22) Extension below 4-note space-top cluster with a 5th"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <c d e f f,>2._\markup{dots limit 0: OK/Marginal (may need dot on E space below staff) } }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <c d e f f,>2._\markup{dots limit 1: OK (unnecessary dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <c d e f f,>2._\markup{dots limit 2: OK (unnecessary dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <c d e f f,>2._\markup{dots limit 3: OK (unnecessary dot on A space)} }
}


\markup "23) Extension below 4-note line-top cluster with a 3rd"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d e f g b,>2._\markup{dots limit 0: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d e f g b,>2._\markup{dots limit 1: FAIL (need dot on A space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d e f g b,>2._\markup{dots limit 2: OK } }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d e f g b,>2._\markup{dots limit 3: OK (unnecessary dot on G space)} }
}


\markup "24) Extension below 4-note line-top cluster with a 4th"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d e f g a,>2._\markup{dots limit 0: FAIL (need dot on A space; possibly not on G space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d e f g a,>2._\markup{dots limit 1: FAIL (need dot on A space; possibly not on G space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d e f g a,>2._\markup{dots limit 2: OK (unnecessary dot on G space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d e f g a,>2._\markup{dots limit 3: OK (unnecessary dot on G space)} }
}


\markup "25) Extension below 4-note line-top cluster with a 5th"

\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 0
  \relative c'{ <d e f g g,>2._\markup{dots limit 0: FAIL (need dot on A space; possibly not on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 1
  \relative c'{ <d e f g g,>2._\markup{dots limit 1: OK (unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 2
  \relative c'{ <d e f g g,>2._\markup{dots limit 2: OK (unnecessary dot on B space)} }
}
\new Staff {
  \override Staff.DotColumn.chord-dots-limit = 3
  \relative c'{ <d e f g g,>2._\markup{dots limit 3: OK (unnecessary dot on B space)} }
}