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What do the numbers above and below the staffs represent? I was assuming that the white-circled numbers under the bass parts were the thoroughbass and that the black-circled numbers above were the scale degrees, though that doesn't seem to be the case.

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Thank you for helping!

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This example is following Bob Gjerdingen's convention for schemata.

From the introduction to his Music in the Galant Style (pp. 20-21):

Names of scale steps. When I refer to the steps of a scale or key from an eighteenth-century perspective, I often use the names favored at that time. In place of the nineteenth-century English syllables doh, ray, me, fah, sol, and lah, the earlier musicians used the Latin forms ut (or do), re. mi, fa, sol, and la. In referring to the steps of a scale or key as features of a schema, I use numbers within circles. For features of the melody, the circles are black [...]. For features of the bass, the circles are white [...]. For passages that modulate between keys, such fixed scale-degree designations poorly represent the mobile cognition of pitch. I will argue that older forms of note naming may have been superior for those contexts.

Both the melody and bass numbers are representing scale degrees in the local key. As Albrecht has already noted in his answer, the excerpt begins in G minor and then moves to B-flat major, so the numbers refer to the scale degrees in those keys.

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I was assuming that the white-circled numbers under the bass parts were the thoroughbass and that the black-circled numbers above were the scale degrees ...

You are right, this is not the case.

I guess : The numbers are relating to the moveable do (DOREMI= 123).

The excerpt begins in Gm: G,A,Bb,C,D = 12345

l.h. G =1, r.h. D =5

in the second line (2nd bar) we are in Bb: Bb=Do=1

r.h. Bb,C,D, = 1,2,3, l.h. Eb=4 and E = #4

Edit:

the black-circled numbers are above the melody (and not the r.h. - I can’t write here on my tab and still see the whole display).

The white-circled are ”solfegging” (doremi) the bass-line.

  • You're probably correct, but why are some places that could have a number in a circle blank? – Tim Jan 11 at 8:37
  • Because this seem to be just a pedagogical assistance to practice the solfege. It won’t make sense to define each single note - as it isn’t necessary to mark the fingering of each single note. I’ve never seen this before but I used similar helping hints when teaching. Edited I guess ;) – Albrecht Hügli Jan 11 at 8:44
  • Except that solfege isn't directly related to fingering. All it does is identify each note in relation to the others. – Tim Jan 11 at 9:02
  • In relation to the key! it doesn’t change until the the piece is modulating. That’s why the numbering is marked again when the tonic is Gm: latido = 123 – Albrecht Hügli Jan 11 at 9:28
  • Understand that. You mentioned it in relation to fingering. – Tim Jan 11 at 9:36

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