One way to do this is by creating an opening sentence with a clear cadence in the original key using all three main chordal functions - tonic, dominant, and subdominant, their inversions, and related chords. For example, T-II42-D65-T or T-S64-T-D56-T or T-T6-S-S6-D-D42-T6 etc.
Another way to establish the mode is to play a long tonic chord and emphasize chordal notes in the passages with runs in sixteenth notes. For example, in the mode of D minor, the notes of the tonic chord are D-F-A. Therefore, while one hand holds the tonic chord, the other plays the passages and the most frequently heard notes (at least on stronger beats) are D, F, and A.
Today's sight-reading piece is Versus I Primi Toni (p. 1) by Abraham van den Kerckhoven (ca.1618-1701) who was a Flemish organist and composer of the Baroque period. His numerous short versets and several lengthy pieces in contrapuntal manner have survived to this day.
In this verset, the long-held tonic chord lasts 7.5 measures. Later, while looking at the bass line, we can distinguish the following chords: D6-T-S-VII-III-D-S-T64-VI-S6-T64-D-T6-VII6-T.
Interestingly, at the very end there is a 4-3 suspension (counting the interval between the tenor and bass) but if you count the interval between the tenor and soprano, you get 7th-8th. Normally, 7th resolves to 6th. Therefore, it is very rare to see a final tonic chord with double third - usually we double the root of the chord in such case.
I hope you will notice these harmonic details while you play this verset.
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