Holmboe's last quartet work which is unoffi­cially also String Quartet No. 21 was the last work he ever composed and was unfinished on his death in 1996. His pupil Per NørgÃ¥rd has finished the quartet and himself characterizes his contribution by saying that the score existed “in an only partly completed form which could however be written out with only a few cases of doubt”. With only two movements and a play­ing time of about nine minutes it is at its exist­ing length the shortest of Holmboe's string quar­tets. The first movement takes the form of one long arch in a rocking triple time which constantly shiftsamong different tempo and pulse sensations. At the same time the rhythmic en­ergy increases until the movement in a faster Con moto tempo accelerates to a more flowing 12/8 time coloured both rhythmically by cross-­rhythms in duple time and timbrally by harmon­ics in the viola. In its middle section Con fuoco the movement culminates in both tempo and expression until it falls calm in brief recapitula­tions in reverse order of the first two sections. The rocking feeling continues in the second movement but now at a more extroverted level from the outset Allegro and pizzicato. The en­ergy builds up further as the mood intensifies to Con fuoco while all instruments go over to bowed playing but like the first movement this movement ends Adagio here however not as a gradual attenuation but through a sudden shift in tempo to a calm imitative passage before the movement slowly thins out to the almost inaudible through a last dense open sounding chord with a brief violin solo above it. The quartet is dedicated to Holmboe's wife MeLa May Holmboe and was given its first performance by the Kontra Quartet on 22nd March 1997 at the Carl Nielsen Academy of Music in Odense Denmark.

Quartet No. 1 in G Major, K.80 Quartet No. 2 in D Major, K.155 Quartet No. 3 in G Major, K.156 Quartet No. 4 in C Major, K.157 Quartet No. 5 in F Major, K.158 Quartet No. 6 in B-flat Major, K.159 Quartet No. 7 in E-flat Major, K.160 Quartet No. 8 in F Major, K.168 Quartet No. 9 in A Major, K.169 Quartet No. 10 in C Major, K.170 Quartet No. 11 in E-flat Major, K.171 Quartet No. 12 in B-flat Major, K.172 Quartet No. 13 in D Minor, K.173 Quartet No. 14 in G Major, K.387 Quartet No. 15 in D Minor, K.421 Quartet No. 16 in E-flat Major, K.428 Quartet No. 17 in B-flat Major, K.458 Quartet No. 18 in A Major, K.464 Quartet No. 19 in C Major, K.465 Quartet No. 20 in D Major, K.499 Quartet No. 21 in D Major, K.575 Quartet No. 22 in B-flat Major, K.589 Quartet No. 23 in F Major, K.590