Mensurations

Mensurations and proportions

The mensuration of the great majority of the separate sections of pieces in Choralis Constantinus II is ₵. It is not always signed explicitly, but it is assumed if no sign is present.

Other signs, excluding sesquialtera proportion

Signs that apply to all voices throughout a section:

• Ϲ: Sequence 9, v. 4; also incorrect Ϲ (for ₵) in Sequence 7, v. 2 (D, A, T)
• Օ2: Sequence 8, v. 6; Introit 25, verse
• Օ: Introit 25, antiphon
• Φ: Tract 4, verse 4; Sequence 7, v. 18; Sequence 8, v. 4; Sequence 8, v. 18; Sequence 9, v. 10; Sequence 10, v. 2; Sequence 23, v. 22

Simultaneous change of signs in all voices within a section:

• Ͼ → Φ: Sequence 3, v. 14

Combinations of mensurations that apply throughout a section:

• ₵ + ₵2 (duple proportion): Introit 24, antiphon; Sequence 10, v. 12
• ₵ + Ϲ (subduple proportion): Introit 24, verse; Sequence 12, v. 8
• Օ + Ꙩ (subduple proportion; mensuration canon): Sequence 9, v. 2
• Օ + Ͼ (subduple proportion): Sequence 24, v. 2
• Φ + cut-Ͼ (printed incorrectly as ₵; subduple proportion): Introit 14, verse

Combinations of mensurations and proportions that change within a section:

• • • Ϲ (D, A, T) + Ͼ (B) → all Ͼ → all Ϲ: Sequence 13, v. 2
    • ₵ (D, A, T) + ₵ → 2 → 4 (B): Alleluia 25
    • ₵ (D, A, T) + Օ → Ϲ → ₵ → 2/1 → 4/1 (B): Sequence 1, v. 8
    • ₵ (all) → coloration (all) → Φ + cut-Ɔ + Ϲ + Օ: Tract 5, v. 6
    • ₵ (all) → ₵2 + Ϲ2 + cut-Ɔ → 4 + cut-Ɔ + Ϲ: Sequence 14, v. 20
    • 8 different combinations of most of the above signs and the unique ₵Ɔ: Sequence 25, v. 2

• • • • See Heyden, Musicae for a discussion of these signs.

  Sesquialtera proportion

  Sesquialtera proportion is of two types: groups of three semibreves and groups of three minims.

  • • • The signs of semibreve sesquialtera are ₵3 (mostly at beginnings of sections), 3 (mostly within sections), Օ2/3 (Sequence 4, v. 7 only), Օ/3 (Sequence 9, v. 10 only), and coloration.
      • The signs of minim sesquialtera are 3 and coloration.

  Semibreve sesquialtera is very common. It is found mostly within sections in ₵ (at the beginning, middle, or end), but sometimes throughout a section. It almost always appears in all voices simultaneously. It is in simultaneous combination with ₵ only in the following sections:

  • • • Simultaneous with rests in ₵: Sequence 1, v. 10; Sequence 2, v. 6; Sequnece 23, v. 16
      • Simultaneous with notes in ₵: Sequence 2, v. 8; Sequence 8, v. 14; Sequence 8, v. 20 (overlap resulting from the notation of the canon); Sequence 19, v. 24; Sequence 20, v. 20

  Minim sesquialtera is much less common than semibreve sesquialtera. It appears in the following contexts:

  • • In all voices in the concluding passage of a section: Communion 8; Sequence 13, v. 2; Sequence 19, v. 18; Sequence 21, v. 10
    • In a very brief passage in single voice, combined with ₵: Communion 10; Tract 4, v. 2
    • In extended passages, combined with numerous other signs: Sequence 25, v. 2