Bach: Canon in Hypodiatessaron al rovescio e per augmentationem perpetuus

Perpetual canon at a 4th below in contrary motion and augmentation

If we call the second voice (the follower) g and the first voice (the leader) f, then the relationship between the two voices can be expressed as a function:

g(t) = -f((t-2)/2) - 4

The minus (-) sign indicates that the follower is in contrary motion to the leader. When notes in the leader are rising, notes in the follower move in the opposite direction and fall. It is divided by two because the follower is also in rhythmic augmentation to the leader, whcih means a quarter note in the leader will be a half note in the follower. Halfway through, Bach exchanges registers and does it all again with the upper voice as the follower.

Each voice participates in a desperate struggle to harmonize with each other, like a pair of lovers being torn apart by the hardships of the world.

Category:

Music

Tags:

• bach
• canon
• art of fugue
• somber
• relationships
• classical
• augmentation
• contrary motion
• contrapunctus
• 15
• xv

[petezilla]

The function part is not so important as the "Each voice participates in a desperate struggle to harmonize with each other, like a pair of lovers being torn apart by the hardships of the world." part which is a beautiful commentary!

[Asthfra]

hi, may you explain me the function? the minus (-) sign indicates that the follower is in contrary motion to the leader, ok... (-4) indicates that the follower is fourth note lower? and why (t-2)?

This means I can replace t with a value and find the corresponding NOTE of the follower?

thanks!

[daniel15671]

Words fail in the face of such transcendence.

[atree3]

fascinating

[Thulaandme]

Awesome this music; this is for me a major lesson in the power of music to elevate the mind above the world

thanks!