# Talk:Fifth complement

## Naming and origin

Oh is it really me who coined this term? By analogy of octave complement and in the desire to contrast major and minor keys, the concept should date back to classical era. FloraC (talk) 02:38, 8 September 2020 (UTC)

- It's possible that this term existed before. But I don't remember that I heard or read of it. I also searched the web for it, no success so far. I admit that it's not such a huge step but this is typical for retrospection. The fifth is absolutely important for classical Western music but there is no fifth equivalence ... :) --Xenwolf (talk) 06:35, 8 September 2020 (UTC)

## Eleventh complement

The fifth complement is only applicable to intervals that are smaller than the fifth. Their octave complements don't have an equivalent. Because the octave complement can also be interpreted as mirroring on the unison axis, the multiplicative inverse of an interval can be taken (turning upward into downward intervals). Here we find the perfect downward fifth (2/3) which is octave-reduced into the fourth (`(2/3) * (2/1) → 4/3`

). The perfect eleventh (FJS:**P11**, 8/3) shares the same interval class but has the advantage that octave-reduction is already included if it is used as the completion target for intervals greater than 3/2 (see for example `8/3) / (5/3) → (8/5`

). That's why I suggest to add the eleventh complement to the concept of fifth complement. In may opinion both should be described in the same article (preferably **Fifth complement**) with a redirect added to the **Eleventh complement** lemma. As a consequence "normal" interval pages tend to build link rings of four like this ^{[1]}:

a ↔^{c8}b ↔^{c5}c ↔^{c8}d ↔^{c11}a

- ↑
**Legend**

a, b, c, d: intervals

c8: octave complement

c5: fifth complement

c11: eleventh complement