# EdXI and beyond

Equal divisions of elevenths (e. g. 8/3) and beyond can be conceived of as to use one interval of these as an equivalence, or not. However, the utility of such intervals as bases is limited by the fact that *it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done*. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:

- Equal divisions of elevenths (e. g. 8/3)
- Equal divisions of twelfths (e. g. 3/1 and 20/7)
- Equal divisions of thirteenths (e. g. 10/3)
- Equal divisions of fourteenths (e. g. 7/2)
- Equal divisions of the fifth harmonic
- Equal divisions of the sixth harmonic
- Equal divisions of the seventh harmonic
- Equal divisions of the tenth harmonic
- Equal divisions of the eleventh harmonic
- Equal divisions of the twelfth harmonic
- Equal divisions of the thirteenth harmonic