Arto and Tendo Theory
The arto and tendo tonality system is a unique theory that a new form of tonality can be built from 10:13:15 and 26:30:39 triads. The idea is that because these chords share many of the same properties as major and minor triads, the arto and tendo harmonic system resembles the diatonic system in many ways, however, it also has many distinct characteristics that make it sound nothing like the diatonic scale.
Arto and Tendo Triads
Arto and Tendo triads are literally the same shape as major and minor triads, an arto triad 26:30:39 results by flatting the third of a minor triad by approx one quarter tone. The Tendo triad results by sharping the third in a major triad by approx one quarter tone. The Tendo chord 10:13:15, being of a simpler ratio, is considered to be more consonant than the arto chord which is quite complex. Also, 10:13:15 tendo chord is only slightly more dissonant than the minor chord 10:12:15. Although they appear to be the same, arto and tendo chords are not seven limit, and tuning them to 14:17:21 and 6:7:9 not only tunes the tendo chord horribly, but also causes the two triads to lose their characteristic 15 limit sound.
One interesting phenomenon that happens with arto and tendo is that it is cross tonal. Unlike the diatonic scale which has two distinct flavors of triads, arto and tendo triads and Intervals are able to co-exist on the same root. For example, in the diatonic scale, usually playing a C major triad with an Eb would generally sound disruptive and cause dissonance, where as a C arto triad with the third of a C tendo can be played simultaneously without any harsh discordance. This creates an interesting, subtle ambiguous flavor, but what's even more interesting is that the two triads still sound distinct enough to be considered separate and being played together causes a lack of resolution. This also generates the possibility that both arto and tendo chords can be used in a progression on the same root without going outside of the scale. Likewise, a melody on a tendo chord can play notes of the arto chord of the same root.