HexaNa — a prime Na tonality and hexatonality
Tonalibus 2e-7 hexa – 2021-09 – 59
Tonalibus 2e-7 hexa – 2021-09 – 60
Tonalibus 2e-7 hexa – 2021-09 – 61
Tonalibus 2e-7 hexa – 2021-09 – 62
Scale and sound samples
- Hexatonality matrix: The octave generally includes one Reach step, four whole steps, and a single half step (or semitone). Two or three (or exceptionally all four) whole steps appear consecutively. Thus there are two pairs of consecutive whole steps or a trio plus a single. They are framed by the half step on one side and the Reach step on the other. Exceptionally there can be two Reach, two whole, and two half steps. Plus there is one case with three Reach and three half steps.
- HexaNa: The name indicates that this is the full primary Na(tural harmonics) hexatonality. It is equivalent to HeptaNa or LydAeolian without the minor sixth.
- Step pattern: Ascending from the fundamental (tonic or Do), three consecutive whole steps lead to a half step. Then comes a Reach step. Finally a whole step leads up to the octave.
- Scale intervals: Major second, major third, tritone, quint, and minor seventh.
- Tetra- and trichords: The lower tetrachord is Lydian, and the upper trichord is PentaMin.
- Harmonic axes: There are two axes, one vertical and the other tilted, N-S and ES-WN.
- Primary harmonic anchors: The fundamental or North anchor is partially present with its head and right leg. The East anchor has its right leg and the contrasting or South anchor its head only. The West anchor has both its legs but no head.
- Secondary harmonic anchors: There is one secondary anchor, SW. It strengthens the fundamental or North anchor and quint, plus to a lesser degree the West anchor.
- HexaNa is part of the Na tonalities progression through the whole or part of the sequence of natural harmonics. In the full Na progression or modulation path, secondary harmonics build up from TetraNa towards HeptaNa / LydAeolian. Then the secondary harmonics gradually modulate to tertiaries (or reciprocals) towards NaBal / PhrygIonian and may then resolve to PentaBal / PentaMinLa. Below are detailed graphical modulation path depictions of these and more such progressions.
Tonalibus 1e-3 tonalities – 2021-08 – 75y
Tonalibus 1e-3 tonalities – 2021-08 – 84y
Tonalibus 1e-3 tonalities – 2021-08 – 85y