ReachNaBal — a prime Na tonality and Reach heptatonality
Tonalibus 2b-5 reach – 2023-01 – 72
Tonalibus 2b-5 reach – 2021-09 – 57
Tonalibus 2b-5 reach – 2021-09 – 58
Tonalibus 2b-5 reach – 2021-09 – 59
Tonalibus 2b-5 reach – 2021-09 – 60
Scale and sound samples
- Reach or harmonic tonality matrix: The octave includes one or exceptionally two (double harmonic) Reach steps (augmented seconds) framed by half steps (or semitones) or exceptionally by a whole and a half step. There are either three whole steps or exceptionally just one. If three of them, they are in most cases either a pair and a single one separated by the third half step, or a trio framed by half steps. Exceptionally though all three whole steps are singles. When a trio of consecutive whole steps, they are preceded or followed by two consecutive half steps. The total number of half steps is three, or exceptionally four with two (double harmonic) Reach steps.
- ReachNaBal: The name indicates that the lower tetrachord is ReachNa and that the upper balances the lower by vertically mirroring the Reach step of the lower tetrachord.
- Step pattern: Ascending from the fundamental (tonic or Do), a half step leads to a Reach step. Then comes a whole step followed by two consecutive half steps. Finally a Reach step plus a half step lead up to the octave.
- Scale intervals: Minor second, major third, tritone, quint, minor sixth, and major seventh.
- Penta- and teterachords: The lower pentachord is ReachNa and the upper terachord is Reach.
- Harmonic axes: There are two axes, one vertical and the other tilted: N-S and NE-SW.
- Primary harmonic anchors: The fundamental or North anchor is partially present with its head and right leg only. The contrast or South anchor is fully present. Also partially present with only one leg each are the East and West anchors, the East with its left and the West with its right.
- Secondary harmonic anchors: There are two secondary anchors, NE and NW. They both strengthen the contrast or South anchor. Plus, to a lesser degree, one promotes regressively the East, the other progressively the West.
- ReachNaBal is a primary Na tonality. In the full or slightly shortened Na tonalities progressions depicted below, it transitions the second secondary harmonic to a tertiary.
Tonalibus 1e-3 tonalities – 2021-08 – 75y
Tonalibus 1e-3 tonalities – 2021-08 – 84y
Tonalibus 1e-3 tonalities – 2021-08 – 85y