Here you find what Tonalibus calls anchored Reach heptatonalities, otherwise also known in some cases as harmonic or in one case as a dominant scale. They all include one or two so-called Reach steps or augmented seconds that span three half steps. Their names, as chosen by Tonalibus, reflect their pitch distribution and the position of the Reach interval or intervals. Some of their other names in use show up as well.
Fully anchored subgroup LoloReach
Partially anchored subgroup LoReachUp
Partially anchored subgroup ReachNa
Partially anchored subgroup ReachUp
Partially anchored subgroup NaReach
Reach heptatonalities overview visuals
In the tables below you see an overview of the fully and partially anchored Reach tonalities that are included in the catalogue. There are two cyclic pattern progressions. The single Reach, or single harmonic, pattern includes one Reach step surrounded by half steps, one before and two successively after the Reach step. Then three consecutive whole steps close the circle. The double Reach, or double harmonic, matrix includes two Reach steps per octave, framed by two half tones on both sides, on one side successively, on the other with a whole step interspersed between the two half steps. Of both these pattern cycles only a few tonalities each made it into the catalogue. Some of them are varieties of what’s sometimes called Gypsy scales, and others Neapolitan minor scales.
On the page Tonalities, you find a list of all anchored tonalities included in the catalogue, along with a side-by-side juxtaposition of their scale patterns, as well as a general overview of fundamental pitch distribution patterns.
Common characteristics of Reach heptatonalities
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.