Counting in balanced nonary does not feel like counting in an unbalanced base with a different radix. The base is 9, but the digits do not progress from (0) up to (8). They progress through a centered range:
−4, −3, −2, −1, 0, +1, +2, +3, +4.
That changes the shape of counting.
In ordinary base 9, the first two-digit number is (10), immediately after (8). The new place appears at the moment the old one overflows. In balanced nonary, the lower digit does not overflow from (8) to (0). It moves through negative and positive offsets around zero. As a result, the first two-digit positive number is not (10). It is the number whose higher digit is (+1) and whose lower digit is as negative as possible:
1ᔭ.
In decimal terms, this is (9 − 4 = 5). Counting then proceeds upward through the lower digit values:
1ᔭ, 1Ɛ, 1↊, 1Ɩ, 10, 11, 12, 13, 14.
The zero-ending form 10 appears in the middle of this run, not at the beginning. It is the clean multiple of 9, but it is not the first two-digit number. It is the point where the lower-place offset has returned to zero.
This is the central difference in how “roundness” works while counting. In an unbalanced system, round numbers often mark thresholds: the count reaches a new digit length, and the lower places reset to zero. In balanced nonary, round numbers mark centers. A number ending in zero is round because the lower-place contribution is neutral, not because the count has just crossed into a new block.
The same pattern repeats at every scale. The form 100 is not the first three-digit positive number; it is the centered power 9², with both lower places neutral. The surrounding three-digit numbers extend below and above it by changing the lower digits through their balanced ranges.
This means that the counting tables should be read differently from ordinary base-conversion tables. They are not merely showing decimal numbers rewritten in another notation. They show how balanced nonary advances on its own terms: digits pass through negative offsets, then zero, then positive offsets; round numbers occur at the centers of local ranges; and the written and spoken forms preserve that structure instead of translating it away.