implicitly favoured by many authors. It is spanned by fifths (horizontal direction) and major thirds (vertical direction). Triads correspond to triangles.

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The four figures above represent four Euler Tone-Net Maps each consisting of two successive triads in the sequence. What counts here is not their succession as such, but the fact that tied notes occupy identical positions. The little circular nodes within the triangles together with the connecting edges represent prescricptions for triangles to be glued. The resulting global object cannot be embedded into the Tone-Net.⁴

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This structure somehow reflects the global character of knowledge about harmony. We may conceive the above construction as a protocol of a mental experiment of hermeneutic nature. Instead of directly concluding that the chord sequence is a global structure, we could inspect other theoretical viewpoints. We list some of them:

1. to neglect the independence of fifth- and third-kinship. This is what most scholars do in practice, although often not in their theoretical reasoning (e.g. Heinrich Schenker and his school),
2. to neglect the homogeneity of the tone space, (e.g., not to consider the triad of scale degree II as a proper one, like Moritz Hauptmann)
3. to neglect that tied notes should occupy identical tone positions. This is what Martin Vogel suggests.