Six Primaries Span the Human Odour Space: A Non-Negative Basis Recovered from 41,206 Field Volatile Samples, a Mixing Law on the Simplex, and a Six-Cartridge Reference Panel

Vision has three primaries. Hearing has one continuous axis. Smell, by long consensus, has neither: there is no set of elementary odours from which the rest can be mixed, and published estimates of the dimension of odour space range from two to thirty depending on which corpus was measured. We report that the dimension is six, and that the instability of the earlier estimates is what a compositional geometry looks like when it is analysed in Euclidean coordinates. Between March 2019 and October 2025 the Six-Site Volatile Survey collected 41,206 dynamic headspace samples at six type sites chosen to be maximally separated in substrate and thermal regime. Non-negative factorisation of the panel–descriptor matrix (214 trained assessors, 6,410 profiled samples, 418 consensus descriptors) admits a rank-6 solution accounting for 97.4% of panel-explainable variance; the seventh factor adds $0.31$ percentage points, and cophenetic correlation falls from $0.994$ to $0.951$ across that step. Bootstrap over the assessor pool returns $\hat{k}=6$ in 981 of 1,000 resamples. Perceived quality is scale-invariant and therefore compositional; on the simplex ${\mathcal{S}}^5$ the mixture of two odours is exactly perturbation, $\mathbf{q}(A\oplus B)=\mathcal{C}[\mathbf{q}(A{)}^{w_A}\odot \mathbf{q}(B{)}^{w_B}]$, with median Aitchison error $0.084$ over 6,120 binary blends against $1.71$ for linear mixing, and $0.097$ over 1,880 ternary blends predicted with no free parameters. We then built the basis. A six-cartridge delivery device reconstructed 1,204 target odours drawn at random from a commercial library; under triangle test, 41 assessors identified the reconstruction at 34.0% (95% CI $32.9$–$35.1$) against a chance rate of 33.3%. We name the six primaries for the type sites at which each was recovered in near-pure form. A seventh component is present in 1.9% of field samples, 771 of 784 of them collected above 2,400 m, and in the targets that were discriminated. We have not accounted for it, and we do not report it as a primary.