We present a detailed analysis of the cosmic microwave background structure in the Tenerife Dec=+40 ^ { \circ } data . The effect of local atmospheric contributions on the derived fluctuation amplitude is considered , resulting in an improved separation of the intrinsic CMB signal from noise . Our analysis demonstrates the existence of common structure in independent data scans at 15 and 33 GHz . For the case of fluctuations described by a Gaussian auto-correlation function , a likelihood analysis of our combined results at 15 and 33 GHz implies an intrinsic rms fluctuation level of 48 ^ { +21 } _ { -15 } \mu K on a coherence scale of 4 { } ^ { \circ } ; the equivalent analysis for a Harrison-Zel ’ dovich model gives a power spectrum normalisation of \mbox { $Q _ { rms - ps } $ } = 22 ^ { +10 } _ { -6 } \mu K. The fluctuation amplitude is seen to be consistent at the 68 % confidence level with that reported for the COBE two-year data for primordial fluctuations described by a power law model with a spectral index in the range 1.0 \leq n \leq 1.6 . This limit favours the large scale CMB anisotropy being dominated by scalar fluctuations rather than tensor modes from a gravitational wave background . The large scale Tenerife and COBE results are considered in conjunction with observational results from medium scale experiments in order to place improved limits on the fluctuation spectral index ; we find n = 1.10 \pm 0.10 assuming standard CDM with \mbox { $ \mbox { H } _ { 0 } $ } = 50 \hbox { km } \hbox { s } ^ { -1 } \hbox { Mpc } ^ { -1 } .