The "backwards" chemical shift (δ) scale with larger numbers on the left and smaller numbers on the right is legacy from the 1950's era of continuous wave (CW) NMR. In these early experiments the magnetic field was increased gradually from lower to higher values.
The less shielded nuclei (with today's higher positive δ values) were the first to be detected and placed on the left side of the spectrum. As the field increased the more shielded nuclei (with lower δ values) came into resonance and were placed to the right. The (left) nuclei detected at a lower external field level were said to be "downfield" from the more shielded (right) nuclei which were called "upfield".
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Another scale found in NMR spectroscopy literature from the 1960s and 1970's is the tau (τ)-scale, where τ = 10 ppm − δ. This scale had numeric values increasing from left-to-right across the spectrum, so was no longer "backwards." The (τ)-scale has been abandoned and, like the antiquated "upfield" and "downfield" designations, should be avoided in the modern era of FT NMR.
References
Reich HJ. Structure determination using spectroscopic methods. Syllabus for Course 605. University of Wisconsin, Madison, 2014. (See Section 5.02 for discussion of the "backwards" δ scale). Excellent on-line resource for structural NMR, available at this link.
Reich HJ. Structure determination using spectroscopic methods. Syllabus for Course 605. University of Wisconsin, Madison, 2014. (See Section 5.02 for discussion of the "backwards" δ scale). Excellent on-line resource for structural NMR, available at this link.
Related Questions
What is meant by a chemical shift?
What is meant by a chemical shift?