We measure simultaneously the properties of the energy spectra and the frequencies of the kilohertz quasi-periodic oscillations (QPOs) in 15 low-mass X-ray binaries covering a wide range of X-ray luminosities. In each source, the QPO frequencies cover the same range of approximately 300-1300 Hz, although the sources differ by 2 orders of magnitude in their X-ray luminosities (as measured from the unabsorbed 2-50 keV flux). So the X-ray luminosity does not uniquely determine the QPO frequency. This is difficult to understand since the evidence from individual sources indicates that the frequency and luminosity are very well correlated at least over short timescales. Perhaps beaming effects or bolometric corrections change the observed luminosities, or perhaps part of the energy in mass accretion is used to power outflows, thus reducing the energy emitted in X-rays. It is also possible that the parameters of a QPO model are tuned in such a way that the same range of frequencies appears in all sources. Different modes of accretion may be involved (for example, disk and radial), or multiple parameters may conspire to yield the same frequencies.
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