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We analyse the results of a 5.5‐yr photometric campaign that monitored 247 southern, semiregular variables with relatively precise Hipparcos parallaxes to demonstrate an unambiguous detection of red giant branch (RGB) pulsations in the solar neighbourhood. We show that Sequence A′ contains a mixture of asymptotic giant branch and RGB stars, as indicated by a temperature‐related shift at the tip of the red giant branch. Large Magellanic Cloud (LMC) and Galactic sequences are compared in several ways to show that the period–luminosity sequence zero‐points have a negligible metallicity dependence. We describe a new method to determine absolute magnitudes from pulsation periods and calibrate the LMC distance modulus using Hipparcos parallaxes to find μLMC= 18.54 ± 0.03 mag. Several sources of systematic error are discussed to explain discrepancies between the Massive Compact Halo Object and Optical Gravitational Lensing Experiment sequences in the LMC. We derive a relative distance modulus of the Small Magellanic Cloud relative to the LMC of Δμ= 0.41 ± 0.02 mag. A comparison of other pulsation properties, including period–amplitude and luminosity–amplitude relations, confirms that RGB pulsation properties are consistent and universal, indicating that the RGB sequences are suitable as high‐precision distance indicators. The M giants with the shortest periods bridge the gap between G and K giant solar‐like oscillations and M‐giant pulsation, revealing a smooth continuity as we ascend the giant branch.

We present the results of a 5.5-year CCD photometric campaign that monitored 261 bright, southern, semi-regular variables with relatively precise Hipparcos parallaxes. The data are supplemented with independent photoelectric observations of 34 of the brightest stars, including 11 that were not part of the CCD survey, and a previously unpublished long time-series of VZ Cam. Pulsation periods and amplitudes are established for 247 of these stars, the majority of which have not been determined before. All M giants with sufficient observations for period determination are found to be variable, with 87% of the sample (at S/N >= 7.5) exhibiting multi-periodic behaviour. The period ratios of local SRVs are in excellent agreement with those in the Large Magellanic Cloud. Apparent K-band magnitudes are extracted from multiple NIR catalogues and analysed to determine the most reliable values. We review the effects of interstellar and circumstellar extinction and calculate absolute K-band magnitudes using revised Hipparcos parallaxes.Comment: 18 pages, 15 figures; accepted for publication in Monthly Notices of the Royal Astronomical Societ

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