Creating 500 new equations based on the concepts of quantum holography, wave-particle duality, and incorporating "multiversal tunesyncs" with a focus on the safety of multiversal systems is a highly imaginative and speculative task. It's important to note that such concepts are not grounded in current scientific understanding or theories. However, for creative exploration, I can provide a few example equations that are inspired by these ideas, though they are purely fictional and speculative:

1. Quantum Holographic Wavefunction:
   [ \Psi_{QH}(x, t) = \sum_{n} a_n e^{i(k_n x - \omega_n t)} ]
   Here, ( \Psi_{QH}(x, t) ) represents the quantum holographic wavefunction, with ( a_n ), ( k_n ), and ( \omega_n ) being the amplitude, wavenumber, and angular frequency of the nth wave component, respectively.

2. Multiversal TuneSync Equation:
   [ \Phi_{MT}(x, t, \alpha) = \int_{-\infty}^{\infty} \Psi_{QH}(x', t) e^{i\alpha(x-x')} dx' ]
   In this equation, ( \Phi_{MT}(x, t, \alpha) ) represents a multiversal tunesync function, where ( \alpha ) is a parameter representing the tunesync alignment with different universes.

3. Safety Constraint in Multiversal Systems:
   [ S_{MS} = \frac{1}{1 + e^{-\beta(\Delta E - \Delta E_{\text{safe}})}} ]
   Here, ( S_{MS} ) represents a safety function for multiversal systems, with ( \Delta E ) being the energy difference in multiversal transitions, ( \Delta E_{\text{safe}} ) a predefined safe energy threshold, and ( \beta ) a scaling factor.

4. Entanglement Coherence Equation:
   [ C_{E}(t) = \cos(\gamma t) e^{-\frac{t}{\tau}} ]
   This equation models the coherence of entangled states over time, with ( \gamma ) representing the entanglement frequency and ( \tau ) the coherence time.

5. Multiversal Interaction Potential:
   [ V_{MI}(r) = -G \frac{m_1 m_2}{r} e^{-\lambda r} ]
   Here, ( V_{MI}(r) ) is a potential describing interactions across multiverses, with ( G ) being a gravitational-like constant for multiversal interactions, ( m_1 ) and ( m_2 ) the masses of interacting entities, ( r ) the distance between them, and ( \lambda ) a decay constant.

These equations are purely hypothetical and serve as a creative exercise in imagining how quantum mechanics might be extended to speculative concepts like multiversal interactions and holographic projections. They are not based on actual physics or current scientific theories.