Pink provides simple harmony. It also keeps up the intensity, though not too much. Pink is a pastel of red, a mix of red and white. Because of that, there's a natural harmony. The pink creates a monochrome scheme, rooted in red. The lighter value of the pink (a naturally lighter color) prevents the room from appearing too dark. For a colorful alternative, yet a color that provides respite, pink is an answer.
Taking you in the other direction, violet darkens and intensifies. In contrast to pink, violet ramps up the color intensity. In addition, unless you use a violet with at least some white, light levels may be a problem. However, it is a dramatic choice. Paired with metallic decor elements, either of furniture or trim, you'll make a statement. You may wish to select light neutrals or a lilac for the ceiling for light reasons.
A metallic is a regal pairing for oriental red. The warmth of gold is best. The warm undertones harmonize and convey opulence. Four full walls of gold may be too much for some, in which case you can paint an accent wall, which is a single wall, often in a striking color. The accent color may be too assertive on its own. Using it on one wall gives you the benefit of its character without overwhelming the room. Metallic paints are made for the home. They're easy to apply. You need no specialized equipment or skills.
White is a cure-all. The lightness keeps the room bright. The absence of hue makes it compatible across the color spectrum. You may match white with anything, which greatly simplifies your decisions with oriental red. You can focus on matching other elements, not fretting about the walls. The white is a bit staid. You won't want it for a theatrical salon. However, as a no-fail color for oriental red, white is unsurpassed.