Although OTRCAT.com does not have recordings of every series listed below, the following is
quick reference guide to old time radio show series, theme music title, and composer (when available).

• Painted Dreams
  Theme: I'm Yours [from the 1930 musical "Simple Simon"]
  John "Johnny" Green (m); E. Y. "Yip" Harburg (w)
  
• Parker Family, The
  Theme: Deep Purple
  Peter De Rose (m); Mitchell Parish (w)
  
• Passing Parade, The
  Theme: Romeo and Juliet (Fantasy Overture)
  Piotr Ilyich ["Peter"] Tchaikovsky
  
• Pat Novak For Hire [starring Jack Webb]
  Open Theme: Pat Novak Main Title
  George Basil ["Buzz" or "Buzzy"] Adlam
  
• Close Theme: Pat Novak End Credits
  George Basil ["Buzz" or "Buzzy"] Adlam
  
• Paul Whiteman [orchestra shows] - Signature Theme on various shows: "Rhapsody In Blue [Theme From...]" - George Gershwin
• Pepper Young's Family - "Au Matin" (In the Morning) [from "Morceaux De Salon Choisis"](Op.83) - Benjamin Louis Godard
• Personal Column of the Air, The
  Theme: L'Amour Toujours L'Amour [aka: Love Everlasting]
  Rudolph Friml (m); Catherine Chisholm (w)
  
• Perry Mason
  Theme: [original theme - title unknown]
  Paul Taubman (??); William Meeder (??)
  
• Pet Milk Show, The
  Theme: You And The Night And The Music [from the 1934 musical "Revenge With Music"]
  Arthur Schwartz (m); Howard Dietz (w)
  
• Phil Baker Show, The
  1. Theme 1: "Armour Theme Song, The" - Kenneth ["Kenn"] Sisson
  2. Theme 2: "Rolling Along" - Phil Baker
• Phil Harris/Alice Fay Show, The
  Main Theme: Sunday
  Jule Styne; Ned Miller; Chester Conn
  
• Secondary Theme: Rose Room (1917)
  Art Hickman (m); Harry H. Williams (w+m)
  
• Theme 3: It's A Big Wide Wonderful World [from the 1940 musical revue "All In Fun"]
  John Rox
  
• Philco Radio Hour, The / Philco Concert Orchestra
  Theme: Mem'ries (Golden Memory Days) [aka: "Memories"] (1928)
  Harold Sanford (m); Henry M. Neely (w)
  
• Phillip Morris Playhouse
  Theme 1: On the Trail [from "The Grand Canyon Suite"]
  Ferde Grofe
  
• Theme 2: Phillip Morris Playhouse Theme
  Rene ("Aime") Garriguenc
  
• Theme 3: Phillip Morris Broadway Playhouse Theme
  George Bassman; Charles Martin
  
• Pick and Pat
  Theme: Jolly Coppersmith, The
  Carl Peter
  
• Pickens Sisters, The
  Theme: Just You and I
  Ray Gold
  
• Pillsbury Flour Radio Hour, The -- see "Today's Children"
  Theme: Lonely Heart
  
  
• Pillsbury House Party, The --
  see "Art Linkletter"
  
  Poet's Gold
  Theme: Clair de Lune [from the "Suite Bergamasque"]
  Claude Achille Debussy
  
• Ponds Players, The
  Theme: Babbie Waltzes, The [from the play, "The Little Minister"] (1897)
  William Fuerst
  
• Ponds Program, The
  Theme: My Love
  Victor Young (m); Ned Washington (w)
  
• Portia Faces Life
  Theme 1: Portia
  Lew White
  
• Theme 2: Portia Faces Life Theme
  Anthony Mottola
  
• Theme 3: Kerry Dance, The [aka: The Cuckoo] [possible Errata]
  Margaret Casson (m); J. L. Molloy (w)
  
• Pot O' Gold
  Theme: Pot O' Gold (In The Air)
  Harry [??] Salter
  
• Presenting Al Jolson (NBC, 1932 - 33)
  Theme: My Mammy [from the 1918 vaudeville revue "Sinbad" starring Al Jolson]
  Walter Donaldson (m); Sam Lewis (w); Joe Young (w)
  
• Pretty Kitty Kelly
  Theme: Kerry Dance, The [aka: The Cuckoo]
  Margaret Casson (m); J. L. Molloy (w)
  
• Princess Pat Pageant, The --
  see "A Tale Of Today"
  
  Princess Pat Players, The --
  see "A Tale Of Today"
  
  Prudential Family Hour, The
  Open Theme: Intermezzo [theme from the 1940 film "Intermezzo (A Love Story)"]
  Heinz Provost (m); Robert Henning (w); (or it could be an Intermezzo by Brahms or Mascagni)
  
• Close Theme: Bless This House (1932)
  Helen Taylor; Maye H. Brahe
  
• Pursuit of Happiness
  Theme: Of Thee I Sing [title song of 1931 Broadway musical]
  George Gershwin (m); Ira Gershwin (w)
  
• Pulitzer Prize Playhouse
  Theme: Pulitzer Prize Playhouse - theme (1946)
  Bernard ["Bernie"] Green (psuedonym of Bernard Greenwald)