Grainer wrote his theme for strings, brass, and percussion. Because the BBC wanted a futuristic sounding theme for the show, the theme was recorded by the BBC Orchestra and the analogue track given to the BBC Radiophonic Workshop. The BBC Radiophonic Workshop was a newly-created department within the BBC which created a wide range of sound effects and electronic sounds for BBC radio and television. Delia Derbyshire oversaw the translation of the traditional them into an electronic one for the show. She was assisted by technician Dick Mills.
To create the futuristic sound, a complex process was painstakingly followed. Each note was individually cut out of the soundtrack, sped up or slowed down, white noise added, and test-tone oscillator sounds of the right frequency added. The main bassline is actually a single plucked cello string. It was sampled over and over and over to create the dum-dum-dum/dum-dum-dum bassline. As the bassline rose and fell, the sample was played at higher or lower speed to change its pitch. The melody was created by changing the tone created by an oscillator. Sometimes actual oscillator sound was used, but sometimes the sound was played back at a higher or lower speed to create the right pitch. To create glissando, a keyboard was patched into an oscillator and tones played through it. The rhythmic hissing was added to the theme by playing back filtered white noise. The create the sense of many of the same instrument playing at once, multiple versions of each layer of the bassline and melody were added to create dynamic tones.
Each distinct orchestration (bassline, second bassline, melody, high melody, glissandoes, hisses) was created on its own tape. The tapes were played back and re-recorded using a microphone, because there were not multi-track tape machines at the time. (Imagine: The machines had to be started on time and stay in sync!)
Grainer tried to get Derbyshire a credit (and share of the royalties) on the soundtrack, but the BBC said she was a staff technician and could not get one.
The Doctor Who theme was altered for the first time in 1970 at the start of the Third Doctor's tenure. An echo of the bassline at the start of the theme, the "middle eight" (or bridge) removed from the theme, a repetitive glissando motif added as the title of the episode appeared.
In 1980, the Doctor Who theme was altered again. Radiophonic Workshop staff member Peter Howell re-recorded the theme using modern synthesisers. The bassline was re-created on a Yamaha CS-80. The hissing noises were replaced with a reverse echo of the basline. The melody was re0created on an ARP Odyssey Mk II, the high melody re-created on an EMS Vocoder 5000, and the "middle eight" re-created on a Roland Jupiter-4. The key of the theme was also changed to a higher pitch.
The Doctor Who theme was changed AGAIN in 1986 by Dominic Glynn. A sub-bassline was added, the high melody made more ethereal, the bass slides removed, and a more melodic sets of tones replaced the glissandos under the episode titles. The bassline was re-created on a Roland Juno-6, the high and low melodies re-created on a Yamaha DX21, and the hissing effects re-created on a Korg 770.
Radiophonic Workshop staff member Keff McCulloch re-created the Doctor Who theme YET AGAIN in 1987. McCulloch used a Sequential Circuits Prophet-5 synthesiser for almost all the effects. A strong hissing was added to the beginning, and heavy vibrato added to the stronger, cleaner high melody. The "middle eight" was added to the theme again, and a theremin-like quality added to the latter half of the theme. The key was also changed. Delia Derbyshire was reportedly VERY VERY unhappy with this theme...
In 2005, composer Murray Gold arranged the Doctor Who theme for the rebooted series. Samples from the 1963 theme were used for most of the bassline and theme. However, low strings, brass, and percussion were added to give the theme a more symphonic sound. Also audible are sounds of a Dalek raygun and the TARDIS materialisation sound effects.
Two major changes were made to the theme at this time. The first was timed with the visual effects, which depicted a TARDIS flying toward the camera. The camera then spun in slow-motion around the TARDIS. To emphasize this slewing, a soundboard was used to change the pitch and tone of the theme.
The second major change was the addition of staccato, rising and falling strings -- an element known "The Chase" -- to the theme, equal in volume to the melody. As the theme fades out, the strings and horns take over from the melody.
In 2007, the BBC ordered all series to shorten their themes. Gold re-arranged the theme to be shorter, but he also replaced the basssline with drums, piano, and bass guitar and added flutes to "The Chase" counter-melody.
Murray Gold completely reworked the theme in 2010 for the Matt Smith era. A new, ominous, rising series of horns opens the show -- replacing for the first time the hissing stinger which had been the theme's trademark since 1963. Furthermore, the electronic melody (based on the 1963 theme samples) was thrown out, and the entire high melody and low melody re-created on a synthesizer. Percussion now underlies every tone of the melody, and a wordless chorus added under the episode titles.