This contrast only occurs initially. In theory there might be medial contrasts such as *redash/rehash, but none showed up in the dictionary. The /h/ sound does not occur finally in RP. The /d/ sound is spelled with <d> and the /h/ sound <h> or <wh> in who. Notice how the homograph do makes pairs with with hoe and who, and similarly house makes pairs with douse and dowse.
The contrast is between a voiced stop and a voiceless fricative, well separated in the mouth. It is not a problem for learners.
Interesting pairs include:
deafer heifer
Devon heaven
dialling hireling
dollar holler
Doris Horace
The mean density value is 2.1%. The list makes 132 semantic distinctions, a loading of 55%.
D he dad had daft haft dairy hairy daisies hazes daisy hazy dale hail dales hails dale hale dally Halle dam ham dams hams dammed hammed damming hamming damn ham dammed hammed damming hamming damns hams damper hamper dampers hampers dandle handle dandled handled dandles handles dandling handling dandy handy dank hank danker hanker dare hair dares hairs dare hare daring haring dared hared dare Herr dark hark darken hearken darkened hearkened darkening hearkening darkens hearkens dart hart darts harts dart heart darted hearted darts hearts Dartford Hertford dash hash dashed hashed dashes hashes dashing hashing date hate dated hated dates hates dating hating daunt haunt daunted haunted daunting haunting daw haw daws haws daw hoar daw whore daws whores dawn horn dawned horned dawning horning dawns horns day hay days haze daze haze dazed hazed dazing hazing dead head deadline headline deadlines headlines deafer heifer deal heal dealing healing deals heals deal heel deals heels dealing heeling dealer healer dealers healers dear hear dears hears dear here dearer hearer Dec heck deck heck decks hecks deed heed deeds heeds dell hell dells hells delve helve delves helves den hen dens hens dense hence dep hep Devon heaven dew hew dews hews dew hue dews hues dew Hugh dewy Hughie dhow how dhows house dowse house Di hi Di hie Di high dialling hireling Dick hick die hi die hie dying hieing dies hies died hied die high died hide dike hike diked hiked dikes hikes diking hiking dim him dim hymn dimmed hymned dimming hymning dims hymns dined hind dint hint dints hints dire higher dirt hurt dirts hurts ditch hitch ditched hitched ditches hitches ditching hitching dither hither dive hive dived hived dives hives diving hiving do ho do hoe doe ho doe hoe does hoes does hose do who do's whose dock hock docked hocked docking hocking docks hocks doer who're dog hog dogged hogged dogging hogging dogs hogs dole hole doled hold doles holes doling holing dollar holler dollars hollers Dolly holly dome home domes homes dominie hominy don Hon done Hun doom whom door haw doors haws door hoar door whore doors whores dope hope doped hoped dopes hopes doping hoping Doris Horace Dorking hawking dory hoary dosed host dot hot dots hots dotted hotted dotting hotting Doug hug douse house dowered Howard dowse house dowsing housing downed hound doze hose dozed hosed dozes hoses dozing hosing dub hub dubs hubs duchies hutches dude hewed due hew dues hews due hue dies hues due Hugh dug hug dugs hugs dull hull dulled hulled dulling hulling dulls hulls dumb hum dump hump dumped humped dumping humping dumps humps dun Hun duns Huns dune hewn dung hung dunk hunk dunks hunks dunking hunking dusk husk dusky husky duskier huskier duskiest huskiest Dutch hutch dye hi dye hie dyes hies dyeing hieing dye high dyer higher dyer hire dyers hires
John Higgins, Shaftesbury, February 2010.