Tennessee, to believe the old mythmakers, is backwater mountaineers, moonshine whiskey, redeye gravy, coonskin-cap politics and Grand Ole Opry.

This year it is also the scene of one of the nation's most expensive and sophisticated election campaigns - likely to cost more than $10 million, or more than $9 a vote.

The high spending is being led by a tobacco-chewing banker friend of Bert Lance named Jaked Butcher, who desperately wants to be governor.

Butcher, a Democrat, has practically rewritten political spending rules here.

He rented an entire amusement park for $9.551 and invited everyone in town to come. He rented a baseball stadium and fed some 16,000 persons free barbecue dinners. On the Fourth of July he sent a truckload of watermelons to a park in a black area of Memphis. And he bought $3,200 worth of blankets from a senior citizens' group "for promotional purposes."

He isn't a tightwad with traditional electioneering expenses, either. According to Butcher's finance reports, his payroll during the weeks before the Democratic primary included 324 persons - more than twice as many paid staffers as Jimmy Carter had before the Democratic National Convention in 1976.His television commercials appeared so frequently during the summer that the Knoxville Journal twitted him in an editorial cartoon: "We interrupt this Jake Butcher political ad to bring you a Jack Butcher political ad."

Butcher isn't alone among big spenders. His three top opponents in the bitterly contested Democratic primary spend a total of $2.5 million. On the Republican side, gubernatorial hopeful Lamar Alexander, a former Nixon White House aide, spent $672,940, including $2,229 on tailormade suits, in a much easier race. And Senate Minority Leader Howard H. Baker Jr. spent $836,848 on a campaign in which he had no serious opposition.

Even by conservative estimates, the cost of the campaigns for Senate and governor are expected to exceed $10 million this year in a state where only 1.4 million voters cast ballots in 1976.

"That's the kind of spending you might expect from a state the size of California, but not Tennessee," says Common Cause vice president Fred Wertheimer, an authority on campaign spending. "It's a dramatic example of the arms-race mentality that has swept over politics. It indicates the extent campaign financing has gotten out of hand in this country."

Inflation shares the blame for the spiraling costs. When Sen. Baker began planning his campaign budget last spring, his advertising agency found that television ad rates had gone up 300 percent since he ran in 1972, radio rates had increased 60 to 65 percent, printing costs 45 percent and newspaper ad rates 48 percent.

A campaign button that cost 9 cents in 1972 costs 13 cents today; a 5-cent bumper sticker costs 8 cents today; one 30-second spot on Sunday evening in Memphis or Nashville now sells for $750.

But inflation is only part of the problem.

"Tennessee is a very political state, and there's a lot of money around," says Tom Ingram, Alexander's campaign manager. "There are some very wealthy people here."

State election finance laws are weak. Unlike federal law, there's no limit on individual contributions to a campaign for governor. Thus, donations of $5,000 to $10,000 are common from friends of candidates and from businessmen who could benefit from having a friend in the governor's office.

Moreover, both Butcher and Alexander have previously run unsuccessfully for governor, and this may be their last chance at the brass ring. They don't want to be outspent.

Baker can't afford to be outspent. His presidential ambitions hinge in part on an impressive reelection victory. But his opponent, Jane Eskind, is a Democrat of immense personal wealth who senses a chance of a stunning upset in November. By Sep. 8, she had already loaned her campaign $275,000, according to Federal Election Commission reports.

Baker plans to spend $1.6 million, Eskind $1.1 million. Alexander plans to spend about $1.6 million, Butcher $3.8 million to $4 million.

Frank Woods, a key Butcher adviser, maintains this isn't out of line with previous Tennessee campaigns.

"Our opponents are just trying to make an issue because they haven't been as successful in raising money," he said. "I really don't like the charge that we're trying to buy the election. The ability to raise money demonstates leadership, organization and the character of the candidate. I think it's a positive rather than a negative factor."

On his state election reports, Butcher said he spent $2.2 million during the primary - a figure Woods insists reflects all spending. Butcher's defeated Democratic opponents, however, allege that his free-spending campaign couldn't have cost less than $4.million.

Every time we turned around there was money, money, money," says Irby Simpkins, finance chairman for Democrat Bob Clement. "Practically speaking, I'd say he spent between $6 and $7 million."

"There was no big secret about it, because we were bidding for the same services and support from different groups at the same time," added Simpkins, now a top adviser to Republican Alexander. "Every time I spent one dollar" for Clement "they spent 10."

Butcher did face two highly visible office holders: Nashville Mayor Richard Fulton and Public Service Commissioner Clement, whose father used to be governor. Butcher, who has never held public office, had to pay for television and newspaper exposure that they received free.

Alexander, the GOp nominee, faced no serious prmary opposition, and attracted considerable free publicity with a campaign gimmick - a walk across the state in wool shirt and kakhi pants. He was able to coast through to the primary spending only $81,691 on television, $9,618 on printing, and $328 on newspaper ads, according to his campaign reports.

Everything Butcher did was first class.

When he needed a media adviser, he turned to Deloss Walktr, a Memphis political consultant who has advised a shost of successful Southern Democrats. When he needed a pollster, he hired Pat Caddell, Jimmy Carter's pollster. When he need an airplan, he rented a 10-passenger King Air, the Cadillac of private executive turboprops.

He paid Walker $878,201 to handle television advertising, billboards, campaign brochures and other duties. He put one of the state's best known ad men on his payroll and paid $34,000 to out-of-state firms to conduct issue surveys and prepare issue papers.

Just during the 10 days before the primary, Butcher reported spending $23,359 on food, $3,343 on liquor and $2,695 on entertainment. And that didn't count the tens of thousands his campaign spent ferrying Democratic notables by private planes from their homes to intimate dinners with Butcher, or the huge receptions for the masses he threw earlier in the campaign.

In addition to the $878,201 tha the paid Waler, Butcher spent $26,204 on radio ads, $46,352 on newspaper ads, $46,411 on printing and $8,337 on yard signs.

There were Jake Butcher T-shirts, Jake Butcher ballons, Jake Butcher hand fans, Jake Butcher buses, and scores of Jake Butcher paid workers tacking up yard signs, passing out literature, serving barbecued dinners and taking voters to the polls.

Butcher, his opponents like to joke, was such a free spender that voters calling his headquarters for a ride to the polls on primary day not only got a ride, but also were allowed to keep the car.

The story is apocryphal. But Nashville Mayor Fulton says, "To my knowledge there's never been a campaign here like it or anywhere else."

Fulton, who finished third in the race, had counted on the support of organized labor and blacks. He got neither. He charged that Butcher spent more than $50,000 to buy the endorsement of the Tennessee Voters Council, the state's influential black caucus.

"I've been in public office for 20 years and I've never witnessed an effort to literally buy an office such as is being made today," he said at the time.

Butcher's forces dismiss such talk as sour grapes. They maintain that their candidate has attracted wide-spread support because he is successful banker who businessmen feel they can trust to take politics out of government.

"I personally feel that it is good to have Kennedy-type or Butcher-type people in government," says adviser Woods, who is president of the Butcher-controlled United American Bank of Nashville.