The major flame colors are red, orange, yellow, white, and blue. The major flame colors are based on the five types of natural flames that occur on earth as well as five of the six major types of stars that exist. The hotter stars are, the smaller they tend to be.
Power Breakdown
#1 Red
Though red flames were the least hot variation, they were often the biggest when used by benders. A major reason for this is because users had to exert less energy to create these flames allowing them to produce more with the same amount of effort. When forming large open flames, they often had an orange core or inner flame. Roughly 10% of firebenders had red outer and/or inner flames.
#2 Orange
Kanna Foloki (not to be confused with Katara's grandmother Kanna) used a variation of highly explosive dark orange flames. Kanna's dark orange fire had golden inner flames.
Orange flames were the most common type of fire. Over 80% of firebenders had orange fire. These flames often contained a yellow inner flames. Despite being orange, these flames still had variation (just as red and yellow flames also did). Some benders (15%) had dark orange flames which were a bit less hot than other orange forms of fire but tended to be more explosive. Other benders (10%) had light orange flames, which were a little hotter and more precise than standard orange fire.
Some firebenders had dark yellow or gold inner flames instead of yellow. Still others had bright yellow inner flames.
#3 Yellow
Yellow fire was naturally blinding and hotter than the average orange fire. However, using them came with the disadvantage of telegraphing a bender's location. Of all the major fire colors, yellow is the most visible. It is a disadvantage to bend these flames at day or night. On the other hand, yellow flames traveled faster than other forms of fire giving these firebenders unique fighting styles. The use of yellow flames demanded practitioners to be highly mentally active and have good stamina in order to effectively harness them. In order to have primarily yellow flames, a bender had to have sharper than average discipline, form, and tenacity.
During Sozin's comet many firebenders who typically had orange flames, suddenly gained the ability to command completely yellow flames. Outside of Sozin's comet, around 5% of firebenders had yellow outer flames. Another reason some benders were unable to learn how to create yellow flames is due to societal inequality. Nobles and richer members of society had access to better training, schools, and had more time to develop their skills than commoners who often spent time herding for their parents when they returned from school.
Benders with yellow fire as their primary color either had entirely yellow flames or had white inner flames. The one's with white inner flames had deadlier fire and a better chance of blinding enemies when attacking. Most variation among yellow firebenders was whether their outer flames were bright yellow, dark yellow, or gold. Of all these variants gold flames were the least hot but were aesthetically revered by some elders as benders who had "the greatest balance". This balance referred to how individuals with gold flames were generally more focused than people with orange fire but were not as overzealous as people with bright yellow flames. Some elders in the Fire Nation believed flame colors greater than yellow were 'unhealthy colors'.
These views were largely suppressed during the rise of Sozin's empire, when he believed in "dominance at all costs". Reality was even many benders with regular or bright yellow flames already had unhealthy levels of persistence which led to their abilities. However, there were more benders that could use yellow flames and be at balance due to being moderately adroit.
#4 White
It was rare that someone primarily wielded white fire. These flames were the most blinding and could temporarily stun opponents in battle. White fire came with the disadvantage of being telegraphed when used at night making that user an easy target to spot for archers, benders, airships, and tanks. It took a sheer amount of discipline to be able to control these flames. The only reason Macai wielded them is because his father heavily trained him during his younger years and Macai eventually developed his own drive to further his development after years of training in his childhood.
White flames often were the inner flames of gifted benders who's outer flames would usually be orange, yellow, or red. Less than 0.01% of firebenders (one in a thousand) were capable of bending primarily white flames. Even then, most firebenders capable of this ability would never bend fully white flames because they would not train enough to perform this feat. The only known bender with this ability at this time, is Macai. Macai had to give up a lot of his childhood to constantly train in order to take himself to this level.
White flames in particular were a near impossibility for commoners to learn. Macai though not a royal (who had access to the absolute best resources, tricks, and trainers in the Fire Nation) was still a noble. Nobles had access to better schools, facilities, and knowledge in general. In addition to his nobility, Macai's father was an uptight General who demanded Macai become an outstanding warlord to enhance his legacy.
#5 Blue
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The use of predominantly blue fire, is extremely rare. To hardness such an ability takes a mix of determination, discipline, perfectionism, and an unhealthy level of zeal. Azula's blue flames were linked to her father's emotional abandonment of her and praise of materialistic success. Azula pushed herself constantly to earn his love but never seemed to get what she desired. This led to her continually striving for more and more to fill her void until she created flames that were nearly perfect at the cost of her peace and inner stability.
These actions that started in her childhood created seeds that would later lead to her insanity. Fortunately, she would gain it back in time and find ways to use her classic flames more naturally after becoming instinctively accustomed to her advanced abilities. The use of such hot fire alone does not make someone the deadliest firebender because other factors like technique, flame size, physical fitness, experience, and adaptability can factor into who wins a bending fight. Still, the use of such flames gives someone a distinct advantage in a direct engagement where it requires less effort to overpower another firebender.
Only 0.001% of firebenders (one in a hundred thousand) were able to bend blue fire. Keep in mind, the Fire Nation's population is only in tens of millions and benders only make up around a fifth of the world's population. Furthermore, even less of them would have the discipline to train themselves to be remotely sharp enough to have a special fire power like this. Even among those benders, none seemed to have the mentality to have sleepless nights, self-denial, mental stimulation, and intelligence to create those flames. Macai admitted that he himself would never be able to wield blue flames because he was not as focused on his bending as Azula.
Macai needed pressure from his father Eyre to inspire himself to work heavily and even Eyre was slightly limited in how hard he could push his son by Yosari. Eyre pushed Macai more when they were together and during the later years of Macai's childhood Eyre was separated from him. Macai also didn't focus as much as Azula on bending because he focused a bit more of his time on his physical conditioning (mainly lifting weights and performing strength exercises though both performed many cardio drills and Azula spent more time working on acrobatics). It is for this same reason and because she had access to even more knowledge being in the royal family, that she was able to learn how to conduct lightning.
Other Flame Colors
Other flame colors are not natural and can only be created through artificial means or the use of alcohols or chemicals in real life, which means they have spiritual connotations in the AMJ universe. This also means that you will not see someone gain use of these flames from conventional means such as personality traits, discipline, skill level, and zeal.
An example of this is that visible black flames do not naturally form but they can be created through the use of salts and chemicals. So, if they were ever used in AMJ they wouldn't correlate to any specific temperature because artificial flames can be any temperature. More than likely, they would have an average temperature, but they would be used due to a spiritual reason or magic.
Behind the Scenes
Author Brian Hanes often writes in the Sci-Fi genre including Hane's original series "Infinite Domain: Inception". In addition to this, Hanes is a major Star Wars, Mass Effect, and Halo fan with a great admiration for the genre. This leads to his fascination with scientific aspects of nature and fire. Because of this, Brian adds a scientific spin to his fanon Avatar adaptation.
In real life, orange flames are the most common form scene. Red flames are often seen, with lower intensity flames that burn for long durations. Yellow flames can be seen with particularly hot fires. It is common for the red, orange, and yellow flame types to be combined in one great flame. White flames are usually mixed with red, orange, or yellow flames are will lie deep within their cores. Sometimes white flames can be seen with charcoal grills. Blue flames are usually seen when heated by gas ovens or are used for industrial purposes.