Blues Scale In C:
C, Eb, F, F#(or Gb), G Bb.
Root - Flat Third - Fourth - Sharp Fourth/Flat Fifth - Fifth - Flat 7th.

In the original post, you just indicated the flat third and seventh.
There are six notes in the scale, but you will find other notes in blues
songs (like Heartbreak Hotel as your example with the E Natural).
There is also a flat fifth between the fourth and fifth, plus no second
or sixth to the scale.
There are different styles of blues, but the blues that most people know
like in C for example with this chord pro:
C C7 F7 C7 G7 C - G7
Contributed to developing early forms of rock and roll, but when they
switch to the fifth chord on the last line of the verse, they switch
to the fourth before the tonic chord.
(They also don't always use seventh chords)
The fifth and fourth chord is usually just a major chord (but they
use a blues scale)
C C7 F C G7(or G) F C - G7

Also, a while back when I was reading history books about the blues;
the blues as we know it has both African and European origins.
The blues as we know it developed in the Mississippi Delta with both
black and white influences.

Traditional African tribes commonly used a pentatonic scale similar
to the blues scale, and notes from this scale, and the major scale
(used in Europe) were combined to form the six-note blues scale.
The chord harmonization was constructed from European origin. The
I IV V pro. The three phrase format in which the first two phrases
are the same, was used in many traditional European folk songs.

The rhythm, came from both. In Africa, music was based on percussion
instruments, using "polyrhythms".
Polyrhytms are when two different rhythms, not in the same Time Signature are played, simultaneously.
As both rhythms play, they have make sure that both rhythms start each
measure and end each measure at the same time.
(Play them as if they were evenly the same.
Example: 2/4 and 3/4
is a simple polyrhythm. One rhythm has to play the two counts in 2/4
evenly with the rhythm playing three counts in 3/4.
(It sounds weird to explain)

Now, European rhythm; Rhythm and Time Signature changes.
European music, often has rhythm changes and/or Time signature changes
in the songs; and the transition has to be made smoothly keeping the
same steady beat.

Both of these rhythm styles I have found in Blues. There is equally
as much European influence as there is African influence in the early
development of Blues music.

Content of the lyrics: Field hollers, work songs, jail songs, chain
gang songs; sorrows they went through, love.
That's an outline of some of the categories that the early blues
lyrics content. Now, that is where the black man took control of the
blues. After the blues were developed, much of the artists were of
African American ancestry.
(Slave Trade years in Mississippi Delta, is the explanation for these
categories)

Also, the banjo was the early instrument of the blues. It was invented
in Africa, and the guitar was introduced to the blues in the early
1900's. Then other instruments such as the harmonica and the bass
followed, eventually.
How the blues became electric guitar, electric bass, and drums; this
was when the blues artists migrated from the Southern States to the
Northern States like Illinois for example.
After the blues was known throughout the South, they began to move
North where the Big Band Jazz was played. The blues made the transition to electric instruments to compete with Big Band/Jazz, and
adopted some of the instruments they used.

That's a brief outline, I can give you some websites if anyone's
interested, in more blues history; with more detail.