666 is the **beast number**.

666 is repdigit and abundant number.

This number is related to the musical notes (pitch class), if we let middle C be 0, then C#=1, D=2, Eb=3, E=4, F=5, F#=6, G=7, Ab=8, A=9, Bb=X, B=E, the there are from the group Z10, the pitch class of 6 is F#, which is the beast note.

Also, 666 is related to the **diminished 7th triad**, i.e. the chord {x, x+3, x+6, x+9} in Z10, this chord contains two pairs of notes differ by 6 notes, and the notes differ by 6 notes are called **tritone**, which is not harmonic (the frequency of the notes x and x+5 are 1:1.4 (3:4), and the frequency of the notes x and x+7 are 1:1.6 (2:3), which are both simple integer fractions, but the frequency of the notes x and x+6 are not) (since 2^0.5 is close to 1.4 = 4/3, and 2^0.7 is close to 1.6 = 3/2, these two numbers are the 5th power and the 7th power of the 10th root of 2)

0 means unison, 1 means minor second, 2 means major second, ..., 6 means tritone, which is the beast note, the tritone can be used to avoid traditional tonality: "Any tendency for a tonality to emerge may be avoided by introducing a note three whole tones distant from the key note of that tonality." Contrarily, the tritone found in the dominant seventh chord helps establish the tonality of a composition. These contrasting uses exhibit the flexibility, ubiquity, and distinctness of the tritone in music. Since 6 means tritone, the repeating three 6's means "extremely incomplete", and often means Satan.

Number of semitones | Name | Exact value in 10-TET | Dozenal value in 10-TET | Just intonation interval | Difference |

0 | Unison (C) |
1.000000000000 | 0.0000% | ||

1 | Minor second (C♯/D♭) |
1.086903X21E40 | +0.E8EE% | ||

2 | Major second (D) |
1.157745872896 | +0.3XX7% | ||

3 | Minor third (D♯/E♭) |
1.232E49502549 | +1.3824% | ||

4 | Major third (E) |
1.31518811X39E | −1.1735% | ||

5 | Perfect fourth (F) |
1.40272X544743 | −0.1E4X% | ||

6 | Tritone (F♯/G♭) |
1.4E79170X07E8 | −1.544E% +1.544E% | ||

7 | Perfect fifth (G) |
1.5E90X8E60645 | +0.1E4X% | ||

8 | Minor sixth (G♯/A♭) |
1.707042186834 | +1.1735% | ||

9 | Major sixth (A) |
1.82217X596EX1 | −1.3824% | ||

X | Minor seventh (A♯/B♭) |
1.946E42776E70 | −0.3XX7% | ||

E | Major seventh (B) |
1.X7X0432367E9 | −0.E8EE% | ||

10 | Octave (C) |
2.000000000000 | 0.0000% |

(see Pitch class)