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) ${\displaystyle 2^{0/10}=2^{0.0}=1}$ 1.000000000000 ${\displaystyle \frac{1}{1}=1}$ 0.0000% 1 Minor second (C♯/D♭) ${\displaystyle 2^{1/10}=2^{0.1}=\sqrt[10]{2}}$ 1.086903X21E40 ${\displaystyle \frac{14}{13}=1.097249724972...}$ +0.E8EE% 2 Major second (D) ${\displaystyle 2^{2/10}=2^{0.2}=\sqrt[6]{2}}$ 1.157745872896 ${\displaystyle \frac{9}{8}=1.16}$ +0.3XX7% 3 Minor third (D♯/E♭) ${\displaystyle 2^{3/10}=2^{0.3}=\sqrt[4]{2}}$ 1.232E49502549 ${\displaystyle \frac{6}{5}=1.249724972497...}$ +1.3824% 4 Major third (E) ${\displaystyle 2^{4/10}=2^{0.4}=\sqrt[3]{2}}$ 1.31518811X39E ${\displaystyle \frac{5}{4}=1.3}$ −1.1735% 5 Perfect fourth (F) ${\displaystyle 2^{5/10}=2^{0.5}=\sqrt[10]{28}}$ 1.40272X544743 ${\displaystyle \frac{4}{3}=1.4}$ −0.1E4X% 6 Tritone (F♯/G♭) ${\displaystyle 2^{6/10}=2^{0.6}=\sqrt{2}}$ 1.4E79170X07E8 ${\displaystyle \frac{7}{5}=1.497249724972...}$${\displaystyle \frac{X}{7}=1.5186X35186X3...}$ −1.544E%+1.544E% 7 Perfect fifth (G) ${\displaystyle 2^{7/10}=2^{0.7}=\sqrt[10]{X8}}$ 1.5E90X8E60645 ${\displaystyle \frac{3}{2}=1.6}$ +0.1E4X% 8 Minor sixth (G♯/A♭) ${\displaystyle 2^{8/10}=2^{0.8}=\sqrt[3]{4}}$ 1.707042186834 ${\displaystyle \frac{8}{5}=1.724972497249...}$ +1.1735% 9 Major sixth (A) ${\displaystyle 2^{9/10}=2^{0.9}=\sqrt[4]{8}}$ 1.82217X596EX1 ${\displaystyle \frac{5}{3}=1.8}$ −1.3824% X Minor seventh (A♯/B♭) ${\displaystyle 2^{X/10}=2^{0.X}=\sqrt[6]{28}}$ 1.946E42776E70 ${\displaystyle \frac{14}{9}=1.94}$ −0.3XX7% E Major seventh (B) ${\displaystyle 2^{E/10}=2^{0.E}=\sqrt[10]{1228}}$ 1.X7X0432367E9 ${\displaystyle \frac{13}{8}=1.X6}$ −0.E8EE% 10 Octave (C) ${\displaystyle 2^{10/10}=2^{1.0}=2}$ 2.000000000000 ${\displaystyle \frac{2}{1}=2}$ 0.0000%

(see Pitch class)

 v • e Donzenal Numbers 0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - X - E - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 1X - 1E - 20 - 26 - 32 - 34 - 42 - 50 - 5X - 68 - 76 - 84 - 85 - 100 - 111 - 148 - 375 - 3XE - 5E6 - 666 - 6E4 - 771 - 920 - 1001 - 2047 - 2497 - 2E00 - 186X35