666

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