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)

666

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