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User:Hyacinth/Irrational intervals

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Here is a list of irrational intervals. As such most of them don't have any notation since they are outside just intonation (all rational intervals) and all equal temperaments, which, though irrational, are only in the form xy/z and are found at List of pitch intervals. Rational intervals 1, 2, 3, and 4 are included for context.

Harmonics/Harmonic series
Name Letter Ratio Ratio Cents Audio TET
Perfect unison C 20/12 : 1 0 : 1 0.00 Play ALL
Name Letter Ratio Ratio Cents Audio TET
12 root of 2 C/D 122 : 1
or 21/12 : 1
1.05946 : 1 100.00 Play 12
Square root of 5/
Half a just M3
... √5 : 2 2.23607 : 2 193.16 Play ...
1st Feigenbaum constant δ ≈ 2φ/ln(2) : 4 4.66920 : 4 267.81 Play ...
Silver ratio δS 1+√2 : 2 2.41421 : 2 325.86 Play ...
Square root of 6/
Half a just P5
... √6 : 2 2.44949 : 2 350.98 Play ...
2nd Feigenbaum constant α ≈ (2φ+1 / ln(2)+1) : 2 2.50291 : 2 388.33 Play ...
Square root of 7/
Half a just H7
... √7 : 2 2.64575 : 2 484.41 Play ...
Euler's constant ... e : 2 2.71828 : 2 531.23 Play ...
Tritone/Half an octave F/G 26/12 : 1
or √2 : 1
1.41421 : 1 600.00 Play all even
Wallis product ... π : 2 3.14159 : 2 781.79 Play ...
Golden ratio φ (1+√5)/2 : 1 1.61803 : 1 833.09 Play ...
Square root of 3/
Half a tritave
... √3 : 1 1.73205 : 1 950.98 Play ...
... ... ... ... ... ... ...
Perfect octave C' 212/12 : 1 2 : 1 1200.00 Play all
octave
based
... ... ... ... ... ... ...
Square root of 5 ... √5 : 1 2.23607 : 1 1393.16 Play
Silver ratio δS 1+√2 : 1 2.41421 : 1 1525.86 Play ...
Square root of 6 ... √6 : 1 2.44949 : 1 1550.98 Play ...
2nd Feigenbaum constant α ≈ 2φ+1 :
ln(2)+1
2.50291 : 1 1588.33 Play ...
Square root of 7 ... √7 : 1 2.64575 : 1 1684.41 Play ...
Euler's constant ... e : 1 2.71828 : 1 1731.23 Play ...
... ... ... ... ... ... ...
Tritave ... 3 : 1 3 : 1 1901.96 Play ...
... ... ... ... ... ... ...
Pi ... π : 1 3.14159 : 1 1981.79 Play ...
... ... ... ... ... ... ...
Two octaves C 4 : 1 4 : 1 2400.00 Play 12
... ... ... ... ... ... ...
1st Feigenbaum constant δ ≈ 2φ/ln(2) : 1 4.66920 : 1 2667.81 Play ...

See also

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