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