Harmonics 13–26
The harmonics 13–26 (also harmonic series segment 13::26 or harmonic series mode 13) are a scale that consists of harmonics 13 through 26 (13:14:…:26) and repeats at the octave. Used as a tuning system, it is also called 13afdo. Due to being odd, it does not contain a perfect fifth above the root.
| Prime factorization | 13 (prime) |
| Dual sharp fifth | 20/13 (745.786c) |
| Dual flat fifth | 19/13 (656.985c) |
Intervals
| # | Cents | Ratio | Decimal | Interval name | Audio |
|---|---|---|---|---|---|
| 0 | 0.00 | 1/1 | 1.0000 | perfect unison | |
| 1 | 128.30 | 14/13 | 1.0769 | tridecimal supraminor second | |
| 2 | 247.74 | 15/13 | 1.1538 | subminor third | |
| 3 | 359.47 | 16/13 | 1.23077 | (greater) tridecimal neutral third | |
| 4 | 464.42 | 17/13 | 1.3077 | septendecimal subfourth | |
| 5 | 563.38 | 18/13 | 1.3846 | tridecimal augmented fourth | |
| 6 | 656.99 | 19/13 | 1.4615 | undevicesimal subfifth | |
| 7 | 745.79 | 20/13 | 1.53846 | tridecimal semitenth | |
| 8 | 830.25 | 21/13 | 1.61539 | tridecimal supraminor sixth | |
| 9 | 910.79 | 22/13 | 1.69231 | tridecimal major sixth | |
| 10 | 987.75 | 23/13 | 1.76923 | vicesimotertial minor seventh | |
| 11 | 1061.43 | 24/13 | 1.84615 | tridecimal neutral seventh | |
| 12 | 1132.09 | 25/13 | 1.92308 | lesser tridecimal diminished octave | |
| 13 | 1200.0 | 2/1 | 2.0000 | perfect octave |
| View • Talk • EditOvertone scales | |
|---|---|
| Small modes | 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 |
| Larger modes | 30 • 32 • 36 • 48 • 60 • 128 |
| Families | /2: 2 • 4 • 8 • 16 • 32 • 128 /3: 3 • 6 • 9 • 12 • 15 • 18 • 21 • 24 /5: 5 • 10 • 15 • 20 • 25 • 30 • 35 • 60 • 80 /7: 7 • 14 • 21 • 28 • 35 • 56 /11: 11 • 22 • 33 /13: 13 • 26 |
| Related | Harmonic series • Subharmonic series • Carlos harmonic scale • Ringer scale • Primodality |