Harmonics 13–26: Difference between revisions
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Created page with "'''13afdo''' (arithmetic frequency division of the octave), or '''13odo''' (otonal division of the octave), divides the octave into thirteen parts of 1/13 each. A..." Tags: Visual edit Mobile edit Mobile web edit |
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{{Infobox harmonics|13}} | |||
{{Harmonics intro|13}} Due to being odd, it does not contain a perfect fifth above the root. | |||
== Intervals == | |||
{| class="wikitable center-all" | |||
! # | |||
! 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 | |||
| [[File:Jid_14_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 2 | |||
| 247.74 | |||
| [[15/13]] | |||
| 1.1538 | |||
| subminor third | |||
| [[File:Jid_15_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 3 | |||
| 359.47 | |||
| [[16/13]] | |||
| 1.23077 | |||
| (greater) tridecimal neutral third | |||
| [[File:Jid_16_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 4 | |||
| 464.42 | |||
| [[17/13]] | |||
| 1.3077 | |||
| septendecimal subfourth | |||
| [[File:Jid_17_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 5 | |||
| 563.38 | |||
| [[18/13]] | |||
| 1.3846 | |||
| tridecimal augmented fourth | |||
| [[File:Jid_18_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 6 | |||
| 656.99 | |||
| [[19/13]] | |||
| 1.4615 | |||
| undevicesimal subfifth | |||
| [[File:Jid_19_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 7 | |||
| 745.79 | |||
| [[20/13]] | |||
| 1.53846 | |||
| tridecimal semitenth | |||
| [[File:Jid_20_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 8 | |||
| 830.25 | |||
| [[21/13]] | |||
| 1.61539 | |||
| tridecimal supraminor sixth | |||
| [[File:ji-21-13-csound-foscil-220hz.mp3]] | |||
|- | |||
| 9 | |||
| 910.79 | |||
| [[22/13]] | |||
| 1.69231 | |||
| tridecimal major sixth | |||
| [[File:Jid_22_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 10 | |||
| 987.75 | |||
| [[23/13]] | |||
| 1.76923 | |||
| vicesimotertial minor seventh | |||
| [[File:Jid_23_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 11 | |||
| 1061.43 | |||
| [[24/13]] | |||
| 1.84615 | |||
| tridecimal neutral seventh | |||
| [[File:Jid_24_13_pluck_adu_dr220.mp3]] | |||
|- | |||
| 12 | |||
| 1132.09 | |||
| [[25/13]] | |||
| 1.92308 | |||
| lesser tridecimal diminished octave | |||
| [[File:Ji-25-13-csound-foscil-220hz.mp3]] | |||
|- | |||
| 13 | |||
| 1200.0 | |||
| [[2/1]] | |||
| 2.0000 | |||
| perfect octave | |||
| [[File:Jid_2_1_pluck_adu_dr220.mp3]] | |||
|} | |||
{{Navbox harmonics}} | |||
Latest revision as of 00:08, 11 October 2026
| Prime factorization | 13 (prime) |
| Dual sharp fifth | 20/13 (745.786c) |
| Dual flat fifth | 19/13 (656.985c) |
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.
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 |