Harmonics 15–30: Difference between revisions
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{{Infobox | {{Infobox harmonics|15}} | ||
{{Harmonics intro|15}} | |||
== Intervals == | |||
{| class="wikitable center-all" | |||
! # | |||
! Cents | |||
! Ratio | |||
! Decimal | |||
! Interval name | |||
! Audio | |||
|- | |||
| 0 | |||
| 0.00 | |||
| [[1/1]] | |||
| 1.0000 | |||
| perfect unison | |||
| | |||
|- | |||
| 1 | |||
| 111.73 | |||
| [[16/15]] | |||
| 1.0667 | |||
| just diatonic semitone | |||
| [[File:Jid_16_15_pluck_adu_dr220.mp3]] | |||
|- | |||
| 2 | |||
| 216.69 | |||
| [[17/15]] | |||
| 1.1333 | |||
| septendecimal whole tone | |||
| [[File:Jid_17_15_pluck_adu_dr220.mp3]] | |||
|- | |||
| 3 | |||
| 315.64 | |||
| [[6/5]] | |||
| 1.2000 | |||
| just minor third | |||
| [[File:Jid_6_5_pluck_adu_dr220.mp3]] | |||
|- | |||
| 4 | |||
| 409.24 | |||
| [[19/15]] | |||
| 1.2667 | |||
| large undevicesimal major third | |||
| [[File:Jid_19_15_pluck_adu_dr220.mp3]] | |||
|- | |||
| 5 | |||
| 498.04 | |||
| [[4/3]] | |||
| 1.3333 | |||
| just perfect fourth | |||
| [[File:Jid_4_3_pluck_adu_dr220.mp3]] | |||
|- | |||
| 6 | |||
| 582.51 | |||
| [[7/5]] | |||
| 1.4000 | |||
| narrow tritone | |||
| [[File:Jid_7_5_pluck_adu_dr220.mp3]] | |||
|- | |||
| 7 | |||
| 663.05 | |||
| [[22/15]] | |||
| 1.4667 | |||
| undecimal diminished fifth | |||
| [[File:Jid_22_15_pluck_adu_dr220.mp3]] | |||
|- | |||
| 8 | |||
| 740.01 | |||
| [[23/15]] | |||
| 1.5333 | |||
| vicesimotertial ultraminor sixth | |||
| [[File:Ji-23-15-csound-foscil-220hz.mp3]] | |||
|- | |||
| 9 | |||
| 813.68 | |||
| [[8/5]] | |||
| 1.6000 | |||
| just minor sixth | |||
| [[File:Jid_8_5_pluck_adu_dr220.mp3]] | |||
|- | |||
| 10 | |||
| 884.36 | |||
| [[5/3]] | |||
| 1.6667 | |||
| just major sixth | |||
| [[File:Jid_5_3_pluck_adu_dr220.mp3]] | |||
|- | |||
| 11 | |||
| 952.26 | |||
| [[26/15]] | |||
| 1.7333 | |||
| tridecimal semitwelfth | |||
| [[File:Jid_26_15_pluck_adu_dr220.mp3]] | |||
|- | |||
| 12 | |||
| 1017.60 | |||
| [[9/5]] | |||
| 1.8000 | |||
| just minor seventh | |||
| [[File:Jid_9_5_pluck_adu_dr220.mp3]] | |||
|- | |||
| 13 | |||
| 1080.55 | |||
| [[28/15]] | |||
| 1.8667 | |||
| septimal grave major seventh | |||
| [[File:Jid_28_15_pluck_adu_dr220.mp3]] | |||
|- | |||
| 14 | |||
| 1141.31 | |||
| 29/15 | |||
| 1.9333 | |||
| | |||
| | |||
|- | |||
| 15 | |||
| 1200.00 | |||
| [[2/1]] | |||
| 2.0000 | |||
| perfect octave | |||
| [[File:Jid_2_1_pluck_adu_dr220.mp3]] | |||
|} | |||
{{Navbox harmonics}} | |||
Latest revision as of 00:09, 11 October 2026
| Prime factorization | 3 × 5 |
| Dual sharp fifth | 23/15 (740.006c) |
| Dual flat fifth | 22/15 (663.049c) |
The harmonics 15–30 (also harmonic series segment 15::30 or harmonic series mode 15) are a scale that consists of harmonics 15 through 30 (15:16:…:30) and repeats at the octave. Used as a tuning system, it is also called 15afdo.
Intervals
| # | Cents | Ratio | Decimal | Interval name | Audio |
|---|---|---|---|---|---|
| 0 | 0.00 | 1/1 | 1.0000 | perfect unison | |
| 1 | 111.73 | 16/15 | 1.0667 | just diatonic semitone | |
| 2 | 216.69 | 17/15 | 1.1333 | septendecimal whole tone | |
| 3 | 315.64 | 6/5 | 1.2000 | just minor third | |
| 4 | 409.24 | 19/15 | 1.2667 | large undevicesimal major third | |
| 5 | 498.04 | 4/3 | 1.3333 | just perfect fourth | |
| 6 | 582.51 | 7/5 | 1.4000 | narrow tritone | |
| 7 | 663.05 | 22/15 | 1.4667 | undecimal diminished fifth | |
| 8 | 740.01 | 23/15 | 1.5333 | vicesimotertial ultraminor sixth | |
| 9 | 813.68 | 8/5 | 1.6000 | just minor sixth | |
| 10 | 884.36 | 5/3 | 1.6667 | just major sixth | |
| 11 | 952.26 | 26/15 | 1.7333 | tridecimal semitwelfth | |
| 12 | 1017.60 | 9/5 | 1.8000 | just minor seventh | |
| 13 | 1080.55 | 28/15 | 1.8667 | septimal grave major seventh | |
| 14 | 1141.31 | 29/15 | 1.9333 | ||
| 15 | 1200.00 | 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 |