Harmonics 14–28: Difference between revisions
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{{Infobox | {{Infobox harmonics|14}} | ||
==Theory== | {{Harmonics intro|14}} | ||
The esoteric [[Factor 9 grid]] scale is a mode of | |||
== | == Theory == | ||
The esoteric [[Factor 9 grid]] scale is a mode of this scale starting on the 11th step from the tonic, of which 12 or 13 notes were conveniently selected for "A = 432 Hz" conspiracy purposes. It contains [[supraminor]] and [[supermajor]] triads above the root. | |||
== Intervals == | |||
{| class="wikitable center-all" | |||
! # | |||
! Cents | |||
! Ratio | |||
! Decimal | |||
! Interval name | |||
! Audio | |||
|- | |||
| 0 | |||
| 0.0 | |||
| [[1/1]] | |||
| 1.0000 | |||
| perfect unison | |||
| | |||
|- | |||
| 1 | |||
| 119.4 | |||
| [[15/14]] | |||
| 1.0714 | |||
| septimal diatonic semitone | |||
| [[File:Jid_15_14_pluck_adu_dr220.mp3]] | |||
|- | |||
| 2 | |||
| 231.2 | |||
| [[8/7]] | |||
| 1.1429 | |||
| supermajor second | |||
| [[File:Jid_8_7_pluck_adu_dr220.mp3]] | |||
|- | |||
| 3 | |||
| 336.1 | |||
| [[17/14]] | |||
| 1.2149 | |||
| septendecimal supraminor third | |||
| [[File:Jid_17_14_pluck_adu_dr220.mp3]] | |||
|- | |||
| 4 | |||
| 435.1 | |||
| [[9/7]] | |||
| 1.2857 | |||
| supermajor third | |||
| [[File:Jid_9_7_pluck_adu_dr220.mp3]] | |||
|- | |||
| 5 | |||
| 528.7 | |||
| [[19/14]] | |||
| 1.3571 | |||
| hendrix fourth | |||
| [[File:Jid_19_14_pluck_adu_dr220.mp3]] | |||
|- | |||
| 6 | |||
| 617.5 | |||
| [[10/7]] | |||
| 1.4286 | |||
| high tritone | |||
| [[File:Jid_10_7_pluck_adu_dr220.mp3]] | |||
|- | |||
| 7 | |||
| 702.0 | |||
| [[3/2]] | |||
| 1.5000 | |||
| just perfect fifth | |||
| [[File:Jid_3_2_pluck_adu_dr220.mp3]] | |||
|- | |||
| 8 | |||
| 782.4 | |||
| [[11/7]] | |||
| 1.5714 | |||
| undecimal minor sixth | |||
| [[File:Jid_11_7_pluck_adu_dr220.mp3]] | |||
|- | |||
| 9 | |||
| 859.4 | |||
| [[23/14]] | |||
| 1.6428 | |||
| vicesimotertial neutral sixth | |||
| [[File:Jid_23_14_pluck_adu_dr220.mp3]] | |||
|- | |||
| 10 | |||
| 933.1 | |||
| [[12/7]] | |||
| 1.7143 | |||
| supermajor sixth | |||
| [[File:Jid_12_7_pluck_adu_dr220.mp3]] | |||
|- | |||
| 11 | |||
| 1003.8 | |||
| [[25/14]] | |||
| 1.7857 | |||
| (septimal) middle minor seventh | |||
| [[File:Jid_25_14_pluck_adu_dr220.mp3]] | |||
|- | |||
| 12 | |||
| 1071.7 | |||
| [[13/7]] | |||
| 1.8571 | |||
| tridecimal submajor seventh | |||
| [[File:Jid_13_7_pluck_adu_dr220.mp3]] | |||
|- | |||
| 13 | |||
| 1137.0 | |||
| [[27/14]] | |||
| 1.9286 | |||
| septimal major seventh | |||
| [[File:Jid_27_14_pluck_adu_dr220.mp3]] | |||
|- | |||
| 14 | |||
| 1200.0 | |||
| [[2/1]] | |||
| 2.0000 | |||
| perfect octave | |||
| [[File:Jid_2_1_pluck_adu_dr220.mp3]] | |||
|} | |||
Factor 9 grid can be obtained if the scale is rotated to start at 12/7 instead of 1/1. | Factor 9 grid can be obtained if the scale is rotated to start at 12/7 instead of 1/1. | ||
== Scales == | |||
* 14:15:18:19:21:22:26:28 Apex{{idiosyncratic}} | |||
* 14:16:18:21:24:28 ''septimal minor pentatonic'' | |||
{{Navbox harmonics}} | |||
Latest revision as of 00:08, 11 October 2026
| Prime factorization | 2 × 7 |
| Fifth | 21/14 (701.955c) |
The harmonics 14–28 (also harmonic series segment 14::28 or harmonic series mode 14) are a scale that consists of harmonics 14 through 28 (14:15:…:28) and repeats at the octave. Used as a tuning system, it is also called 14afdo.
Theory
The esoteric Factor 9 grid scale is a mode of this scale starting on the 11th step from the tonic, of which 12 or 13 notes were conveniently selected for "A = 432 Hz" conspiracy purposes. It contains supraminor and supermajor triads above the root.
Intervals
| # | Cents | Ratio | Decimal | Interval name | Audio |
|---|---|---|---|---|---|
| 0 | 0.0 | 1/1 | 1.0000 | perfect unison | |
| 1 | 119.4 | 15/14 | 1.0714 | septimal diatonic semitone | |
| 2 | 231.2 | 8/7 | 1.1429 | supermajor second | |
| 3 | 336.1 | 17/14 | 1.2149 | septendecimal supraminor third | |
| 4 | 435.1 | 9/7 | 1.2857 | supermajor third | |
| 5 | 528.7 | 19/14 | 1.3571 | hendrix fourth | |
| 6 | 617.5 | 10/7 | 1.4286 | high tritone | |
| 7 | 702.0 | 3/2 | 1.5000 | just perfect fifth | |
| 8 | 782.4 | 11/7 | 1.5714 | undecimal minor sixth | |
| 9 | 859.4 | 23/14 | 1.6428 | vicesimotertial neutral sixth | |
| 10 | 933.1 | 12/7 | 1.7143 | supermajor sixth | |
| 11 | 1003.8 | 25/14 | 1.7857 | (septimal) middle minor seventh | |
| 12 | 1071.7 | 13/7 | 1.8571 | tridecimal submajor seventh | |
| 13 | 1137.0 | 27/14 | 1.9286 | septimal major seventh | |
| 14 | 1200.0 | 2/1 | 2.0000 | perfect octave |
Factor 9 grid can be obtained if the scale is rotated to start at 12/7 instead of 1/1.
Scales
- 14:15:18:19:21:22:26:28 Apex[idiosyncratic term]
- 14:16:18:21:24:28 septimal minor pentatonic
| 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 |