Harmonics 4–8: Difference between revisions
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{{Infobox harmonics|4}} | |||
[[File:4ado scale.wav|thumb]] | [[File:4ado scale.wav|thumb]] | ||
{{Harmonics intro|4}} The notes of this scale create a [[4:5:6:7|harmonic seventh chord]]. | |||
The smallest [[edo]]s that maintain 25% or lower relative error on all intervals of this scale are [[10edo]] and [[15edo]], though they are not very accurate. The next two edos, [[22edo]] and [[31edo]], are the smallest that approximate this scale with appreciable accuracy. | |||
== Intervals == | == Intervals == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |||
! # | ! # | ||
! Cents | ! Cents | ||
! Ratio | ! Ratio | ||
! Decimal | |||
! Interval name | ! Interval name | ||
! Audio | ! Audio | ||
| Line 13: | Line 19: | ||
| 0 | | 0 | ||
| [[1/1]] | | [[1/1]] | ||
| 1.0000 | |||
| perfect unison | | perfect unison | ||
| | | | ||
| Line 19: | Line 26: | ||
| 386.3 | | 386.3 | ||
| [[5/4]] | | [[5/4]] | ||
| 1.2500 | |||
| just major third | | just major third | ||
| [[File:Jid_5_4_pluck_adu_dr220.mp3]] | | [[File:Jid_5_4_pluck_adu_dr220.mp3]] | ||
| Line 25: | Line 33: | ||
| 702.0 | | 702.0 | ||
| [[3/2]] | | [[3/2]] | ||
| 1.5000 | |||
| just perfect fifth | | just perfect fifth | ||
| [[File:Jid_3_2_pluck_adu_dr220.mp3]] | | [[File:Jid_3_2_pluck_adu_dr220.mp3]] | ||
| Line 31: | Line 40: | ||
| 968.8 | | 968.8 | ||
| [[7/4]] | | [[7/4]] | ||
| 1.7500 | |||
| harmonic seventh | | harmonic seventh | ||
| [[File:Jid_7_4_pluck_adu_dr220.mp3]] | | [[File:Jid_7_4_pluck_adu_dr220.mp3]] | ||
| Line 37: | Line 47: | ||
| 1200.0 | | 1200.0 | ||
| [[2/1]] | | [[2/1]] | ||
| 2.0000 | |||
| perfect octave | | perfect octave | ||
| [[File:Jid_2_1_pluck_adu_dr220.mp3]] | | [[File:Jid_2_1_pluck_adu_dr220.mp3]] | ||
|} | |} | ||
{{Navbox harmonics}} | |||
Latest revision as of 23:50, 10 October 2026
| Prime factorization | 22 |
| Fifth | 6/4 (701.955c) |
The harmonics 4–8 (also harmonic series segment 4::8 or harmonic series mode 4) are a scale that consists of harmonics 4 through 8 (4:5:6:7:8) and repeats at the octave. Used as a tuning system, it is also called 4afdo. The notes of this scale create a harmonic seventh chord.
The smallest edos that maintain 25% or lower relative error on all intervals of this scale are 10edo and 15edo, though they are not very accurate. The next two edos, 22edo and 31edo, are the smallest that approximate this scale with appreciable accuracy.
Intervals
| # | Cents | Ratio | Decimal | Interval name | Audio |
|---|---|---|---|---|---|
| 0 | 0 | 1/1 | 1.0000 | perfect unison | |
| 1 | 386.3 | 5/4 | 1.2500 | just major third | |
| 2 | 702.0 | 3/2 | 1.5000 | just perfect fifth | |
| 3 | 968.8 | 7/4 | 1.7500 | harmonic seventh | |
| 4 | 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 |