Harmonics 4–8: Difference between revisions
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CompactStar (talk | contribs) Created page with "'''4ado''' is the arithmetic equal division of the octave into four parts of 1/4 each. == Intervals == {| class="wikitable center-all" ! # ! Cents ! Ratio ! Interval..." |
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{{Infobox harmonics|4}} | |||
[[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 | |||
|- | |- | ||
| 0 | | 0 | ||
| 0 | | 0 | ||
| [[1/1]] | | [[1/1]] | ||
| 1.0000 | |||
| perfect unison | | perfect unison | ||
| | |||
|- | |- | ||
| 1 | | 1 | ||
| 386.3 | | 386.3 | ||
| [[5/4]] | | [[5/4]] | ||
| 1.2500 | |||
| just major third | | just major third | ||
| [[File:Jid_5_4_pluck_adu_dr220.mp3]] | |||
|- | |- | ||
| 2 | | 2 | ||
| | | 702.0 | ||
| [[ | | [[3/2]] | ||
| | | 1.5000 | ||
| just perfect fifth | |||
| [[File:Jid_3_2_pluck_adu_dr220.mp3]] | |||
|- | |||
| 3 | |||
| 968.8 | |||
| [[7/4]] | |||
| 1.7500 | |||
| harmonic seventh | |||
| [[File:Jid_7_4_pluck_adu_dr220.mp3]] | |||
|- | |||
| 4 | |||
| 1200.0 | |||
| [[2/1]] | |||
| 2.0000 | |||
| perfect octave | |||
| [[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 harmonic segment 4::8 (also harmonics 4–8) consists of harmonics 4 through 8 (4:5:6:7:8) and spans one octave above the root. Used as a scale, it is also called mode 4 of the harmonic series. 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 |