Harmonics 30–60: Difference between revisions
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{{Infobox | {{Infobox harmonics|30}} | ||
{{Harmonics intro|30}} Since 30 factors into primes as {{nowrap| 2 × 3 × 5 }}, this scale contains many common [[5-limit]] intervals above its root and is extremely useful for common tonal harmony. | |||
== Intervals == | == Intervals == | ||
| Line 231: | Line 231: | ||
== Scales == | == Scales == | ||
* | * 30:36:40:45:50:55:60 Baobab{{idiosyncratic}} | ||
* [[James Wyness]]' "Kai Udan Arum [[pelog]]": 32 | * 30:35:40:45:47:60 Mushroom{{idiosyncratic}} | ||
* 30:33:36:40:45:50:55:60 Neutral Melodic Minor{{idiosyncratic}} | |||
* 30:32:35:40:44:47:54:60 [[James Wyness]]' "Kai Udan Arum [[pelog]]" | |||
* 30:32:34:36:37:40:41:45:48:50:52:54:56:60 ''loose approximation of [[fluid just intonation]]'' | |||
{{Navbox harmonics}} | |||
Latest revision as of 00:37, 11 October 2026
| Prime factorization | 2 × 3 × 5 |
| Fifth | 45/30 (701.955c) |
The harmonics 30–60 (also harmonic series segment 30::60 or harmonic series mode 30) are a scale that consists of harmonics 30 through 60 (30:31:…:60) and repeats at the octave. Used as a tuning system, it is also called 30afdo. Since 30 factors into primes as 2 × 3 × 5, this scale contains many common 5-limit intervals above its root and is extremely useful for common tonal harmony.
Intervals
| # | Cents | Ratio | Decimal | Interval name | Audio |
|---|---|---|---|---|---|
| 0 | 0 | 1/1 | 1.000 | perfect unison | |
| 1 | 56.2 | 31/30 | 1.0333 | large tricesimoprimal quartertone | |
| 2 | 111.7 | 16/15 | 1.0667 | classic diatonic semitone | |
| 3 | 165.0 | 11/10 | 1.1000 | undecimal submajor second | |
| 4 | 216.7 | 17/15 | 1.1333 | septendecimal whole tone | |
| 5 | 266.9 | 7/6 | 1.1667 | subminor third | |
| 6 | 315.6 | 6/5 | 1.2000 | just minor third | |
| 7 | 363.1 | 37/30 | 1.2333 | trigintaseptimal submajor third | |
| 8 | 409.2 | 19/15 | 1.2667 | Eratosthenes' major third | |
| 9 | 454.2 | 13/10 | 1.3000 | tridecimal semisixth | |
| 10 | 498.0 | 4/3 | 1.3333 | just perfect fourth | |
| 11 | 540.8 | 41/30 | 1.3667 | quadragesimaunal superfourth | |
| 12 | 582.5 | 7/5 | 1.4000 | small septimal tritone | |
| 13 | 623.25 | 43/30 | 1.4333 | large quadragintatertial tritone | |
| 14 | 663.05 | 22/15 | 1.4667 | undecimal diminished fifth | |
| 15 | 702.0 | 3/2 | 1.5000 | just perfect fifth | |
| 16 | 740.0 | 23/15 | 1.5333 | vicesimotertial ultraminor sixth | File:Jid 23 15 pluck adu dr220.mp3 |
| 17 | 777.2 | 47/30 | 1.5667 | quadragintaseptimal subminor sixth | |
| 18 | 813.7 | 8/5 | 1.6000 | just minor sixth | |
| 19 | 849.4 | 49/30 | 1.6333 | septimal neutral sixth | |
| 20 | 884.5 | 5/3 | 1.6667 | just major sixth | |
| 21 | 918.6 | 17/10 | 1.7000 | septendecimal major sixth | |
| 22 | 952.3 | 26/15 | 1.7333 | tridecimal semitwelfth | |
| 23 | 985.2 | 53/30 | 1.7667 | quinquagintatertial minor seventh | |
| 24 | 1017.6 | 9/5 | 1.8000 | just minor seventh | |
| 25 | 1049.4 | 11/6 | 1.8333 | undecimal neutral seventh | |
| 26 | 1080.6 | 28/15 | 1.8667 | septimal grave major seventh | |
| 27 | 1111.2 | 19/10 | 1.9000 | Eratosthenes' major seventh | |
| 28 | 1141.3 | 29/15 | 1.9333 | undetricesimal supermajor seventh | |
| 29 | 1170.9 | 59/30 | 1.9667 | undexsexagesimal suboctave | |
| 30 | 1200.0 | 2/1 | 2.0000 | perfect octave |
Scales
- 30:36:40:45:50:55:60 Baobab[idiosyncratic term]
- 30:35:40:45:47:60 Mushroom[idiosyncratic term]
- 30:33:36:40:45:50:55:60 Neutral Melodic Minor[idiosyncratic term]
- 30:32:35:40:44:47:54:60 James Wyness' "Kai Udan Arum pelog"
- 30:32:34:36:37:40:41:45:48:50:52:54:56:60 loose approximation of fluid just intonation
| 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 |