Harmonics 30–60: Difference between revisions

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WIP
{{Infobox harmonics|30}}
{{Infobox ADO|steps=30}}
 
'''30ado''' is the [[ADO|arithmetic equal division of the octave]] into thirty parts of 1/30 each. Due to 30 being 2*3*5, this ADO contains most common 5-limit intervals and is extremely useful.
{{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 18: Line 18:
| perfect unison
| perfect unison
|
|
|-
| 1
| 56.2
| [[31/30]]
| 1.0333
| large tricesimoprimal quartertone
| [[File:Ji-31-30-csound-foscil-220hz.mp3]]
|-
| 2
| 111.7
| [[16/15]]
| 1.0667
| classic diatonic semitone
| [[File:Jid_16_15_pluck_adu_dr220.mp3]]
|-
| 3
| 165.0
| [[11/10]]
| 1.1000
| undecimal submajor second
| [[File:Jid_11_10_pluck_adu_dr220.mp3]]
|-
| 4
| 216.7
| [[17/15]]
| 1.1333
| septendecimal whole tone
| [[File:Jid_17_15_pluck_adu_dr220.mp3]]
|-
|-
| 5
| 5
Line 25: Line 53:
| subminor third
| subminor third
| [[File:Jid_7_6_pluck_adu_dr220.mp3]]
| [[File:Jid_7_6_pluck_adu_dr220.mp3]]
|-
| 6
| 315.6
| [[6/5]]
| 1.2000
| just minor third
| [[File:Jid_6_5_pluck_adu_dr220.mp3]]
|-
| 7
| 363.1
| 37/30
| 1.2333
| trigintaseptimal submajor third
|
|-
| 8
| 409.2
| [[19/15]]
| 1.2667
| Eratosthenes' major third
| [[File:Jid_19_15_pluck_adu_dr220.mp3]]
|-
| 9
| 454.2
| [[13/10]]
| 1.3000
| tridecimal semisixth
| [[File:Jid_13_10_pluck_adu_dr220.mp3]]
|-
|-
| 10
| 10
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| just perfect fourth
| just perfect fourth
| [[File:Jid_4_3_pluck_adu_dr220.mp3]]
| [[File:Jid_4_3_pluck_adu_dr220.mp3]]
|-
| 11
| 540.8
| 41/30
| 1.3667
| quadragesimaunal superfourth
|
|-
| 12
| 582.5
| [[7/5]]
| 1.4000
| small septimal tritone
| [[File:Jid_7_5_pluck_adu_dr220.mp3]]
|-
| 13
| 623.25
| 43/30
| 1.4333
| large quadragintatertial tritone
|
|-
| 14
| 663.05
| [[22/15]]
| 1.4667
| undecimal diminished fifth
| [[File:Jid_22_15_pluck_adu_dr220.mp3]]
|-
|-
| 15
| 15
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| just perfect fifth
| just perfect fifth
| [[File:Jid_3_2_pluck_adu_dr220.mp3]]
| [[File:Jid_3_2_pluck_adu_dr220.mp3]]
|-
| 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
| [[File:Jid_8_5_pluck_adu_dr220.mp3]]
|-
| 19
| 849.4
| 49/30
| 1.6333
| septimal neutral sixth
|
|-
|-
| 20
| 20
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| [[5/3]]
| [[5/3]]
| 1.6667
| 1.6667
| just minor sixth
| just major sixth
| [[File:Jid_5_3_pluck_adu_dr220.mp3]]
| [[File:Jid_5_3_pluck_adu_dr220.mp3]]
|-
| 21
| 918.6
| [[17/10]]
| 1.7000
| septendecimal major sixth
| [[File:Jid_17_10_pluck_adu_dr220.mp3]]
|-
| 22
| 952.3
| [[26/15]]
| 1.7333
| tridecimal semitwelfth
| [[File:Jid_26_15_pluck_adu_dr220.mp3]]
|-
| 23
| 985.2
| 53/30
| 1.7667
| quinquagintatertial minor seventh
|
|-
| 24
| 1017.6
| [[9/5]]
| 1.8000
| just minor seventh
| [[File:Jid_9_5_pluck_adu_dr220.mp3]]
|-
|-
| 25
| 25
Line 53: Line 193:
| undecimal neutral seventh
| undecimal neutral seventh
| [[File:Jid_11_6_pluck_adu_dr220.mp3]]
| [[File:Jid_11_6_pluck_adu_dr220.mp3]]
|-
| 26
| 1080.6
| [[28/15]]
| 1.8667
| septimal grave major seventh
| [[File:Jid_28_15_pluck_adu_dr220.mp3]]
|-
| 27
| 1111.2
| [[19/10]]
| 1.9000
| Eratosthenes' major seventh
| [[File:Jid_19_10_pluck_adu_dr220.mp3]]
|-
| 28
| 1141.3
| 29/15
| 1.9333
| undetricesimal supermajor seventh
|
|-
| 29
| 1170.9
| 59/30
| 1.9667
| undexsexagesimal suboctave
|
|-
|-
| 30
| 30
Line 62: Line 230:
|}
|}


== Scales ==
* 30:36:40:45:50:55:60 Baobab{{idiosyncratic}}
* 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]]''


[[Category:ADO]]
{{Navbox harmonics}}

Latest revision as of 00:37, 11 October 2026

Harmonics 30–60
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

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
Retrieved from "https://en.xen.wiki/index.php?title=Harmonics_30–60&oldid=239231"