30afdo: Difference between revisions

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WIP
{{Infobox AFDO|steps=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.
'''30afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''30odo''' ([[otonal division]] of the octave), divides the octave into thirty parts of 1/30 each. It is a superset of [[29afdo]] and a subset of [[31afdo]]. As a scale it may be known as [[Harmonic mode|mode 30 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-30]] scale. Since 30 factors into primes as {{nowrap| 2 × 3 × 5 }}, this afdo contains many common [[5-limit]] intervals above its root and is extremely useful for common tonal harmony.


== Intervals ==
== Intervals ==
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| 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
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| 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
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| 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
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|}
|}


 
== Scales ==
[[Category:ADO]]
* Mushroom: 35/30—40/30—45/30—47/30—60/30
* [[James Wyness]]' "Kai Udan Arum [[pelog]]": 32/30—35/30—40/30—44/30—47/30—54/30—60/30
* ''Loose approximation of [[fluid just intonation]]'': 16/15—17/15—6/5—37/30—4/3—41/30—3/2—8/5—5/3—26/15—9/5—28/15—2/1

Latest revision as of 03:59, 30 July 2025

← 29afdo 30afdo 31afdo →
Prime factorization 2 × 3 × 5
Fifth 45/30 (701.955c)

30afdo (arithmetic frequency division of the octave), or 30odo (otonal division of the octave), divides the octave into thirty parts of 1/30 each. It is a superset of 29afdo and a subset of 31afdo. As a scale it may be known as mode 30 of the harmonic series or the Over-30 scale. Since 30 factors into primes as 2 × 3 × 5, this afdo 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

  • Mushroom: 35/30—40/30—45/30—47/30—60/30
  • James Wyness' "Kai Udan Arum pelog": 32/30—35/30—40/30—44/30—47/30—54/30—60/30
  • Loose approximation of fluid just intonation: 16/15—17/15—6/5—37/30—4/3—41/30—3/2—8/5—5/3—26/15—9/5—28/15—2/1
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