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{{Infobox AFDO|steps=30}}
{{Infobox AFDO|steps=30}}


'''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. 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. Due to 30 being 2 × 3 × 5, this AFDO contains many 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 ==
Line 19: Line 19:
|
|
|-
|-
|1
| 1
|56.2
| 56.2
|[[31/30]]
| [[31/30]]
|1.0333
| 1.0333
|large tricesimoprimal quartertone
| large tricesimoprimal quartertone
|[[File:Ji-31-30-csound-foscil-220hz.mp3]]
| [[File:Ji-31-30-csound-foscil-220hz.mp3]]
|-
|-
|2
| 2
|111.7
| 111.7
|[[16/15]]
| [[16/15]]
|1.0667
| 1.0667
|classic diatonic semitone
| classic diatonic semitone
|[[File:Jid_16_15_pluck_adu_dr220.mp3]]
| [[File:Jid_16_15_pluck_adu_dr220.mp3]]
|-
|-
|3
| 3
|165.0
| 165.0
|[[11/10]]
| [[11/10]]
|1.1000
| 1.1000
|undecimal submajor second
| undecimal submajor second
|[[File:Jid_11_10_pluck_adu_dr220.mp3]]
| [[File:Jid_11_10_pluck_adu_dr220.mp3]]
|-
|-
|4
| 4
|216.7
| 216.7
|[[17/15]]
| [[17/15]]
|1.1333
| 1.1333
|septendecimal whole tone
| septendecimal whole tone
|[[File:Jid_17_15_pluck_adu_dr220.mp3]]
| [[File:Jid_17_15_pluck_adu_dr220.mp3]]
|-
|-
| 5
| 5
Line 54: Line 54:
| [[File:Jid_7_6_pluck_adu_dr220.mp3]]
| [[File:Jid_7_6_pluck_adu_dr220.mp3]]
|-
|-
|6
| 6
|315.6
| 315.6
|[[6/5]]
| [[6/5]]
|1.2000
| 1.2000
|just minor third
| just minor third
|[[File:Jid_6_5_pluck_adu_dr220.mp3]]
| [[File:Jid_6_5_pluck_adu_dr220.mp3]]
|-
|-
|7
| 7
|363.1
| 363.1
|37/30
| 37/30
|1.2333
| 1.2333
|septentrigesimal submajor third
| trigintaseptimal submajor third
|
|  
|-
|-
|8
| 8
|409.2
| 409.2
|[[19/15]]
| [[19/15]]
|1.2667
| 1.2667
|Eratosthenes' major third
| Eratosthenes' major third
|[[File:Jid_19_15_pluck_adu_dr220.mp3]]
| [[File:Jid_19_15_pluck_adu_dr220.mp3]]
|-
|-
|9
| 9
|454.2
| 454.2
|[[13/10]]
| [[13/10]]
|1.3000
| 1.3000
|tridecimal semisixth
| tridecimal semisixth
|[[File:Jid_13_10_pluck_adu_dr220.mp3]]
| [[File:Jid_13_10_pluck_adu_dr220.mp3]]
|-
|-
| 10
| 10
| 498.0
| 498.0
|[[4/3]]
| [[4/3]]
| 1.3333
| 1.3333
| just perfect fourth
| just perfect fourth
|[[File:Jid_4_3_pluck_adu_dr220.mp3]]
| [[File:Jid_4_3_pluck_adu_dr220.mp3]]
|-
|-
|11
| 11
|540.8
| 540.8
|41/30
| 41/30
|1.3667
| 1.3667
|unquadragesimal superfourth
| quadragesimaunal superfourth
|
|  
|-
|-
|12
| 12
|582.5
| 582.5
|[[7/5]]
| [[7/5]]
|1.4000
| 1.4000
|small septimal tritone
| small septimal tritone
|[[File:Jid_7_5_pluck_adu_dr220.mp3]]
| [[File:Jid_7_5_pluck_adu_dr220.mp3]]
|-
|-
|13
| 13
|623.25
| 623.25
|43/30
| 43/30
|1.4333
| 1.4333
|large trequadragesimal tritone
| large quadragintatertial tritone
|
|
|-
|-
|14
| 14
|663.05
| 663.05
|[[22/15]]
| [[22/15]]
|1.4667
| 1.4667
|undecimal diminished fifth
| undecimal diminished fifth
|[[File:Jid_22_15_pluck_adu_dr220.mp3]]
| [[File:Jid_22_15_pluck_adu_dr220.mp3]]
|-
|-
| 15
| 15
| 702.0
| 702.0
|[[3/2]]
| [[3/2]]
| 1.5000
| 1.5000
| just perfect fifth
| just perfect fifth
|[[File:Jid_3_2_pluck_adu_dr220.mp3]]
| [[File:Jid_3_2_pluck_adu_dr220.mp3]]
|-
|-
|16
| 16
|740.0
| 740.0
|[[23/15]]
| [[23/15]]
|1.5333
| 1.5333
|vicesimotertial ultraminor sixth
| vicesimotertial ultraminor sixth
|[[File:Jid_23_15_pluck_adu_dr220.mp3]]
| [[File:Jid_23_15_pluck_adu_dr220.mp3]]
|-
|-
|17
| 17
|777.2
| 777.2
|47/30
| 47/30
|1.5667
| 1.5667
|septenquadragesimal subminor sixth
| quadragintaseptimal subminor sixth
|
|
|-
|-
|18
| 18
|813.7
| 813.7
|8/5
| 8/5
|1.6000
| 1.6000
|just minor sixth
| just minor sixth
|[[File:Jid_8_5_pluck_adu_dr220.mp3]]
| [[File:Jid_8_5_pluck_adu_dr220.mp3]]
|-
|-
|19
| 19
|849.4
| 849.4
|49/30
| 49/30
|1.6333
| 1.6333
|septimal neutral sixth
| septimal neutral sixth
|
|  
|-
|-
| 20
| 20
| 884.5
| 884.5
|[[5/3]]
| [[5/3]]
| 1.6667
| 1.6667
| just major sixth
| just major sixth
|[[File:Jid_5_3_pluck_adu_dr220.mp3]]
| [[File:Jid_5_3_pluck_adu_dr220.mp3]]
|-
|-
|21
| 21
|918.6
| 918.6
|[[17/10]]
| [[17/10]]
|1.7000
| 1.7000
|septendecimal major sixth
| septendecimal major sixth
|[[File:Jid_17_10_pluck_adu_dr220.mp3]]
| [[File:Jid_17_10_pluck_adu_dr220.mp3]]
|-
|-
|22
| 22
|952.3
| 952.3
|[[26/15]]
| [[26/15]]
|1.7333
| 1.7333
|tridecimal semitwelfth
| tridecimal semitwelfth
|[[File:Jid_26_15_pluck_adu_dr220.mp3]]
| [[File:Jid_26_15_pluck_adu_dr220.mp3]]
|-
|-
|23
| 23
|985.2
| 985.2
|53/30
| 53/30
|1.7667
| 1.7667
|trequinquagesimal minor seventh
| quinquagintatertial minor seventh
|
|  
|-
|-
|24
| 24
|1017.6
| 1017.6
|[[9/5]]
| [[9/5]]
|1.8000
| 1.8000
|just minor seventh
| just minor seventh
|[[File:Jid_9_5_pluck_adu_dr220.mp3]]
| [[File:Jid_9_5_pluck_adu_dr220.mp3]]
|-
|-
| 25
| 25
| 1049.4
| 1049.4
|[[11/6]]
| [[11/6]]
| 1.8333
| 1.8333
| undecimal neutral seventh
| undecimal neutral seventh
|[[File:Jid_11_6_pluck_adu_dr220.mp3]]
| [[File:Jid_11_6_pluck_adu_dr220.mp3]]
|-
|-
|26
| 26
|1080.6
| 1080.6
|[[28/15]]
| [[28/15]]
|1.8667
| 1.8667
|septimal grave major seventh
| septimal grave major seventh
|[[File:Jid_28_15_pluck_adu_dr220.mp3]]
| [[File:Jid_28_15_pluck_adu_dr220.mp3]]
|-
|-
|27
| 27
|1111.2
| 1111.2
|[[19/10]]
| [[19/10]]
|1.9000
| 1.9000
|Eratosthenes' major seventh
| Eratosthenes' major seventh
|[[File:Jid_19_10_pluck_adu_dr220.mp3]]
| [[File:Jid_19_10_pluck_adu_dr220.mp3]]
|-
|-
|28
| 28
|1141.3
| 1141.3
|29/15
| 29/15
|1.9333
| 1.9333
|novemvigesiaml supermajor seventh
| undetricesimal supermajor seventh
|
|  
|-
|-
|29
| 29
|1170.9
| 1170.9
|59/30
| 59/30
|1.9667
| 1.9667
|novemquinquagesiaml suboctave
| undexsexagesimal suboctave
|
|  
|-
|-
| 30
| 30
| 1200.0
| 1200.0
|[[2/1]]
| [[2/1]]
| 2.0000
| 2.0000
| perfect octave
| perfect octave
|[[File:Jid_2_1_pluck_adu_dr220.mp3]]
| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
|}
|}


 
== Scales ==
[[Category:AFDO]]
* 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
Retrieved from "https://en.xen.wiki/w/30afdo"