View source for 30afdo

{{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. 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 ==
{| class="wikitable center-all"
! #
! Cents
! Ratio
! Decimal
! Interval name
! Audio
|-
| 0
| 0
| [[1/1]]
| 1.000
| 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
| 266.9
| [[7/6]]
| 1.1667
| subminor third
| [[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
| 498.0
| [[4/3]]
| 1.3333
| just perfect fourth
| [[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
| 702.0
| [[3/2]]
| 1.5000
| just perfect fifth
| [[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
| 884.5
| [[5/3]]
| 1.6667
| just major sixth
| [[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
| 1049.4
| [[11/6]]
| 1.8333
| undecimal neutral seventh
| [[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
| 1200.0
| [[2/1]]
| 2.0000
| perfect octave
| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
|}

== 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