Subharmonics 18–36: Difference between revisions

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~~'''18ifdo''' ([[IFDO~~|inverse-arithmetic frequency division of the octave]]), or '''18udo''' ([[utonal division]] of the octave) would divide the [[octave]] into eighteen inverse-arithmetically equal parts. It is a superset of [[17ifdo]] and a subset of [[19ifdo]], its inverse is [[18afdo]]. As a [[scale]] it may also be known as mode 18 ~~of the subharmonic series or the Under-18 scale.~~

Directly above its root it contains copies of [[~~6ifdo~~]] and [[~~9ifdo~~]], making it a comprehensive scale for under-3 harmony, the [[utonal]] version of over-3 [[primodality]].

Directly above its root it contains copies of [[Subharmonics 6–12|subharmonics 6–12]] and [[Subharmonics 9–18|subharmonics 9–18]], making it a comprehensive scale for under-3 harmony, the [[utonal]] version of over-3 [[primodality]].

Above its root it contains a fairly even mix of [[5-limit]] intervals familiar to [[12edo]] listeners, and higher limit [[xenharmonic]] sonorities.

Coincidentally, ~~18ifdo~~ has the property that its first step is similar in size to a [[24edo]]-step, and its 18th step is similar in size to a [[12edo]]-step.

Coincidentally, this scale has the property that its first step is similar in size to a [[24edo]]-step, and its 18th step is similar in size to a [[12edo]]-step.

The first serious attempt made at documenting and using ~~18ifdo~~ was made by the [[Monthly Tunings]] Facebook group (a smaller group within the larger [[Xenharmonic Alliance]]). They voted it as the monthly tuning for September 2026, and made the first attempts to explore this tuning.

The first serious attempt made at documenting and using this scale was made by the [[Monthly Tunings]] Facebook group (a smaller group within the larger [[Xenharmonic Alliance]]). They voted it as the monthly tuning for September 2026, and made the first attempts to explore this tuning.

== Intervals ==

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; [[Claudi Meneghin]]

* [https://www.youtube.com/shorts/e0da1CkFNZI ''A 2-in-1 canon in F for organ (short version), in 18-IFDO, for baroque oboe and bassoon''] (2026)

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-{{Infobox IFDO|steps=18}}
+{{Infobox subharmonics|18}}
-'''18ifdo''' ([[IFDO|inverse-arithmetic frequency division of the octave]]), or '''18udo''' ([[utonal division]] of the octave) would divide the [[octave]] into eighteen inverse-arithmetically equal parts. It is a superset of [[17ifdo]] and a subset of [[19ifdo]], its inverse is [[18afdo]]. As a [[scale]] it may also be known as mode 18 of the subharmonic series or the Under-18 scale.
+{{Subharmonics intro|18}}
-Directly above its root it contains copies of [[6ifdo]] and [[9ifdo]], making it a comprehensive scale for under-3 harmony, the [[utonal]] version of over-3 [[primodality]].
+Directly above its root it contains copies of [[Subharmonics 6–12|subharmonics 6–12]] and [[Subharmonics 9–18|subharmonics 9–18]], making it a comprehensive scale for under-3 harmony, the [[utonal]] version of over-3 [[primodality]].
 Above its root it contains a fairly even mix of [[5-limit]] intervals familiar to [[12edo]] listeners, and higher limit [[xenharmonic]] sonorities.
-Coincidentally, 18ifdo has the property that its first step is similar in size to a [[24edo]]-step, and its 18th step is similar in size to a [[12edo]]-step.
+Coincidentally, this scale has the property that its first step is similar in size to a [[24edo]]-step, and its 18th step is similar in size to a [[12edo]]-step.
-The first serious attempt made at documenting and using 18ifdo was made by the [[Monthly Tunings]] Facebook group  (a smaller group within the larger [[Xenharmonic Alliance]]). They voted it as the monthly tuning for September 2026, and made the first attempts to explore this tuning.
+The first serious attempt made at documenting and using this scale was made by the [[Monthly Tunings]] Facebook group  (a smaller group within the larger [[Xenharmonic Alliance]]). They voted it as the monthly tuning for September 2026, and made the first attempts to explore this tuning.
 == Intervals ==
@@ Line 243: / Line 243: @@
 ; [[Claudi Meneghin]]
 * [https://www.youtube.com/shorts/e0da1CkFNZI ''A 2-in-1 canon in F for organ (short version), in 18-IFDO, for baroque oboe and bassoon''] (2026)
+{{Navbox subharmonics}}