3ifdo: Difference between revisions
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+subsets and supersets and clarify |
Note that this is the first nontrivial ifdo |
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{{Infobox IFDO|steps=3}} | {{Infobox IFDO|steps=3}} | ||
'''3ifdo''' ([[IFDO|inverse-arithmetic frequency division of the octave]]), or '''3-UDO''' ([[utonal division]] of the octave), if the attempt is made to use it as an actual [[tuning system]], would divide the [[octave]] into three inverse-arithmetically equal parts. It is a superset of 2ifdo (equivalent to [[2afdo]]) and a subset of [[4ifdo]]. As a [[scale]] it may also be known as mode 3 of the subharmonic series or the Under-3 scale. The notes of this IFDO form a [[just minor triad]] in root position. | '''3ifdo''' ([[IFDO|inverse-arithmetic frequency division of the octave]]), or '''3-UDO''' ([[utonal division]] of the octave), if the attempt is made to use it as an actual [[tuning system]], would divide the [[octave]] into three inverse-arithmetically equal parts. It is a superset of 2ifdo (equivalent to [[2afdo]]) and a subset of [[4ifdo]]. 3ifdo is the first nontrivial ifdo since it is the first ifdo to demonstrate [[chirality]]. Its inverse is [[3afdo]]. As a [[scale]] it may also be known as mode 3 of the subharmonic series or the Under-3 scale. The notes of this IFDO form a [[just minor triad]] in root position. | ||
== Intervals == | == Intervals == | ||
Revision as of 12:35, 8 January 2025
| ← 2ifdo 3ifdo 4ifdo → | |
|---|---|
| Prime factors | 3 |
| Fifth | 6 / 4 (701.9 cents) |
3ifdo (inverse-arithmetic frequency division of the octave), or 3-UDO (utonal division of the octave), if the attempt is made to use it as an actual tuning system, would divide the octave into three inverse-arithmetically equal parts. It is a superset of 2ifdo (equivalent to 2afdo) and a subset of 4ifdo. 3ifdo is the first nontrivial ifdo since it is the first ifdo to demonstrate chirality. Its inverse is 3afdo. As a scale it may also be known as mode 3 of the subharmonic series or the Under-3 scale. The notes of this IFDO form a just minor triad in root position.
Intervals
| # | Cents | Ratio | Interval name | Audio |
|---|---|---|---|---|
| 0 | 0.00 | 1/1 | perfect unison | |
| 1 | 315.64 | 6/5 | just minor third | |
| 2 | 701.96 | 3/2 | just perfect fifth | |
| 3 | 1200.00 | 2/1 | perfect octave |