AFDO: Difference between revisions
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[[File:ADO-4.jpg|350px|center]] | [[File:ADO-4.jpg|350px|center]] | ||
These lengths are related to the inverse of ratios in the system. The above picture shows the differences between divisions of length in | These lengths are related to the inverse of ratios in the system. The above picture shows the differences between divisions of length in [[12afdo]] system. On the contrary, we have equal divisions of length in [[EDL]] systems (→ [https://sites.google.com/site/240edo/equaldivisionsoflength(edl) EDL system]): | ||
[[File:ADO-5.jpg|346px|center]] | [[File:ADO-5.jpg|346px|center]] | ||
== Relation to superparticular ratios == | == Relation to superparticular ratios == | ||
An AFDO has step sizes of [[superparticular ratio]]s with increasing numerators. For example, [[ | An AFDO has step sizes of [[superparticular ratio]]s with increasing numerators. For example, [[5afdo]] has step sizes of [[6/5]], [[7/6]], [[8/7]], and [[9/8]]. | ||
== Relation to otonality & harmonic series == | == Relation to otonality & harmonic series == | ||
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In 2023, [[Flora Canou]] revived the old term, reinterpreting the word "arithmetic" as a reference to the [[Wikipedia: Arithmetic mean|arithmetic mean]] in addition to arithmetic progressions, then extended it through the other [[Pythagorean means]], and later through all [[power mean]]s. As it was shown that ''arithmetic'' alone was insufficient to define the object since frequency could not be assumed, the term was eventually changed to AFDO, showing both the type of power mean and the sampled resource. | In 2023, [[Flora Canou]] revived the old term, reinterpreting the word "arithmetic" as a reference to the [[Wikipedia: Arithmetic mean|arithmetic mean]] in addition to arithmetic progressions, then extended it through the other [[Pythagorean means]], and later through all [[power mean]]s. As it was shown that ''arithmetic'' alone was insufficient to define the object since frequency could not be assumed, the term was eventually changed to AFDO, showing both the type of power mean and the sampled resource. | ||
== Properties == | |||
* ''n''-afdo has [[maximum variety]] ''n''. | |||
* Except for 1afdo and 2afdo, AFDOs are [[chiral]]. The inverse of ''n''-afdo is ''n''-ifdo. | |||
** 1afdo is equivalent to 1ifdo and 1edo; | |||
** 2afdo is equivalent to 2ifdo. | |||
== Individual pages for AFDOs == | == Individual pages for AFDOs == | ||
=== By size === | === By size === | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
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* [http://www.soundtransformations.btinternet.co.uk/Danerhudyarthemarmonicseries.htm Magic of Tone and the Art of Music] by the late [[Dane Rhudyar]] | * [http://www.soundtransformations.btinternet.co.uk/Danerhudyarthemarmonicseries.htm Magic of Tone and the Art of Music] by the late [[Dane Rhudyar]] | ||
== | == References == | ||
[[Category: | [[Category:Just intonation]] | ||
[[Category:Acronyms]] | [[Category:Acronyms]] | ||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||