IFDO: Difference between revisions
mNo edit summary |
|||
| (7 intermediate revisions by 2 users not shown) | |||
| Line 5: | Line 5: | ||
For example, in [[12ifdo]] the first degree is [[24/23]], the second is 24/22 ([[12/11]]), and so on. For an IFDO system, the difference between ''inverse'' interval ratios is equal (they form an inverse-arithmetic progression), rather than their difference between interval ratios being equal as in [[AFDO]] systems (an arithmetic progression). All IFDOs are subsets of [[just intonation]], and up to transposition, any IFDO is a superset of a smaller IFDO and a subset of a larger IFDO (i.e. ''n''-ifdo is a superset of (''n'' - 1)-ifdo and a subset of (''n'' + 1)-ifdo for any integer ''n'' > 1). | For example, in [[12ifdo]] the first degree is [[24/23]], the second is 24/22 ([[12/11]]), and so on. For an IFDO system, the difference between ''inverse'' interval ratios is equal (they form an inverse-arithmetic progression), rather than their difference between interval ratios being equal as in [[AFDO]] systems (an arithmetic progression). All IFDOs are subsets of [[just intonation]], and up to transposition, any IFDO is a superset of a smaller IFDO and a subset of a larger IFDO (i.e. ''n''-ifdo is a superset of (''n'' - 1)-ifdo and a subset of (''n'' + 1)-ifdo for any integer ''n'' > 1). | ||
When treated as a [[scale]], the IFDO is equivalent to the undertone scale, also known as an aliquot scale<ref>''1/1, The Journal of the Just Intonation Network'', Volume 4, Number 1, Winter 1988, p.6, Michael Sloper. </ref>. An IFDO is equivalent to a UDO ([[utonal division]] of the octave). It may also be called an ''n''-ELDO ([[equal length division]] of the octave) since it includes the pitches found by dividing the length of a string or resonating chamber into ''n'' equal parts; however, this more general acronym is typically reserved for divisions of irrational intervals (unlike the octave) which are therefore not subsets of just intonation. | When treated as a [[scale]], the IFDO is equivalent to the undertone scale, also known as an aliquot scale<ref>''1/1, The Journal of the Just Intonation Network'', Volume 4, Number 1, Winter 1988, p.6, Michael Sloper. </ref>. However, an undertone scale often has an assumption of a tonic whereas an IFDO simply describes all the theoretically available pitch relations. Therefore, a passage built on 1/(12::22) could be said to be in Mode 12, but is technically covered by 11ifdo. | ||
An IFDO is equivalent to a UDO ([[utonal division]] of the octave). It may also be called an ''n''-ELDO ([[equal length division]] of the octave) since it includes the pitches found by dividing the length of a string or resonating chamber into ''n'' equal parts; however, this more general acronym is typically reserved for divisions of irrational intervals (unlike the octave) which are therefore not subsets of just intonation. | |||
== Formula == | == Formula == | ||
| Line 37: | Line 39: | ||
[[file:Edl2.JPG]] | [[file:Edl2.JPG]] | ||
=== Individual pages for EDLs === | |||
* [[23edl]] | |||
== Relation to superparticular ratios == | == Relation to superparticular ratios == | ||
| Line 42: | Line 47: | ||
== Relation to utonality and subharmonic series == | == Relation to utonality and subharmonic series == | ||
We can consider an IFDO system as a [[Otonality and utonality|utonal system]]. ''Utonality'' is a term introduced by [[Harry Partch]] to describe chords whose notes are the undertones (divisors) of a given fixed tone. Considering IFDO, a utonality is a collection of pitches which can be expressed in ratios that have the same numerators. For example, 7/4, 7/5, 7/6 form an utonality in which 7 as the numerator is called a "[ | We can consider an IFDO system as a [[Otonality and utonality|utonal system]]. ''Utonality'' is a term introduced by [[Harry Partch]] to describe chords whose notes are the undertones (divisors) of a given fixed tone. Considering IFDO, a utonality is a collection of pitches which can be expressed in ratios that have the same numerators. For example, 7/4, 7/5, 7/6 form an utonality in which 7 as the numerator is called a "[[numerary nexus]]". | ||
== Properties == | |||
* ''n''-ifdo has [[maximum variety]] ''n''. | |||
* Except for 1ifdo and 2ifdo, IFDOs are [[chiral]]. The inverse of ''n''-ifdo is ''n''-afdo. | |||
** 1ifdo is equivalent to 1afdo and 1edo; | |||
** 2ifdo is equivalent to 2afdo. | |||
== Individual pages for IFDOs == | == Individual pages for IFDOs == | ||
=== By size === | === By size === | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| Line 328: | Line 338: | ||
== External links == | == External links == | ||
* [https://web.archive.org/web/20220630142502/https://sites.google.com/site/240edo/equaldivisionsoflength(edl) | * [https://web.archive.org/web/20220630142502/https://sites.google.com/site/240edo/equaldivisionsoflength(edl) ''Equal divisions of length''] — from [[Shaahin Mohajeri]]’s website ''96~EDO'' (96edo.com), archived by Wayback Machine | ||
== | == References == | ||
[[Category: | [[Category:Just intonation]] | ||
[[Category:Acronyms]] | [[Category:Acronyms]] | ||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
[[Category:Utonality]] | [[Category:Utonality]] | ||
[[Category:Subharmonic series]] | [[Category:Subharmonic series]] | ||