ELD: Difference between revisions

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An ELD will be equivalent to some [[ALS|ALS (arithmetic length sequence)]]; specifically n-ELD((p-1)/n) = n-ALSp.

It is possible to — instead of equally dividing the octave in 12 equal parts by pitch — divide it into 12 equal parts by '''length'''. You will have 12-ELDO. However, that's not exactly ideal because, as with arithmetic sequences, different acronyms are used to distinguish rational (JI) tunings from irrational (non-JI) tunings, and so ELD are typically reserved for irrational tunings, such as 12-ELDφ. So it would be more appropriate to name this tuning 12-UDO, for ~~otonal divisions of the octave and~~ utonal divisions of the octave~~, respectively~~.

It is possible to — instead of equally dividing the octave in 12 equal parts by pitch — divide it into 12 equal parts by '''length'''. You will have 12-ELDO. However, that's not exactly ideal because, as with arithmetic sequences, different acronyms are used to distinguish rational (JI) tunings from irrational (non-JI) tunings, and so ELD are typically reserved for irrational tunings, such as 12-ELDφ. So it would be more appropriate to name this tuning 12-UDO, for utonal divisions of the octave.

Note that because frequency is the inverse of length, if a frequency lower than the root pitch's frequency is asked for, the length will be greater than 1; at this point the physical analogy to a length of string breaks down somewhat, since it is not easy to imagine dynamically extending the length of a string to accommodate such pitches. However, it is not much of a stretch (pun intended) to tolerate lengths > 1, if the analogy is adapted to a switching from one string to another, and any string length imaginable is instantly available.

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 An ELD will be equivalent to some [[ALS|ALS (arithmetic length sequence)]]; specifically n-ELD((p-1)/n) = n-ALSp.
-It is possible to — instead of equally dividing the octave in 12 equal parts by pitch — divide it into 12 equal parts by '''length'''. You will have 12-ELDO. However, that's not exactly ideal because, as with arithmetic sequences, different acronyms are used to distinguish rational (JI) tunings from irrational (non-JI) tunings, and so ELD are typically reserved for irrational tunings, such as 12-ELDφ. So it would be more appropriate to name this tuning 12-UDO, for otonal divisions of the octave and utonal divisions of the octave, respectively.
+It is possible to — instead of equally dividing the octave in 12 equal parts by pitch — divide it into 12 equal parts by '''length'''. You will have 12-ELDO. However, that's not exactly ideal because, as with arithmetic sequences, different acronyms are used to distinguish rational (JI) tunings from irrational (non-JI) tunings, and so ELD are typically reserved for irrational tunings, such as 12-ELDφ. So it would be more appropriate to name this tuning 12-UDO, for utonal divisions of the octave.
 Note that because frequency is the inverse of length, if a frequency lower than the root pitch's frequency is asked for, the length will be greater than 1; at this point the physical analogy to a length of string breaks down somewhat, since it is not easy to imagine dynamically extending the length of a string to accommodate such pitches. However, it is not much of a stretch (pun intended) to tolerate lengths > 1, if the analogy is adapted to a switching from one string to another, and any string length imaginable is instantly available.