Delta-rational chord: Difference between revisions

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A '''delta-rational''' ('''DR''') chord is a chord ~~with [[dyad]]s which are close to having~~ simple integer ratios between frequency ''differences'' of dyads, called '''deltas''', with the dyads in question assumed to ''not'' overlap (Δ, capital delta, is often used to denote "difference").

A '''delta-rational''' ('''DR''') chord is a chord that has simple integer ratios between frequency ''differences'' of some pair of dyads, called '''deltas''', with the dyads in question assumed to ''not'' overlap (Δ, capital delta, is often used to denote "difference").

DR chords are approximations of JI chords, in which the frequency differences of dyads are ''exactly'' simple integer ratios. But unlike JI chords, a DR chord need not have integer ratios between frequencies of notes. For example, the [[13edo]] chord 0-3-8-10\13 (0¢-277¢-738¢-923¢) is close to being delta-rational, because the frequency difference of the dyad 8-10\13 is 0.994 times the frequency difference of the dyad 0-3\13. (In 0\13-3\13-8\13-924.159¢, the 3rd and 4th notes would have exactly the same frequency difference as the dyad 0-3\13.)

Revision as of 10:11, 13 February 2024 view source Akselai (talk \| contribs) 252 edits No edit summary ← Older edit		Revision as of 13:45, 13 February 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,672 edits The exact DR definition should be given first. Tags: Mobile edit Mobile web edit Newer edit →
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	A '''delta-rational''' ('''DR''') chord is a chord ~~with [[dyad]]s which are close to having~~ simple integer ratios between frequency ''differences'' of dyads, called '''deltas''', with the dyads in question assumed to ''not'' overlap (Δ, capital delta, is often used to denote "difference").		A '''delta-rational''' ('''DR''') chord is a chord that has simple integer ratios between frequency ''differences'' of some pair of dyads, called '''deltas''', with the dyads in question assumed to ''not'' overlap (Δ, capital delta, is often used to denote "difference").

	DR chords are approximations of JI chords, in which the frequency differences of dyads are ''exactly'' simple integer ratios. But unlike JI chords, a DR chord need not have integer ratios between frequencies of notes. For example, the [[13edo]] chord 0-3-8-10\13 (0¢-277¢-738¢-923¢) is close to being delta-rational, because the frequency difference of the dyad 8-10\13 is 0.994 times the frequency difference of the dyad 0-3\13. (In 0\13-3\13-8\13-924.159¢, the 3rd and 4th notes would have exactly the same frequency difference as the dyad 0-3\13.)		DR chords are approximations of JI chords, in which the frequency differences of dyads are ''exactly'' simple integer ratios. But unlike JI chords, a DR chord need not have integer ratios between frequencies of notes. For example, the [[13edo]] chord 0-3-8-10\13 (0¢-277¢-738¢-923¢) is close to being delta-rational, because the frequency difference of the dyad 8-10\13 is 0.994 times the frequency difference of the dyad 0-3\13. (In 0\13-3\13-8\13-924.159¢, the 3rd and 4th notes would have exactly the same frequency difference as the dyad 0-3\13.)