Delta-N ratio: Difference between revisions
m +category |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 1: | Line 1: | ||
{{Beginner| Abc, high quality commas, and epimericity }} | {{Beginner|Abc, high quality commas, and epimericity}} | ||
{{Wikipedia| Superpartient ratio }} | {{Wikipedia|Superpartient ratio}} | ||
The '''delta''' of a [[ratio]] is simply the difference between its numerator and its denominator. (Delta is also known as degree of epimoricity.) A ratio with a delta of N is called a '''delta-N ratio'''. | The '''delta''' of a [[ratio]] is simply the difference between its numerator and its denominator. (Delta is also known as degree of epimoricity.) A ratio with a delta of N is called a '''delta-N ratio'''. | ||
{| class="wikitable" style="text-align:center;" | {| class="wikitable" style="text-align:center;" | ||
|+ | |+ Examples | ||
! Delta-1 ratios | |||
! | | 2/1 | ||
|2/1 | | 3/2 | ||
|3/2 | | 4/3 | ||
|4/3 | | 5/4 | ||
|5/4 | | 6/5 | ||
|6/5 | | 7/6 | ||
|7/6 | | etc. | ||
|etc. | |||
|- | |- | ||
! | ! Delta-2 ratios | ||
|3/1 | | 3/1 | ||
|5/3 | | 5/3 | ||
|7/5 | | 7/5 | ||
|9/7 | | 9/7 | ||
|11/9 | | 11/9 | ||
|13/11 | | 13/11 | ||
|etc. | | etc. | ||
|- | |- | ||
! | ! Delta-3 ratios | ||
|4/1 | | 4/1 | ||
|5/2 | | 5/2 | ||
|7/4 | | 7/4 | ||
|8/5 | | 8/5 | ||
|10/7 | | 10/7 | ||
|11/8 | | 11/8 | ||
|etc. | | etc. | ||
|- | |- | ||
! | ! Delta-4 ratios | ||
|5/1 | | 5/1 | ||
|7/3 | | 7/3 | ||
|9/5 | | 9/5 | ||
|11/7 | | 11/7 | ||
|13/9 | | 13/9 | ||
|15/11 | | 15/11 | ||
|etc. | | etc. | ||
|} | |} | ||
Thus [[superparticular]] ratios are delta-1 ratios, and '''superpartient ratios''' are all ratios ''except'' delta-1 ratios. The delta-N terminology was coined by [[Kite Giedraitis]]. | Thus [[superparticular]] ratios are delta-1 ratios, and '''superpartient ratios''' are all ratios ''except'' delta-1 ratios. The delta-N terminology was coined by [[Kite Giedraitis]]. | ||
| Line 55: | Line 55: | ||
== Superpartient subcategories == | == Superpartient subcategories == | ||
Superpartient ratios can be grouped into subcategories based on the exact difference between the numerator and the denominator. This is known as the '''degree of epimoricity''' (not to be confused with ''epimericity'' | Superpartient ratios can be grouped into subcategories based on the exact difference between the numerator and the denominator. This is known as the '''degree of epimoricity''' (not to be confused with ''epimericity''—see link below), or '''delta''' (proposed by [[Kite Giedraitis]]). This is particularly useful when considering ratios that are [[comma]]s. | ||
These subcategories are named as superbipartient, supertripartient, superquadripartient, etc., or in [[Delta-N|delta-N terminology]] as delta-2, delta-3, delta-4, etc. Superparticular or epimoric ratios can likewise be named delta-1. | These subcategories are named as superbipartient, supertripartient, superquadripartient, etc., or in [[Delta-N|delta-N terminology]] as delta-2, delta-3, delta-4, etc. Superparticular or epimoric ratios can likewise be named delta-1. | ||