Don Page comma: Difference between revisions

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By a '''Don Page comma''' is meant a [[comma]] computed from two other intervals by the method suggested by the Don Page paper, [http://arxiv.org/abs/0907.5249 ''Why the Kirnberger Kernel Is So Small'']. If ''a'' and ''b'' are two rational numbers greater than 1, define {{nowrap| ''r'' {{=}} ((''a'' - 1)(''b'' + 1)) / ((''b'' - 1)(''a'' + 1)) }}. Suppose ''r'' reduced to lowest terms is ''p''/''q'', and ''a'' and ''b'' are written in [[monzo]] form as '''u''' and '''v'''. Then the Don Page comma is defined as DPC(''a'', ''b'') = ''q'''''u''' - ''p'''''v''', or else minus that if the size in [[cent]]s is less than zero. The reason for introducing monzos is purely numerical; if monzos are not used the numerators and denominators of the Don Page comma quickly become so large they cannot easily be handled. In ratio form, the Don Page comma can be written {{nowrap| ''a''<sup>''q''</sup>/''b''<sup>''p''</sup> }}, or the reciprocal of that if that is less than 1.

Revision as of 16:04, 17 February 2025 view source Lériendil (talk \| contribs) autopatrolled, Interface administrators, Sysops 7,596 edits m Changed protection level for "Don Page comma" ([Edit=Allow only administrators] (expires 17:04, 17 February 2025 (UTC)) [Move=Allow only administrators] (expires 17:04, 17 February 2025 (UTC))) ← Older edit		Revision as of 16:20, 17 February 2025 view source Lériendil (talk \| contribs) autopatrolled, Interface administrators, Sysops 7,596 edits don paging all over the place rn Newer edit →
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			{{Legacy\|Don_Page_comma}}
	By a '''Don Page comma''' is meant a [[comma]] computed from two other intervals by the method suggested by the Don Page paper, [http://arxiv.org/abs/0907.5249 ''Why the Kirnberger Kernel Is So Small'']. If ''a'' and ''b'' are two rational numbers greater than 1, define {{nowrap\| ''r'' {{=}} ((''a'' - 1)(''b'' + 1)) / ((''b'' - 1)(''a'' + 1)) }}. Suppose ''r'' reduced to lowest terms is ''p''/''q'', and ''a'' and ''b'' are written in [[monzo]] form as '''u''' and '''v'''. Then the Don Page comma is defined as DPC(''a'', ''b'') = ''q'''''u''' - ''p'''''v''', or else minus that if the size in [[cent]]s is less than zero. The reason for introducing monzos is purely numerical; if monzos are not used the numerators and denominators of the Don Page comma quickly become so large they cannot easily be handled. In ratio form, the Don Page comma can be written {{nowrap\| ''a''<sup>''q''</sup>/''b''<sup>''p''</sup> }}, or the reciprocal of that if that is less than 1.		By a '''Don Page comma''' is meant a [[comma]] computed from two other intervals by the method suggested by the Don Page paper, [http://arxiv.org/abs/0907.5249 ''Why the Kirnberger Kernel Is So Small'']. If ''a'' and ''b'' are two rational numbers greater than 1, define {{nowrap\| ''r'' {{=}} ((''a'' - 1)(''b'' + 1)) / ((''b'' - 1)(''a'' + 1)) }}. Suppose ''r'' reduced to lowest terms is ''p''/''q'', and ''a'' and ''b'' are written in [[monzo]] form as '''u''' and '''v'''. Then the Don Page comma is defined as DPC(''a'', ''b'') = ''q'''''u''' - ''p'''''v''', or else minus that if the size in [[cent]]s is less than zero. The reason for introducing monzos is purely numerical; if monzos are not used the numerators and denominators of the Don Page comma quickly become so large they cannot easily be handled. In ratio form, the Don Page comma can be written {{nowrap\| ''a''<sup>''q''</sup>/''b''<sup>''p''</sup> }}, or the reciprocal of that if that is less than 1.