Fudging: Difference between revisions
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'''Fudging''', or virtual tempering, is the use of one [[just intonation]] interval to approximate another. | '''Fudging''', or virtual tempering, is the use of one [[just intonation]] interval to approximate another. | ||
==Fudgers== | == Fudgers == | ||
Below are listed fudging intervals (or '''fudgers''') which are all ratios between two 15-limit [[tonality diamond]] intervals (listed in the fifth column) which come within a comma of less than eight cents (listed in the fourth column) of a 15-limit tonality diamond interval (listed in the third column). If the [[comma]] is less than 1, the fudger is flat of the interval it approximates; if greater than 1, sharp of it. | Below are listed fudging intervals (or '''fudgers''') which are all ratios between two 15-limit [[tonality diamond]] intervals (listed in the fifth column) which come within a comma of less than eight cents (listed in the fourth column) of a 15-limit tonality diamond interval (listed in the third column). If the [[comma]] is less than 1, the fudger is flat of the interval it approximates; if greater than 1, sharp of it. | ||
===Up-fudge=== | === Up-fudge === | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! Fudger | ||
! | ! Cents | ||
! | ! Approximately | ||
! | ! Comma(s) | ||
! ( | ! (Example) intervals | ||
! | ! Name | ||
|- | |- | ||
| [[242/225]] | | [[242/225]] | ||
| Line 833: | Line 832: | ||
|} | |} | ||
===Down-fudge=== | === Down-fudge === | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 1,437: | Line 1,435: | ||
| [9/7 26/11] | | [9/7 26/11] | ||
|} | |} | ||
== Limit-raising and limit-lowering fudgers == | == Limit-raising and limit-lowering fudgers == | ||
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However, indiscriminate tempering can lead to problems. For example, [[112/75]], 121/81, 338/225, 182/121 and 176/117 are all fudged fifths, with commas [[676/675]], [[364/363]], [[352/351]], [[243/242]] and [[225/224]]. Tempering them all out leads to 34d tempering, a rather crude system by comparison. | However, indiscriminate tempering can lead to problems. For example, [[112/75]], 121/81, 338/225, 182/121 and 176/117 are all fudged fifths, with commas [[676/675]], [[364/363]], [[352/351]], [[243/242]] and [[225/224]]. Tempering them all out leads to 34d tempering, a rather crude system by comparison. | ||
[[Category:15-odd-limit]] | |||
[[Category:Method]] | |||
[[Category:Terms]] | |||
[[Category:Lists of intervals]] | |||
[[Category:Just intonation]] | |||