Diarithmedia: Difference between revisions
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'''25921/25920''', the '''diarithmedia''' is a [[23-limit]] and 2.3.5.7.23-[[subgroup]] [[square superparticular]] square-particular ratio of about 0.067 [[cent]]s. It is the difference between [[161/160]] and [[162/161]], and between [[49/45]] and [[24/23]]<sup>2</sup>, and therefore tempering this comma out splits the syntonic comma, [[81/80]] into exact halves alongside 49/45. As a further consequence, it equates [[161/144]], the "arithmetic meantone" (being the arithmetic mean of [[9/8]] and [[10/9]]) with [[180/161]] and splits [[5/4]] in half, providing a way to use hemithirds without equating 9/8 and 10/9 together. | '''25921/25920''', the '''diarithmedia''', is a [[23-limit]] and 2.3.5.7.23-[[subgroup]] [[square superparticular]] square-particular ratio of about 0.067 [[cent]]s. It is the difference between [[161/160]] and [[162/161]], and between [[49/45]] and [[24/23]]<sup>2</sup>, and therefore tempering this comma out splits the syntonic comma, [[81/80]] into exact halves alongside 49/45. As a further consequence, it equates [[161/144]], the "arithmetic meantone" (being the arithmetic mean of [[9/8]] and [[10/9]]) with [[180/161]] and splits [[5/4]] in half, providing a way to use hemithirds without equating 9/8 and 10/9 together. | ||
== Etymology == | == Etymology == | ||
Revision as of 21:57, 20 September 2024
| Interval information |
reduced
S46/S48
25921/25920, the diarithmedia, is a 23-limit and 2.3.5.7.23-subgroup square superparticular square-particular ratio of about 0.067 cents. It is the difference between 161/160 and 162/161, and between 49/45 and 24/232, and therefore tempering this comma out splits the syntonic comma, 81/80 into exact halves alongside 49/45. As a further consequence, it equates 161/144, the "arithmetic meantone" (being the arithmetic mean of 9/8 and 10/9) with 180/161 and splits 5/4 in half, providing a way to use hemithirds without equating 9/8 and 10/9 together.
Etymology
The name diarithmetic media was proposed by Flora Canou in 2023, for being the separatrix between an arithmetic-mean interval and an inverse-arithmetic-mean interval. It was shortened to diarithmedia by Lériendil in 2024.