33/28: Difference between revisions
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In [[11-limit]] [[just intonation]], '''33/28''' is an '''undecimal minor third''', specifically the '''pentacircle minor third''', measuring about 284. | In [[11-limit]] [[just intonation]], '''33/28''' is an '''undecimal minor third''', specifically the '''pentacircle minor third''', measuring about 284.4 [[cent]]s. It is the fifth inverse of the pentacircle major third [[14/11]]. | ||
In many notation systems based on the [[5L 2s|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is a major second, as it is a [[9/8|Pythagorean major second]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. | |||
However, it is only flat of the Pythagorean minor third of [[32/27]] (about 294.1{{c}}) by a [[896/891|pentacircle comma (896/891)]], which makes it function sometimes as a minor third, hence the names. | |||
{{Todo|expand}} | |||
[[Category:Pentacircle]] | [[Category:Pentacircle]] | ||
Latest revision as of 09:16, 16 January 2026
| Interval information |
pentacircle minor third
In 11-limit just intonation, 33/28 is an undecimal minor third, specifically the pentacircle minor third, measuring about 284.4 cents. It is the fifth inverse of the pentacircle major third 14/11.
In many notation systems based on the diatonic chain-of-fifths notation with commatic alterations (e.g. FJS, HEJI), it is a major second, as it is a Pythagorean major second plus an instance of 22/21, which is a stack consisting of an undecimal quartertone (33/32) and a septimal comma (64/63), neither of which changes the scale degree or quality.
However, it is only flat of the Pythagorean minor third of 32/27 (about 294.1 ¢) by a pentacircle comma (896/891), which makes it function sometimes as a minor third, hence the names.