33/28: Difference between revisions

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Created page with "{{Infobox Interval | Name = undecimal minor third | Color name = loru 2nd, 1or2 | Sound = jid_13_11_pluck_adu_dr220.mp3 }} In 11-limit just intonation, '''33/28''' i..."
 
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{{Infobox Interval
{{Infobox Interval
| Name = undecimal minor third
| Name = undecimal minor third, pentacircle minor third
| Color name = loru 2nd, 1or2
| Color name = loru 2nd, 1or2
| Sound = jid_13_11_pluck_adu_dr220.mp3
}}
}}


In [[11-limit]] [[just intonation]], '''33/28''' is the '''undecimal minor third''', measuring about 284.. It is the fifth inverse of the undecimal major third [[14/11]].
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]]

Latest revision as of 09:16, 16 January 2026

Interval information
Ratio 33/28
Factorization 2-2 × 3 × 7-1 × 11
Monzo [-2 1 0 -1 1
Size in cents 284.447¢
Names undecimal minor third,
pentacircle minor third
Color name loru 2nd, 1or2
FJS name [math]\displaystyle{ \text{M2}^{11}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.85175
Weil norm (log2 max(n, d)) 10.0888
Wilson norm (sopfr(nd)) 25
Open this interval in xen-calc

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.