25/16: Difference between revisions
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'''25/16''', the '''classic(al) augmented fifth''' or '''diptolemaic augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords|ptolemismic augmented triad]]. | '''25/16''', the '''classic(al) augmented fifth''' or '''diptolemaic augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. It is [[100/99]] sharp of [[99/64]], and tempering out 100/99 makes 1-5/4-25/16 into the [[ptolemismic chords|ptolemismic augmented triad]]. | ||
== Names == | |||
While this interval has been referred to as the ''classic'' or ''classical'' augmented fifth for some time, the term "diptolemaic" [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[User:Aura|Aura]]. The concept of "diptolemaic" intervals builds on the concept of "ptolemaic"<ref>[https://marsbat.space/pdfs/JI.pdf ''Fundamental Principles of Just Intonation and Microtonal Composition''] by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."</ref> intervals, with "diptolemaic" intervals being those that have two factors of 5 in their [[monzo]] and differ from their Pythagorean counterparts by two instances of [[81/80]] in the direction of ratio simplicity— for instance, 25/16 differing from [[6561/4096]]—, while 5-limit intervals that differ from their Pythagorean counterparts by a single instance of 81/80 in the same direction are simply called "ptolemaic" intervals. | |||
== See also == | == See also == | ||
* [[32/25]] – its [[octave complement]] | * [[32/25]] – its [[octave complement]] | ||
== References == | |||
<references/> | |||
[[Category:Fifth]] | [[Category:Fifth]] | ||
[[Category:Augmented fifth]] | [[Category:Augmented fifth]] | ||
[[Category:todo:expand]] | [[Category:todo:expand]] | ||
Revision as of 20:03, 28 January 2023
| Interval information |
diptolemaic augmented fifth
reduced harmonic
[sound info]
25/16, the classic(al) augmented fifth or diptolemaic augmented fifth is the interval obtained by stacking two 5/4 major thirds, however, it gains additional isoharmonic identity from its position between 11/8 and 7/4, so it can frequently be used in conjunction with those, even in chords. It is 100/99 sharp of 99/64, and tempering out 100/99 makes 1-5/4-25/16 into the ptolemismic augmented triad.
Names
While this interval has been referred to as the classic or classical augmented fifth for some time, the term "diptolemaic" was coined on Discord by Flora Canou while discussing a proposal for a consistent naming scheme for different 5-limit intervals with Aura. The concept of "diptolemaic" intervals builds on the concept of "ptolemaic"[1] intervals, with "diptolemaic" intervals being those that have two factors of 5 in their monzo and differ from their Pythagorean counterparts by two instances of 81/80 in the direction of ratio simplicity— for instance, 25/16 differing from 6561/4096—, while 5-limit intervals that differ from their Pythagorean counterparts by a single instance of 81/80 in the same direction are simply called "ptolemaic" intervals.
See also
- 32/25 – its octave complement
References
- ↑ Fundamental Principles of Just Intonation and Microtonal Composition by Thomas Nicholson and Marc Sabat —"'Ptolemaic' refers to intervals combining only the primes 2, 3, and 5."