25/16: Difference between revisions

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'''25/16''', the '''classic(al) 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''' 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 a [[ptolemismic chords|ptolemismic chord]].

While this interval has been referred to as the ''classic augmented fifth'' 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]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.

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-'''25/16''', the '''classic(al) 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''' 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 a [[ptolemismic chords|ptolemismic chord]].
 While this interval has been referred to as the ''classic augmented fifth'' 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]].  Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''.