7/5: Difference between revisions

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{{Infobox Interval

| Name = narrow tritone, lesser septimal tritone, Huygens' tritone

| Name = narrow tritone, lesser septimal tritone, Huygens' tritone, septimal diminished fifth

| Color name = zg5, zogu 5th

| Sound = jid_7_5_pluck_adu_dr220.mp3

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In [[7-limit]] [[just intonation]], '''7/5''' is a '''narrow [[tritone]]''' (or '''Huygens' tritone''') measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[edo]]. It represents the difference between [[7/4]] and [[5/4]]. It being classified as a diminished fifth in both [[Functional Just System|FJS]] and [[Helmholtz-Ellis notation|HEJI]], it can also be named the '''septimal diminished fifth''', as found in the context [[5:6:7|septimal diminished triad (5:6:7)]] and [[4:5:6:7|harmonic seventh chord. (4:5:6:7)]].

While found contextually as a diminished fifth in JI harmony, in some situations it can actually be found as more of a augmented fourth ~~than a diminished fifth~~ – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]]. This is one of the reasons why [[7/4]] can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.

While found contextually as a diminished fifth in JI harmony, in some situations it can actually be found as more of a augmented fourth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]]. This is one of the reasons why [[7/4]] can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.

7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the harmonic seventh chord that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.

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 }}
 {{Infobox Interval
-| Name = narrow tritone, lesser septimal tritone, Huygens' tritone
+| Name = narrow tritone, lesser septimal tritone, Huygens' tritone, septimal diminished fifth
 | Color name = zg5, zogu 5th
 | Sound = jid_7_5_pluck_adu_dr220.mp3
@@ Line 14: / Line 14: @@
 In [[7-limit]] [[just intonation]], '''7/5''' is a '''narrow [[tritone]]''' (or '''Huygens' tritone''') measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[edo]]. It represents the difference between [[7/4]] and [[5/4]]. It being classified as a diminished fifth in both [[Functional Just System|FJS]] and [[Helmholtz-Ellis notation|HEJI]], it can also be named the '''septimal diminished fifth''', as found in the context [[5:6:7|septimal diminished triad (5:6:7)]] and [[4:5:6:7|harmonic seventh chord. (4:5:6:7)]].
-While found contextually as a diminished fifth in JI harmony, in some situations it can actually be found as more of a augmented fourth than a diminished fifth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]]. This is one of the reasons why [[7/4]] can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.
+While found contextually as a diminished fifth in JI harmony, in some situations it can actually be found as more of a augmented fourth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]]. This is one of the reasons why [[7/4]] can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.
 /5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the harmonic seventh chord that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.