Interseptimal interval: Difference between revisions

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* 240¢–260¢ – '''semifourth''' – an interval of this size is around half the size of a perfect fourth.

** The term '''chthonic''' (from ''khthon'', an ancient Greek word referring to spirits of the underworld) refers to the 240-260¢ region by [[Zhea Erose]].<ref>as per [[Primodal Archive]]</ref>

* 440¢–468¢ – '''semisixth''' – an interval of this size is around half the size of a major sixth.

** The term '''naiadic''' (from ''naiad'', a kind of ancient Greek water spirit) refers to the ~~440c–464c~~ region by [[Zhea Erose]], who uses it frequently.

** The term '''naiadic''' (from ''naiad'', a kind of ancient Greek water spirit) refers to the 440–464¢ region by [[Zhea Erose]], who uses it frequently.

* 732¢–760¢ – '''semitenth''' – an interval of this size is around half the size of a minor tenth (i. e., an octave plus a minor third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).

** The term '''cocytic''' was proposed by [[Inthar]], and is carried on with by [[Flora Canou]]<ref>Flora Canou criticizes ''semisixth'' and ''semitenth'' as they fail to make clear whether the interval to be split is major or minor, and prefers ''naiadic'' and ''cocytic''.</ref>.

* 940¢–960¢ – '''semitwelfth''' – an interval of this size is around half the size of a perfect twelfth (i.e. a compound perfect fifth, or tritave). All even [[edt]]s have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.

** The term '''ouranic''' (by analogy with chthonic, and to match with the other terms) is proposed by [[User:Kaiveran|Kaiveran]].

This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi".

This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi". In particular, since these intervals tend to be very well represented by [[Pergen|pergens]] that divide an instance of prime 3 into 2(''n'') parts, we can easily repurpose [[24edo#Quartertone Accidentals|quartertone accidentals]] to represent them, as long as we define our "half-sharps" or "half-flats" to be precisely half of a chromatic semitone (that is, "7/2 fifths" up or down the generator chain). With this in mind, we get the following notational identities for our interseptimals, with the simplest one listed first:

By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now. A key difference is that the tritone is intermediate between two septimal ratios separated by a jubilisma ([[50/49]]), whereas the other interseptimal ranges listed above are between two septimal ratios separated by a slendro diesis ([[49/48]]).

* semifourth/chthonic = semi-augmented second (+11/2), semi-diminished third (-13/2)

* semisixth/naiadic = semi-diminished fourth (-9/2), semi-augmented third (+15/2)

* semitenth/cocytic = semi-augmented fifth (+9/2), semi-diminished sixth (-15/2)

* semitwelfth/ouranic = semi-diminished seventh (-11/2), semi-augmented sixth (+13/2)

While this does not give the interseptimals a single distinct ''notational'' name, it does reflect their ambiguity and flexibility with regards to the surrounding interval categories that many are so fond of. Furthermore, as both identities are exactly 12 notational fifths apart (i.e a direct analogue of the [[Pythagorean comma]]), composers can use a mechanism similar to the [[Color notation|"po and qu" of Color Notation]], or the plus and minus accidentals (+/-) proposed in [[Rational Comma Notation (RCN)|Rational Comma Notation]], to freely switch between the two identities.

By analogy with the "semi" names, the tritone could also be called a semioctave, although the term tritone is so well-established (and so well represented by an unsplit 3-limit) that there seems little reason to change it now. A key difference is that the tritone is intermediate between two septimal ratios separated by a jubilisma ([[50/49]]), whereas the other interseptimal ranges listed above are between two septimal ratios separated by a slendro diesis ([[49/48]]).

== Examples ==

@@ Line 11: / Line 11: @@
 * 240¢–260¢ – '''semifourth''' – an interval of this size is around half the size of a perfect fourth.
+** The term '''chthonic''' (from ''khthon'', an ancient Greek word referring to spirits of the underworld) refers to the 240-260¢ region by [[Zhea Erose]].<ref>as per [[Primodal Archive]]</ref>
 * 440¢–468¢ – '''semisixth''' – an interval of this size is around half the size of a major sixth.
-** The term '''naiadic''' (from ''naiad'', a kind of ancient Greek water spirit) refers to the 440c–464c region by [[Zhea Erose]], who uses it frequently.
+** The term '''naiadic''' (from ''naiad'', a kind of ancient Greek water spirit) refers to the 440–464¢ region by [[Zhea Erose]], who uses it frequently.
 * 732¢–760¢ – '''semitenth''' – an interval of this size is around half the size of a minor tenth (i. e., an octave plus a minor third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).
 ** The term '''cocytic''' was proposed by [[Inthar]], and is carried on with by [[Flora Canou]]<ref>Flora Canou criticizes ''semisixth'' and ''semitenth'' as they fail to make clear whether the interval to be split is major or minor, and prefers ''naiadic'' and ''cocytic''.</ref>.
 * 940¢–960¢ – '''semitwelfth''' – an interval of this size is around half the size of a perfect twelfth (i.e. a compound perfect fifth, or tritave). All even [[edt]]s have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.
+** The term '''ouranic''' (by analogy with chthonic, and to match with the other terms) is proposed by [[User:Kaiveran|Kaiveran]].
-This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi".
+This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi". In particular, since these intervals tend to be very well represented by [[Pergen|pergens]] that divide an instance of prime 3 into 2(''n'') parts, we can easily repurpose [[24edo#Quartertone Accidentals|quartertone accidentals]] to represent them, as long as we define our "half-sharps" or "half-flats" to be precisely half of a chromatic semitone (that is, "7/2 fifths" up or down the generator chain). With this in mind, we get the following notational identities for our interseptimals, with the simplest one listed first:
-By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now. A key difference is that the tritone is intermediate between two septimal ratios separated by a jubilisma ([[50/49]]), whereas the other interseptimal ranges listed above are between two septimal ratios separated by a slendro diesis ([[49/48]]).
+* semifourth/chthonic = semi-augmented second (+11/2), semi-diminished third (-13/2)
+* semisixth/naiadic = semi-diminished fourth (-9/2), semi-augmented third (+15/2)
+* semitenth/cocytic = semi-augmented fifth (+9/2), semi-diminished sixth (-15/2)
+* semitwelfth/ouranic = semi-diminished seventh (-11/2), semi-augmented sixth (+13/2)
+While this does not give the interseptimals a single distinct ''notational'' name, it does reflect their ambiguity and flexibility with regards to the surrounding interval categories that many are so fond of. Furthermore, as both identities are exactly 12 notational fifths apart (i.e a direct analogue of the [[Pythagorean comma]]), composers can use a mechanism similar to the [[Color notation|"po and qu" of Color Notation]], or the plus and minus accidentals (+/-) proposed in [[Rational Comma Notation (RCN)|Rational Comma Notation]], to freely switch between the two identities.
+By analogy with the "semi" names, the tritone could also be called a semioctave, although the term tritone is so well-established (and so well represented by an unsplit 3-limit) that there seems little reason to change it now. A key difference is that the tritone is intermediate between two septimal ratios separated by a jubilisma ([[50/49]]), whereas the other interseptimal ranges listed above are between two septimal ratios separated by a slendro diesis ([[49/48]]).
 == Examples ==