SeventeenTheory: Difference between revisions

Line 7:

and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.

[[File:17fifths|alt=17fifths|17fifths]]

[[File:17fifths-withext.jpg|alt=17fifths|17fifths]]

The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)

Line 13:

So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):

[[File:17versus12names-withext.jpg|alt=17versus12names|17versus12names]]

Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." 17 shares this last property with the quartertone scale (24-EDO).

Line 19:

If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):

[[File:17versus12cents|alt=17versus12cents|17versus12cents]]

[[File:17versus12cents-withext.jpg|alt=17versus12cents|17versus12cents]]

and in pitch/interval classes:

[[File:17versus12pcs-withext.jpg|alt=17versus12pcs|17versus12pcs]]

@@ Line 7: / Line 7: @@
 and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.
-[[File:17fifths|alt=17fifths|17fifths]]
+[[File:17fifths-withext.jpg|alt=17fifths|17fifths]]
 The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)
@@ Line 13: / Line 13: @@
 So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):
-[[File:17versus12names|alt=17versus12names|1x1px|17versus12names]][[File:17versus12names|alt=17versus12names|17versus12names]]
+[[File:17versus12names-withext.jpg|alt=17versus12names|17versus12names]]
 Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." 17 shares this last property with the quartertone scale (24-EDO).
@@ Line 19: / Line 19: @@
 If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):
-[[File:17versus12cents|alt=17versus12cents|17versus12cents]]
+[[File:17versus12cents-withext.jpg|alt=17versus12cents|17versus12cents]]
 and in pitch/interval classes:
-[[File:17versus12pcs|alt=17versus12pcs|17versus12pcs]][[File:17versus12pcs|alt=17versus12pcs|1x1px|17versus12pcs]]
+[[File:17versus12pcs-withext.jpg|alt=17versus12pcs|17versus12pcs]]