Talk:Chain-of-fifths notation: Difference between revisions

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: Btw it's never dictated that only double sharp to double flat should be used. Without higher-order sharp/flats, larger edos are very limited. 26edo, for example, requires Gx to Abb to access every note in the key of C major. Now modulate to any key with more than three accidentals and boom. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:15, 15 November 2020 (UTC)

:: For the record, I have made a two-ring circle chart for 24edo before, and I will say that I have a few tricks for positioning the additional rings relative to one another. If your main ring starts with C-Natural, and F-Demisharp and G-Demiflat are both on the same secondary ring, then the secondary ring is positioned so that F-Demisharp and G-Demiflat are the same distance from C-Natural. However, if your main ring starts with C-Natural, and F-Demisharp and G-Demiflat are on two separate rings, then the two separate secondary rings are perhaps best aligned with the primary ring so that F-Demisharp, C-Natural and G-Demiflat form a straight line. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 13:18, 15 November 2020 (UTC)

== Sufficient condition ==

The decisive point for the usability of this notation is, that the representations of octave and fifth are relatively prime. I'd like to introduce this without making the article to a mathematical text, maybe there is somebody willing to help. I also wonder if the precision of the fifth representation is relevant at all. This would open the discussion about really interesting cases like [[23edo]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:13, 15 November 2020 (UTC)

: Inaccuracy of the fifth doesn't technically invalidate the system. It only has to do with how much sense it makes. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 17:55, 15 November 2020 (UTC)

:: Above condition seemed not sufficient to me from a practical standpoint where the relevant intervals (whole tone, semitone, chroma) should have a positive size. I updated the article accordingly. What do you think? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:33, 15 November 2020 (UTC)

== Background of this article ==

When listening to (and reading in) the [https://youtu.be/rivfU8Rw4IM Scherzo in 26 EDO for Oboe, Horn, and Organ], I (used to the sight-reading of classical music) observed a strange relation between notation and voice leading. The I read the description that (emphasis mine)

: ''The notation is '''normal circle of fifths notation''', except the fifths are 15/26th of an octave, about 10 cents flat of just. This means that sharps and flats raise and lower notes by a little less than a quartertone.''

So I thought it might be worthwhile to shed a little more light on the matter. I already knew this notation from 17, 19 and 31edo, but I hadn't yet examined when exactly you can and cannot use it. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:20, 15 November 2020 (UTC)

== Spelling ==

What is the correct lemma? Is it correct to place dashes between the first tree words? Thanks in advance for your help! --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:23, 15 November 2020 (UTC)

: I suppose the current lemma is correct. Hyphens, not dashes. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 17:55, 15 November 2020 (UTC)

@@ Line 6: / Line 6: @@
 : Btw it's never dictated that only double sharp to double flat should be used. Without higher-order sharp/flats, larger edos are very limited. 26edo, for example, requires Gx to Abb to access every note in the key of C major. Now modulate to any key with more than three accidentals and boom. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:15, 15 November 2020 (UTC)
+:: For the record, I have made a two-ring circle chart for 24edo before, and I will say that I have a few tricks for positioning the additional rings relative to one another.  If your main ring starts with C-Natural, and F-Demisharp and G-Demiflat are both on the same secondary ring, then the secondary ring is positioned so that F-Demisharp and G-Demiflat are the same distance from C-Natural.  However, if your main ring starts with C-Natural, and F-Demisharp and G-Demiflat are on two separate rings, then the two separate secondary rings are perhaps best aligned with the primary ring so that F-Demisharp, C-Natural and G-Demiflat form a straight line. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 13:18, 15 November 2020 (UTC)
 == Sufficient condition ==
 The decisive point for the usability of this notation is, that the representations of octave and fifth are relatively prime. I'd like to introduce this without making the article to a mathematical text, maybe there is somebody willing to help. I also wonder if the precision of the fifth representation is relevant at all. This would open the discussion about really interesting cases like [[23edo]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:13, 15 November 2020 (UTC)
+: Inaccuracy of the fifth doesn't technically invalidate the system. It only has to do with how much sense it makes. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 17:55, 15 November 2020 (UTC)
+:: Above condition seemed not sufficient to me from a practical standpoint where the relevant intervals (whole tone, semitone, chroma) should have a positive size. I updated the article accordingly. What do you think? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:33, 15 November 2020 (UTC)
+== Background of this article ==
+When listening to (and reading in) the [https://youtu.be/rivfU8Rw4IM Scherzo in 26 EDO for Oboe, Horn, and Organ], I (used to the sight-reading of classical music) observed a strange relation between notation and voice leading. The I read the description that (emphasis mine)
+: ''The notation is '''normal circle of fifths notation''', except the fifths are 15/26th of an octave, about 10 cents flat of just. This means that sharps and flats raise and lower notes by a little less than a quartertone.''
+So I thought it might be worthwhile to shed a little more light on the matter. I already knew this notation from 17, 19 and 31edo, but I hadn't yet examined when exactly you can and cannot use it. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:20, 15 November 2020 (UTC)
+== Spelling ==
+What is the correct lemma? Is it correct to place dashes between the first tree words? Thanks in advance for your help! --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:23, 15 November 2020 (UTC)
+: I suppose the current lemma is correct. Hyphens, not dashes. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 17:55, 15 November 2020 (UTC)