The Geekiest Thread Ever
(WARNING: please please don’t read this if you don’t like maths, and don’t read it if you have a low concentration span or if you didn’t enjoy reading "The Curious Incident Of The Dog In The Night-time" by Mark Haddon.)
I was playing tunes with a musician friend Chris last night and we started talking about jig rhythm and how it’s not really like how you see it written down. I’m posting this thread so I can direct Chris to it and he can print out what we worked out last night, and also for the benefit of anyone else who’s geeky enough to be interested.
We challenged ourselves to come up with a solution for representing jig rhythm more accurately in abc, sheetmusic and midi files, in other words, representing the note values so that the rhythm sounds reasonable when you play the midi file.
Our thinking went like this:
In a straight 6/8 rhythm the ratio between any group of 3 quavers is 1:1:1. If you play it through a midi file the rhythm sounds robotic (cut & paste the abc into the box @ http://www.concertina.net/tunes_convert.html and play the midi file):
T: Kesh, The
GAG GAB|ABA ABd|edd gdd|edB dBA|
GAG GAB|ABA ABd|edd gdB|1 AGF G3:|2 AGF G2A||
|:BAB dBd|ege dBG|BAB dBG|ABA AGA|
BAB dBd|ege dBd|gfg aga|1 bgf g2A:|2 bgf g3||
Basically the issue is with the 1st two notes of any group of three. We want the 1st to be slightly longer than the 2nd, but the 3rd to stay as it is. If you divide each quaver into 4, then the note value ratios of the straight rhythm would be 4:4:4, and the values of a dotted rhythm would be (6:2:4)/2 = 3:1:2. However, if you dot the rhythm with ">", that makes the 1st note 3 times longer than the 2nd, and it’s a bit too much, and the rhythm limps too much and doesn’t flow as it should:
T: Kesh, The
G>AG G>AB|A>BA A>Bd|e>dd g>dd|e>dB d>BA|
G>AG G>AB|A>BA A>Bd|e>dd g>dB|1 A>GF G3:|2 A>GF G2A||
|:B>AB d>Bd|e>ge d>BG|B>AB d>BG|A>BA A>GA|
B>AB d>Bd|e>ge d>Bd|g>fg a>ga|1 b>gf g2A:|2 b>gf g3||
So then we tried a ratio that was exactly halfway between the two. Again, if each quaver were divided into 4, then you can represent a "halfway inbetween" rhythm as 5:3:4. This sounds much better and flows nicely. Unfortunately, in order to be able to represent it properly in sheetmusic you have to write it in a time signature of 24/16 or 24/32, and the tunotron can’t cope with it, so you have to leave out the M and L fields from the headers so that it defaults to 4/4 and then just alter the Q field (tempo) so that it plays the midi ridiculously fast:
T: Kesh, The
G5A3G4 G5A3B4|A5B3A4 A5B3d4|e5d3d4 g5d3d4|e5d3B4 d5B3A4|
G5A3G4 G5A3B4|A5B3A4 A5B3d4|e5d3d4 g5d3B4|1 A5G3F4 G12:|2 A5G3F4 G8A4||
|:B5A3B4 d5B3d4|e5g3e4 d5B3G4|B5A3B4 d5B3G4|A5B3A4 A5G3A4|
B5A3B4 d5B3d4|e5g3e4 d5B3d4|g5f3g4 a5g3a4|1 b5g3f4 g8A4:|2 b5g3f4 g12||
That’s as far as Chris and I got with this last night, and then this morning I lay in bed thinking about it, and wondered what would happen if you made the ratio between the 1st two notes 2:1 instead of 1:1, 3:1 or 5:3. If you’re dividing each quaver into 4, then it’s basically (4*2)/3 = 2.666 recurring, so your ratio is 5.333:2.666:4 and if you multiply so that you get whole numbers for your ratio, you get 16:8:12 and then keep halving it you eventually get 4:2:3. This looks okay on a page of sheetmusic because it means that instead of a group of 3 quavers, you’d have a quaver followed by a semiquaver followed by a dotted semiquaver, or if you wanted twice the note values, a crotchet followed by a quaver followed by a dotted quaver. However, yet again, tunotron can’t cope with 18/16 or 18/32 so you have to default to 4/4 and up the tempo. The midi plays it okay, but it sounds slightly too limping for my ear, and I decided I preferred the 5:3:4. I altered the Q field appropriately so that it plays at the same speed as the others.
T: Kesh, The
G4A2G3 G4A2B3|A4B2A3 A4B2d3|e4d2d3 g4d2d3|e4d2B3 d4B2A3|
G4A2G3 G4A2B3|A4B2A3 A4B2d3|e4d2d3 g4d2B3|1 A4G2F3 G6D3:|2 A4G2F3 G6A3||
|:B4A2B3 d4B2d3|e2f2g2e3 d4B2G3|B4A2B3 d4B2G3|A4B2A3 A4G2A3|
B4A2B3 d4B2d3|e2f2g2e3 d4B2d3|g4f2g3 a4g2a3|1 b4g2f3 g6A3:|2 b4g2f3 g9||
So after all that, my question is, which sounds right to your ear, 4:2:3 or 5:3:4?