Scientists (linguists/anthropologists?) are saying that musical ability in humans developed as a consequence of language acquisition. I took the relationship seriously and mapped the chart I have for frequency of tone occurrences onto another chart I have for frequency of letters in English to use sentences to generate melodic series and mapped to another chart for frequency of rhythms.
The tone occurrences I gave before are 1534726 although there is an equal chance of there being a 5 or a 3 etc... Other notes are also like this but I won’t cover them here. Since there is an equal chance, you don’t need to roll dice to determine which one, just assign it a letter and that’s good enough.
The order of letters in English based on frequency are etaoinshrdlcumwfgy....This is more than you need to assign each letter a note. High frequency letters are paired with high frequency notes.
e t a o i n s h r d l c u m w f g y...
1 5 3 4 7 2 6
I also applied techniques I had discovered from studying computer music composition which increases the likelihood that the most frequent pitches; 1, 5, 3 etc... (in that order) will occur on the down beat by a factor of 3, on beat 3 by a factor of 2 and on beats 2 and 4 by a factor of 1. The off beats are not affected.
It means that if a note falling on the down beat currently is the pitch 2, then you have to move it back three places on my mapped chart, which changes it to pitch 3, a more important pitch.
After contemplating the bad results, I thought about how musical phrases rhyme like poetry so tried to generate some music from a book of 100 famous English poems. The results were also less than stellar. Then I remembered something I read about infant vocalizations. Babies universally around the world repeat basic syllables such as mama, dada, papa, doodoo, poopoo, peepee, weewee, kaka and don’t forget bodacious tata’s, yabadabadoo and scoobydoobydoo.
Repetition is a basic principle in music but most modern languages are far from these primal roots. (Although I mentioned before that Bahasa Indonesian uses the repetition of a word to indicate the plural.) The rhymes in the book of famous English poems occur too infrequently at the end of long sentences to be very musical so I started looking to song lyrics especially short repeated things which might be the correct length for generating interesting musical phrases.
So, I generated some melodies from;
Get up stand up. Stand up for your right. Get up stand up. Don’t give up the fight.
We’re jammin, jammin, and I hope you like jammin too.
Holy Mount Zion, Holy Mount Zion, jah siteth in mount Zion.
No woman no cry. No woman no cry.
Sunday Bloody Sunday, Sunday Bloody Sunday Sunday Bloody Sunday
I want to run. I want to hide. I want to tear down the walls that hold me inside.
I wait for you with or without you.
The results are much better but I keep running across the tritone leap from F to B or from B to F. It’s not frequent though so some of the phrases are quite nice.
To avoid problems having to do with voice leading, I experimented with dropping the 2 and 6 from the equation and that leads to a greater frequency of usable melodies but will lean toward the boring side if I also apply the rule about important pitches on the downbeat because then there are just too many repeats of pitches 1, 5 and 3.
All of this ignores rules about how notes move which is a whole other thing.
I have the quarter note being the most frequent, two eighth notes being the second most frequent, a dotted eighth note followed by a sixteenth the third most frequent etc...
In the beginning I had included dotted eighth notes paired with an eighth but that was creating long boring pauses. I also had included 4 sixteenths which seemed to interrupt the flow, so that was also removed.
Now the only fairly long pause occurs, for example, after a note falling on the "e of 1" (as in 1 e & a) followed by a note falling on the "a of 2" etc...
After I’ve circled the parts of the phrase up to the point where it’s not working then I can make the last note longer which is outside the delineated scheme.
Composing music is like an ant looking for food. In the beginning it’s fairly random but with more information the search becomes more focused.
Have a look at this link for rules concerning melodic motion/voice leading especially charts 5 and 8 along with the first paragraph in the chapter called Types of Melodic Intervals. There’s also some cool charts 75% of the way down the page. The article also talks about note length as well as what to do with pitches on either side of a leap.
As far as an example of a pitch series derived from letters in a lyric here is the resulting series from Got a Black Magic Woman, Got a Black Magic Woman etc... Dots indicate holding the note for the indicated number of pulsations. Lower case letters indicate the octave and underlined notes indicate the lower octave
Concerning my second post one could map the order of common interval motion to common letters which might look something like;
The resulting intervals derived from, "Get up. Stand up. Stand up for your right." results in M2 Unison P5 Unison m2 M3 m7 P5 Unison m2 M3 m7 P4 Oct P4 Oct Oct m3 M6 Unison. The tritone has been left out. The octaves also look like they need to be left out. The problem now is in acquiring a guiding principle delineating which direction each interval should move.
We should also assign more letters to the interval of a major second since it occurs with significantly greater frequency. I suspect a minimum of between 6 and 12 letters.
Note durations could be based on interval sizes preceding and following.
I came up with three really good tunes using these methods. I only went through a handful of nonsense to find them after a night and the next day of fiddling. But I’ve altered the interval method.
After looking more closely at the chart of melodic interval motion I’ve remapped the intervals so that intervals which occur significantly more frequently get more letters. With this one, the octave does’t need to be eliminated since it is now more infrequent.
e t a o i n s.........h r d l...c u m.....wf......g.......y.......p......b.......v.........k......j......x
As I said before, this last method probably doesn’t need any special kind of repeating short text. Just use your favorite book, play through the results and then use the best, discarding the rest.
It does make for some interesting decision trees on the staff.
I was worried about finding a rule for deciding which direction an interval should go, either ascending or descending but mostly that is decided for you like this;
If you’ve got an interval of a major second you’re supposed to use, then if you’re assuming the male vocal (mocal?Hehe) range/tessitura and you’re starting at the bottom of that range on C then obviously you must ascend to D. Also, if you’re trying to stay diatonic then the Bb below C, if it were allowed, still would not be an option since its not diatonic.
But, if you’re on G then you can either go to the A above or the F below. However, it’s best not to decide just yet and keep track of where each line goes because there may be some situation where one of the lines terminates because there is an interval combination that won’t work for that line such as if you’re on D and the interval you should travel from there is a Major third. There is no diatonic major third from D (If you’re in C Major) so then you’d have to abandon that line.
I actually came up with a really cool thing when all the lines terminated because of a similar problem. I just used the non diatonic interval on the longest line and then continued from there. It created a Bb in C Major which sounded like a folk melody in the style of Led Zeppelin’s tune that goes "Shoot straighter than before. Dance in the dark of night sing to the morning light...." I can’t remember the name.
Anyway, the other way to decide if you’ve got several good lines to choose from is to give priorities to lines that contain the most number of 1s, 5s, and 3s in that order etc... It was really kind of fun making these babies.
Now I’ve got several ways to come up with new tunes rapidly; traditional transformations on existing melodies, note frequencies mapped to the freqeuncy of English letters which requires short texts and the frequency of intervals mapped to English letters which has no length requirements. Still working on mapping the rhythms although I’ve got something that kind of works already. The chart on the link I gave really opened my eyes to how that should look/sound. Still ruminating.
One of the things I learned from my little experiment is that using language as a source will yield
melodic and rhythmic combinations which are common to English because of common letter combinations and common words such as "the" etc... Many possible and perhaps good combinations will never arise because things like "q" followed by "a" don’t exist.
To overcome the bias of English to common letter/word combinations and to overcome the bottle-neck of using dice perhaps cards or tiles would be best.
There are inherently unavoidable problems with these methods though that we need to be aware of. And will also exist in any computer program.
The pitch frequency method has the problem of not placing important pitches on important beats and creating too frequently the tritone leap. Even worse, it does not frequently enough create motion by step or third.
So, we could use the interval method to evaluate the fitness of anything produced by the pitch frequency method. If the ratio of seconds to other intervals is not within a certain parameter...something like 80% of the ideal, then we can probably say with some confidence that it’s not a good melody without even listening to it. If it’s got a lot of 5ths, 6ths and 7ths and only a couple of seconds and thirds, it’ probably shite.
The problem with the INTERVAL method is that it gets trapped in a back and fourth motion, for example going between G and A or F when it’s calling for all those Major seconds. It also does not place important pitches on important beats. Anything created with this method should be evaluated for fitness by the rules of the first method by simply counting notes and if there aren’t enough 1s, 5s and 3s not being anywhere near the ballpark of the called for parameter, then what the interval method has produced is also probably shite.
It’s not hit and miss if you do this step before listening. Chucking the probable shite into the circular file.
Both methods also create lines longer than four measures without real coherent motifs. Although the first method can get closer if using short rhyming text.
The problem with the rhythm method (there’s a joke in here somewhere) is that it creates a string of unrelated rhythms without much underlying structure. There are repeating rhythms and there are repeating melodic series if using language but they usually don’t line up together, which is O.K. but not the whole ballgame. That is something that also needs to happen that these methods just can’t accommodate. So you’re left with the musical cortex on that count.
So YOU repeat or sequence something YOU find interesting. Hey, you’re a composer now. Wow!
In order to improve the pitch method you’d need tiles or cards. 10 tiles for C, 9 tiles for E, 9 tiles for G, 8 tiles for B, 7 tiles for A, and 7 tiles for D.
Perhaps for the interval method you’d need 1 tile for M7, 1 tile for m7, 1 tile for m6 and 1 tile for the Octave. Then 2 tiles for M6, 3 tiles for the P5, 4 for M3, 5 for m3, 10 tiles for P4, 15 tiles for m2, 20 tiles for the unison and 35 tiles for the M2.
Rhythms are the killer. I’ve got a chart favoring eighth notes by having 10 "pairs of eighth notes" but only one "sixteenth note rest followed by two sixteenth notes followed by another sixteenth note rest" which occurs very infrequently. The total chart has 97 items (9 dotted eighths followed by sixteenths etc...)
One of the things you realize even after only a cursory look at songbooks (I’ve currently got Mariah Carey, U2, Sting, Santana, Bob Marley and George Benson) is that any rhythm can be repeated up to 32 and even 64 times, even a normally very infrequent rhythm. So, there can’t just be one of those infrequent rhythms because we may need to use it 64 times. So it means if we’re going to have enough of the most infrequent rhythm just in case we want to use it that much, we need more items in the list. 97 multiplied by 64 is 6, 008!!!
It would probably take me a couple of weeks to make a bag full of that many tiles with the correct rhythms written on them and I’m not inclined to do it. And I’m still not sure about the weighting. There may need to be exponentially more instances of 2 eighth notes. I’m sure of my melody and interval charts but my current rhythm chart is just an approximation. It was difficult to understand the data because it was recorded in seconds and milliseconds not in eighths, dotted eighths, eighth note triplets etc...
Anyway, the goal is to get to the gems faster, not wade through tons of crap. So, how to focus the search for viable rhythms? Of course one way is to use the existing melodic rhythms from songs we already like. But thats not in the spirit of what I’ve been trying to do here.
There is a similar issue with the interval method. Right now there is only the possibility of having 4 major thirds and 5 minor thirds. Having more than that is within the realm of possibility so the number of tiles may have to be doubled/tripled etc... in order to create that ability.
I just realized that I’ve been miscalculating the number of basic rhythms. It’s closer to 127 basic cells. Now its looking like there are over 186, 000 possible rhythm combinations over 8 beats in 2 measures.
Also, the reason the scholarly journal article measures the rhythms in seconds is because when looking at the sheet music, some common rhythm cells are tied to previous and/or subsequent cells. The cells that tie over cannot even be ranked because you would have to know the cell that it ties to in order to determine if the tied note was short or long. Since it can tie to anything, it cannot be determined how it ranks.
I was able to find some useful information about the frequency of stress patterns in English lyrics. First off, short words are more common than longer words.
There are 995 words that have two syllables where the second syllable is stressed and occur 24, 558 times out of a million words and have a weighted frequency of 19.98%. This is the most frequent stress pattern.
There are 3, 624 words that have two syllables where the first syllable is stressed and occur 67, 693 times out of a million words and have a weighted frequency of 18.08.
These first two are by far the most frequent.
2, 619 words account for three syllables with the stress falling on the first beat and occur 24, 558 times out of a million and have a weight of 9.38.
A three syllable word with the second syllable accented occurs 15, 278 times out of a million words and has a weighted frequency of 10.12. This is the third most common stress pattern.
All of the rest of the words have much fewer instances.
A three syllable word with the third syllable accented occurs only 1, 398 times and has a weighted frequency of 3.79.
A four syllable word with the first syllable accented occurs only 3, 549 times out of a million and has a frequency of 7.14.
A four syllable word with the second syllable stressed occurs 9, 014 times and has a weighted frequency of 6.77. (This is the ONLY kind of word longer than three syllables that occurs in Mariah Carey’s 1 hits. That word is eMOtional. I guess it better be important.)
A four syllable word with stress on the third syllable occurs 6, 831 times and is weighted at 6.72.
A four syllable word with stress on the fourth beat occurs 97 times out of a million words. NOT MUCH!!! and is weighted at 2.62.
Five syllable words aren’t even in the ballpark.
Other useful information is that 90% of all content words such as nouns and pronouns (not verbs, adjectives or adverbs) begin with stressed syllables. A greater frequency of verbs have the second aka last syllable stressed.
I put some new items up on myspace within pics in the folder called Music Composition at http://viewmorepics.myspace.com/index.cf....albumId=1823777
Of course you have to log in first to see them.
It's got the basic rhythm cells from my journal along with the rhythm schemes (called the Scheme Pool on my Music Composition Flow Chart which is also there).
There is also a chart of the first and second measure's possible rhythm schemes where you would plug in the basic cells. There is a second chart for the the placement of anacrussis rhythms in a "second measure".
The thing to look at on my current composition flow chart is how the notes branch on the staff under the "Interval Series" heading. Notice how paths are chosen based on their weight aka predominance of pitches 1,5,3etc...
One of the things I came up with was to use a fit melody as guide tones for subsequent composition. But even after all this work, expert systems are still supposed to be better. That's where you input a melody and perform continuing transformations on it to come up with new material. That's in the lower right hand corner of my Music Composition Flow Chart but just roughed in. There wasn't enough space.
The chart I used a while back which shows simultaneous Top-Down and Bottom-Up decisions is there also as well as rhythms for half of all my favorite drum kit, bass, keyboard and guitar rhythms, as well as a chart of Middle Eastern, Latin, Afro-Cuban and Indonesian hand drum rhythms.
Something for everyone.
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