Commandment 2) THOU SHALT KNOW AND LOVE THY BEAT.
The most important thing in music is rhythm, the most important thing to rhythm is the beat, and the most important thing to the beat is its steadiness.
I can play a familiar melody such as Mary Had a Little Lamb, and make it completely unrecognizable by radically changing the rhythm. However, it is still easily recognizable if it is played in a serial tone row, (maintaining the melodic shape while using large leaps and wild chromaticism) but keep the original rhythmic patterns.
There are two components to a secure sense of rhythm. First you must KNOW where in the score the beat falls. The beat can be any note value assigned as the primary rhythmic motive function. You must understand where in the score these beats occur.
The next part is the “Loving”. You must have a physical sense of the beat. There is no guessing allowed in the beat. Clap your hands, stomp your feet, jump up and down, tap a foot, tap a toe, count out loud; do something to physically feel the presence of the beat or pulse.
Now put these together. Know where you belong in the score as these beats you feel come by. No matter what, you must be where you belong! If your playing is controlled by a steady, known beat, with a thorough understanding as to where you belong in the score with the beat, you will have a secure rhythm. Failure will make your playing rhythmically unintelligible.
One of the things which intervallic music reading teaches us is the correlation between the arrangement of notes on the pages and physical act of reproducing the music on the piano. The movements we make in the act of playing are choreographed directly from the score, as the notes go up the page, we play higher on the keyboard and the shapes of chords are expressed by various and uniform hand shapes. There is a parallel understanding available to us in regards to rhythm.
Musical notation indicates proportional values; two of these equal one of those and three of these equal one of those. The most fundamental aspect of good rhythm is maintaining a steady pulse. The note value assigned to that pulse is irrelevant, the only thing which matters is deciding which note value will be assigned the pulse and keeping that pulse steady. The next step would be to understand which rhythmic signs are equal to two (or three) of our pulse and which signs are half the value.
As in note reading, the ability to name the notes has nothing to do with the ability to play the notes; naming is simply for the convenience of communication between people and with ourselves, the mastery of beat numbering and subdivision syllables will never yield effective rhythm. You can say all the right numbers and syllables, but if you speak them without any reference to the beat or pulse, this knowledge will not give you the correct rhythm. And again the numbers and syllables simply provide a means of identification and labeling and nothing else.
Learning to maintain a steady pulse is something which best begins with some type of larger motor gesture than we experience with simple finger movements. Finger movements are poor pulse keepers for many reasons but primarily it is often a different finger moving for each pulse which weakens the relationship between the movement and the pulse. I have often told my students I really didn’t care what they did, tap their foot, jump up and down, shout… just do something very noticeable. You have to feel the pulse to be aware of its steadiness. I understand, taping ones foot can be unsightly in a performance setting, but it is a very effective method for having a physical action, separate from playing, to keep a steady pulse. As the student matures the foot taping will diminish anyways, learning to feel a steady pulse is just too important not to find something for the student to do.
One of the advantages of foot taping is the built in subdivision. The top of the movement represents the half subdivision.
The most complex musical notations (with the exception of some very modern scores) can usually be broken down to simple 2:1 and 3:1 relationships. Even in the presence of 128th notes; they also have a simple 2:1 relationship to 64th notes. If you assigned the pulse to the 4 beamed 64th notes, the 5 beamed 128th notes take on the same rhythmic simplicity as quarter and eighth notes. As comfort and tempos increases it is a simple matter to move the pulse to the next values, the proportional relationships remain the same.
One of the most misunderstood aspects of rhythm is the meter, sometimes strangely called the “time signature”. The typical explanation for the meaning of the two number will often go like this: “X is the number of beats in a measure and Y gets the beat.” That is pretty worthless! Yes, this information may be partly true, but it doesn’t tell us what those two numbers mean. A more succinct and accurate was of express this information would be to say: ” There are X number of Y’s in a measure.” A perfect example of why the first expression is inaccurate can be found in most compound meters notated in 3/8, 6/8 and 9/8. We most commonly count these meters with the dotted quarter receiving the beat which is a value not present in the first explanation, though it seems to imply there should be.
But neither of these explanations tells us what it means. We should think back to the very origins of music. The original musical instrument was the human voice and we had metered poetry set to simple melodies. The most effective settings were those which fit best with the alternating patterns of accented and unaccented syllables and whose cadences matched the punctuation of the poetry. The meter reflects this poetic patterning. Each meter is made up of accented and unaccented beats, which when text is present, and well set, is reflected in the organization of each measure of music.
So back to our original idea. You must know and love your beat. You must know in the musical score the location of your beat. We can add to this in time the relative importance of that beat to all others based upon the meter of the music. And Love is a feeling, so you must feel your beat; it has to have a physical reality to you.
Trace decay vs. interference.
There are two schools of thinking regarding the cause of forgetting. The first, trace decay, came out of Ebbinghaus’s work. He showed that time was the primary cause of a loss of memory.
There have been other approaches to the question of memory and forgetting. Scientists such as F. C. Barlett used stories instead of word lists to look at the effect time had on memory. He would have subjects read brief stories and then test their recollection of those stories at various time intervals up to 6 months. Though Barlett initially set out his work as a criticism of Ebbinghaus , especially in his use of non-sense syllables; Barlett’s work showed similar types and degrees of memory loss as could be explained in Ebbinghaus’s work.
Another explanation for forgetting was developed in later years and that is the “interference theory”. Briefly, it states that material learned both before and after the target material interferes with the retention of the designated material. A typical example of this type of study would be the following: 3 groups of subjects, one learns the paired group of words A-B and C-D (car – dog and tree – road). The second learns A-B and A-C, and the third would learn just A-B. The groups would then be tested on their ability to accurately recall the various lists. The results typically were the A-B only group would do the best. The A-B and C-D group would do noticeably worse on their A-B list as well as their C-D lists. The A-B and A-C group though would do the worst over all. They would intermix their two lists. This is not unlike the problems we often encountered in repetitive sections in music where the repeated sections have slight variations. It is a common problem to intermix the sections, ultimately having trouble extracting one’s self from the section.
It is a common experience that repetition impacts memory. The more a passage is repeated on day 1 of practice, the better condition it is in when the next day’s work begins. But how much practice does it require to maintain “X” amount of material? How much retention is gain for each repetition? At what point does the diminishing returns outweigh the value of the additional retention?
Ebbinghaus did a series of double tests to find the answer to these questions. He learned 6 series of 16 syllable lists, repeating each list either 8, 16, 24, 32, 42, 53, or 64 times. The next day he repeated the tests, the results were remarkably consistent across all levels of study. Through the course of his study he found that it took an average of 31 repetitions to learn a list of 16 syllables. So the lists learned 8, 16, and 24 times were not learned to his standard of error free reproduction. However the 42, 53, and 64 repetition lists were significantly over studied for his standard.
The next day he relearned the lists and recorded the amount of repetitions and time it took to learn each list to his standard. The results across all lists was an average savings of 12.7 seconds with each test set of 6 lists falling within the narrow range of 12 and 13.7 seconds saved. The average savings per list (out of the 6) was 2.1 seconds and the average time it took to read a list was 6.6 – 6.8 seconds. On average, across the entire exercise he experienced a savings of one repetition for every three repetitions done the preceding day.
And as for the question of diminishing returns, the greatest savings occurred at the 42 repetition level. Some of this he attributed to: “An increase of the readings used for the first learning beyond 64 repetitions proved impracticable, at least for six series of this length. For with this number each test requires about 3/4 of an hour, and toward the end of this time exhaustion, headache, and other symptoms were often felt which would have complicated the complicated(sic) (I think the translation should have said “results”) of the test if the number of repetitions had been increased.”
So when your students asks “Do I really need to play it again????” You can say quite confidently: “Yes, Dr. Ebbinhaus says do it 42 times!” It is indeed true that repetition is the mother of all learning. In coming articles we will look at the effect of thoughtful repetition.
The first area of memorization Ebbinghaus looked at in his dissertation was the effect of the length of the list of non-sense syllables he learned. His first observation was that lists of 7 or fewer required just one reading to be reproducible by memory. This observation is later verified by other researchers as the usual size of the short term memory. The short term memory is often described as having the capacity of 5 – 7 “chunks” of information and lasting no more than 15 seconds.
As the number of syllables increased to 12 the average number of repetitions required for the first errorless reproduction increased to 16.6. Adding just 4 more syllables added nearly 14 more repetitions. The next addition of 8 syllables (24 total) added another 14 repetitions and the final addition of 15 syllables (39 total) added only 11 (55 total) repetitions.
Number of syllables/ Number of repetitions necessary for first errorless reproduction (exclusive of it)
in a series
7 / 1 12 / 16.6 16 / 30.0 24 / 44.0 39 / 55.0
While we could say that if the final group of 39 syllables had been learned in groups of 7 or fewer it would have taken far less effort to get to the first errorless reproduction, we will see in later parts of his dissertation the effect of practice on retention. Retention is the only thing which matters after all.
One of the very first studies in human memory applying scientific processes was published by Hermann Ebbinghaus in 1885 with the essay Uber das Dedachtniss (Memory, A Contribution to Experimental Psychology (English translation title)). Ebbinghaus used himself as the subject in his experiments in learning lists of non-sense words (from a list of 2300 words). Based upon his experiments he described three important theories which can be helpful today in understanding the learning process. They are: 1) interference theory in which earlier learning is covered over by later learning, 2) trace decay is where images or knowledge suffers changes which alter its character, 3) forgetting involves a “crumbling” of various components as opposed to a general obscuring.
Ebbinghaus used himself as the subject of his experiments because he wanted complete control of motivation factors and an awareness of any possible distractions from his experiments. After creating lists of three-letter non-sense words he would read them out loud at a steady rate of 150 per minute and consistent intonation usually emphasizing every fourth. He would continue to read the lists with periodic tests until he was able to reproduce the list without hesitation, a perfect reproduction of the material. He also controlled for external factors such as time of day and personal levels of distractedness. After doing thousands of tests, he performed statistical analysis on his results.
The ability of humans to store information is enormous, however the rate of retention, ability to accurately recall, and rate of forgetting varies greatly and is the area of greatest concern when we look at learning methods. Ebbinghaus examined the rate of rote learning he experienced with his lists. One question he sought an answer to was the effect of repetition on the rate of learning. What was the relationship between practice (repetitions) and learning; how did more practice effect the outcome? What happens when a list was learned a second time; what was the residual impact of initial work on subsequent efforts?
To find the answer to these and many other types of questions he employed lists of non-sense words and practiced them for 8, 16, 24, 32, 42, 53, or 64 repetitions. He would then relearn these lists the next day measure the results. “Learned” is defined as one successful performance of the material by memory. The use of non-sense words was to reduce or eliminate any associative characteristics with meaningful words. The purpose of the study was to look at the rote learning of non-associative and non-sense syllables.
After looking at the rates of learning 16 syllable sequences with 8, 16, 24, 32, 42, 53, and 64 reps he found an average saving of 12 seconds in the re-learning after 24 hours for each repetition. A single repetition of about 7 seconds of work saved 12 seconds of work the next day.
Ebbinghaus also looked at the rate of forgetting (his famous “forgetting curve). A 13 syllable list was re-learned after a 20 min break through 30 day interval. The forgetting metric is the difference between the numbers of reps for the first trial minus the number for the second trial expressed as a percentage of the first trial. The retention rate was found to be after 1/3 hr 60%, 1 hr 45%, 8 hr 35%, 24 hr 34%, 2 days 30%, 5 days 28%, and 30 days 25%. Most of the forgetting occurred within the first 24 hours and even after 30 days enough memory remained to reduce the time it took to relearn the list by 25%.
Ebbinghaus also looked at the position a word appeared in the list and the consequences of its serial position on retention and re-learning. There are two functions he found present. Recency is the recall of recently learned material and primacy is the recall of the first learned. First studied material benefits from the lack of conflicting material and increased rehearsal.
This is a study of purely rote learning of non-associative/nonsense information. It doesn’t show the retention of associative or meaningful material. It does however provide a baseline of learning. Rote learning is the most mechanical learning process and represents learning at its most basic level.
Ebbinghaus showed, through his careful testing of his most reliable subject, himself, a model of learning which still informs our thinking nearly 150 years later. We see the relationship between learning effort and forgetting and learning effort and retention.
In upcoming articles I will look at several aspects of his work which I found helpful in understanding some of the basics of human memory which were relevant to my study at the piano. I know that some of you may find this stuff as dry as dead bones, but I hope at least a few may share some of the AHAAA moments I had as I learned something about how I learn.
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