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| disinventing the wheel > 016 Beats (continued) |
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| Posted: Jun.30.2005 @ 1:46 pm | Lasted edited: Mar.07.2006 @ 10:22 pm |
| The two Flemish musicologists quoted in the previous blog-entry
compacted an impressive amount of BPM data, gathered from radio shows,
BPM lists and recorded music and the result was that the most used BPM
value lays around IOI 450ms (disregarding musical style or genre). This
peak has a steeper decline towards 400ms and a less steeper one towards
600ms, so that both 300ms and 700ms IOI values represent less than 1/3
of the peak magnitude. This only confirms the fact that real-music "beat-specific" IOIs range roughly between 350ms and 650ms. As a curious fact, the only musical genre in which these averages are poignantly not complied with is jazz music, where the two musicologists spotted a huge peak at around 300ms. Now if you go back to blog-entry 007 you will see why: 300ms (around) was there defined as the fastest "swing-able pace". Well, jazz players were simply unable not to treat themselves with it. A lot and in big chunks! Therefore IOI 450ms represents a strong benchmark in the real-music world. The two Flemish musicologists consider that around this value our central nevous system is designed to resonate (or: get entrained) like any other natural damped resonating oscillator (ask a professor of Physics for definition) and this is precisely why at around this pace we start tapping feet and bang heads llike lunatics. |
| disinventing the wheel > 015 DJs love these beats! |
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| Posted: Jun.30.2005 @ 10:31 am |
| If you have ever been a house music fan or a clubbing-freak, you are
already very familiar with the "beats" here discussed, for you have
banged your head a lot at these rates (i.e. 450, 500, 550 and 600ms).
Check BPM charts online and you'll notice that about 75% of the entries
refer to beats between 380 and 620ms (i.e. roughly between 160 and 100
BPM). (Before going further, I must acknowledge the fact that for this and the following blog-entries I relied on information gathered from: Leon van Noorden & Dirk Moelants (authors), Resonance in Perception of Musical Pulse, Journal of New Music Research, 28, March 1999, Swets & Zeitlinger Publishers, The Netherlands, pag. 43-66.) Getting to discriminate and memorize these four isotempi is really hard. I "live" with them since long but I still mistake one for another once in a while. To make things worse, I was unable to devise any tricks (like the legatissiomo performance for IOIs from 200 to 350ms or like the zig-zag test for IOIs around 400-450ms). If you have a friend who is a professional DJ and if he/she happens to be able to tell these beat-rates by heart, ask him/her how he/she managed to acquire this competence – and pass this information to me as well! A good training exercise for these paces (and others as well) is to add to your iTunes application an extension called "iTunes-BPM" and start guessing IOI values. The application is free and you may download it here. As it only displays BPM values and not millisecond-measured IOIs, keep at hand a conversion-list (i.e. BPM to millisecond). Make it as comprehensive as possible: that is, convert to milliseconds all BPM values from 30 to 1200, although you'll probably never have to refer to such extreme values. This way, in time, you will start recognizing IOI values that fall in between our 50ms purely conventional grid (e.g. an IOI that seem to you as being close neither to 500ms nor to 550ms, but a middle value). |
| disinventing the wheel > 014 IOI around 400ms (continued) |
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| Posted: Jun.29.2005 @ 3:50 pm |
| As you have probably noticed, the zig-zag experiment leads us, in
principle, to a slower-than-IOI 400ms isotempo (i.e. 420-430ms). It
seems that the 50ms grid imposed, as a matter of convenience, at the
beginning of this blog, does not help us in this particular case. This
is why I used so many times in the previous entries the word "around" 400ms. Don't worry. If the perceptual approach towards musical time (that's what we study here, in case you didn't know) will have an evolution similar to the Western tuning system, such "adjustments" from the way our brain naturally processes discrete time will surely occur. Are you familiar with the major third on your piano? Well, that's a "wrong" interval, as the natural major third is different (i.e. bigger) and so are many other intervals tempered by Herr Bach 300 years ago. But as we now have no idea as to how this evolution will unfold, let us consider that, after IOI 350ms our 50ms grid should be temporarily enlarged to 75ms and, as a matter of consequence, our next isotempo to be learned corresponds well to the 420-430ms (350ms + 75ms = 425ms) value resulted from the zig-zag experiment. The magnification of the grid is a natural thing to do as the bigger the time-intervals to be considered are, the more difficult is for us to discriminate them accurately. For instance, imagine that you have to tell (cross my heart) that you can feel the difference between a 60 and a 65 minute long experience. The reason for this rests in the fact that our sensory experiences can be discriminated only if between them there exists at least a "just noticeable difference"-specific (JND) interval. The JND is a common place in psychology textbooks and, in the case of time perception, it may vary from 5% (also called the Weber fraction) and 15% in some cases. JND simply represents the minimum difference necessary for similar stimuli to be experienced as different. Now you can see that, if we keep going with the 50ms grid, at some point we shall have to discriminate IOI values (such as 1450ms and 1500ms) that are less then 5% apart (1450 + 5% = 1522; 1500 - 5% = 1425) and, thus, perceptually undiscernible. Despite all that, as educated temporal perception has its own ways, after some practice you will be able to discriminate both IOI 400ms and IOI 420-430ms as distinct isotempi. The same goes for IOI 450ms. Whenever unsure, proceed to the zig-zag test and compare its results to the isotempo you have to name: if the zig-zag isotempo is slower – you probably deal with a 400ms IOI, if faster – with a 450ms IOI. This way you will be able to discern and memorize three tightly spaced isotempi: 400, 420-430 and 450ms. |
| disinventing the wheel > 013 The zig-zag isotempo |
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| Posted: Jun.29.2005 @ 3:20 pm |
| IOI around 400ms was already described as the first fully-fledged "beat
specific" isotempo, as it was descibed as corresponding to the "first
sustainable rate of attention-shift" and the first pace that we can
imagine as a continuous row of thesis pulsations (like a 1/X bar). No psychology textbook helped me disentangle the reasons why our brain processes IOI 400ms (around) in this peculiar way – so I had to devise my own experiments. Whenever I felt unsure about producing with accuracy a IOI around 400ms isotempo (that used to happen long ago, rest assured), I submitted it to the zig-zag test: 
(Quoted from my article A Matter of Perspective) |
| disinventing the wheel > 012 The slowest "melody specific" isotempo |
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| Posted: Jun.29.2005 @ 2:42 pm |
| IOI 350ms took me little time to memorize as it is the slowest "melody
specific" isotempo. Whenever unsure, I used to compare it to IOI around 400ms
(i.e. corresponding to the fastest rate of sustainable attention shift
and the first fully-fledged "beat specific" isotempo). To my
perception, the difference between the two neighbouring isotempi is
immense so it's hard to miss it. Despite that, I accept that it is hard
to differentiate it when compared to IOI 300ms, as the "glueing" effort
in legatissimo performances (see previous blog-entry) is in both cases great. Whereas IOI 250ms is considered by scholars to be the borderline between holistic versus analytical brain-processing of neighbouring pulsations, IOI 350ms can be viewed as the borderline between "melody specific" and "beat specific" isotempi. There is no oddity to have a MM 170 (corresponding to IOI 350ms) mark on a musical score. As a matter of fact, classical metronomes display, as the fastest "beat specific" isotempo, the MM 200 mark, corresponding to IOI 300ms – that meaning that good old common-sense worked well before cognitive musicology and experimental psychology were invented. At IOI 250ms it becomes already hard to consider the specific pace a "beat-rate". At IOI 300ms also, but speed maniacs may consider it an option. At IOI 350ms we can view the specific pace as a kind of temporal mule (i.e. neither horse, nor donkey), meaning that we can imagine it as both melody-specific or beat-specific. Do not mistake the term "beat-specific" for that of "first sustainable rate of attention-shift" as the first refers to classical rhythm theory and encompasses IOI values from 300ms up to around 1500ms (look at a classical metronome) whereas the latter refers specifically to IOIs around 400ms. |
| disinventing the wheel > 011 IOI 250ms (continued) and 300ms |
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| Posted: Jun.29.2005 @ 10:33 am |
| As for the current topic (i.e. IOI 250ms), the best way to
memorize this isotempo is to consider that there are three isotempi
characterized by the fact that they are "melody specific" and expose a
high degree of agogical availability (see definition two blog-entries
back): 200ms, 250ms and 300ms. You will have to practice (listen and perform) them a lot until you'll be able to memorize and categorize them well. To achieve this competence you can use the following trick: perform the three IOIs legatissimo. You will thus notice that the slower the IOI, the more additional effort you'll be employing in order to "glue" one pulsation to another. Try to memorize the various degrees of this effort and relate them to specific paces. It worked for me – it should work for you too. Listen to the three IOIs: 200ms, 250ms, 300ms According to time-scholars, it should be easy for us to categorize the three IOIs, as the first one (i.e. 200ms) is considered to be processed by our brain holsitically while the third (i.e. 300ms) one – analytically, whereas the second one (i.e. 250ms) should be perceived as a border between the two. Well, in terms of practicality, you will have to decide for yourself if that is so. It took me a great deal of time to get to categorize satisfactorily these particular three isotempi, but finally I managed to achieve this competence. Please do not give up too soon and do not expect to memorize the three isotempi in one day. But if you can – congratulations! It means that you have an excellent temporal acuity – something similar to absolute pitch. |
| disinventing the wheel > 010 On the borderline |
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| Posted: Jun.28.2005 @ 7:07 pm |
| IOI 250ms is considered by time-scholars to be the borderline between the
holistic (for faster IOIs) and the analytical (for slower IOIs)
brain-processing of discrete time. As we have already seen, this
borderline has a large "no man's land", as at IOI 200ms we can already,
upon certain circumstances (see the previous entries), perform
attention-shifts. And any attention-shift is an instance of analytical processing. Other scholars claim that the "optimal rate of attention shift" lays somewhere around IOI 600ms. Therefore, from the border with the Republic of Holistic Processing (i.e. 250ms) to the very Kingdom of HM The Optimal Rate of Attention Shift (i.e. 600ms) there is a long way to go – according to time-scholars. Between IOI 200ms and IOI 400ms there is a passageway in which we can perform more and more attention-shifts while producing or listening to isochronal sequences. Attention-shifts? What is that, you may ask. Well, let us say that at around IOI 600ms you can comfortably NOT subjectively pose thesis and arsis values over pulsations. That is, instead of letting your brain decide independently (i.e. top-down perception) which pulsation is a "tick" and which is a "tock", you can imagine them all as "ticks" (thesis values) – like a beat that builds up a 1/X bar. That means that you can perform a full transfer of attention from one "tick" to another (psychologists dixit!). In a later blog-entry we shall see that we can force this sustainable rate of attention-shift up to IOI around 400ms. These said, it follows that berween IOI 200ms and IOI 400ms we deal with a transition from "melody-specific" to "beat-specific" isochronal paces. After IOI 400 and down to about IOI 800ms we enter the realm of fully fledged "beat-specific" isotempi (which we shall discuss in more detail at the right moment). |
| disinventing the wheel > 009 IOI 200ms (continued) |
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| Posted: Jun.28.2005 @ 4:10 pm |
|
Now coming back to more practical matters, let us see how we can come
to recognize and/or spontaneously produce a IOI 200ms isotempo – as the
minimum acton and the shortest attention-shift theories are valid and
great discoveries but they do not help us too much to get an accurate
start for the corresponding isotempo when it comes to actual
performance. IOI 200ms isotempo is, roughly, the first one that allows for some degree of "agogical availability". What is that? It is something opposite to "pulsatory inertia". Huh? Imagine that a music teacher asks you to perform an isochronal melody at IOI 100-150ms... "expressively" that is, using agogics (i.e. a mild form of rubato, in case you didn't know). Due to the fact that at these pace(s) our brain processes neighbouring pulsations holistically, actually there is no space for agogics. The best way to experience that is to perform succesively isochronal melodies at IOI 100ms, 150ms and then at IOI 200ms and try to be temporally "expressive" while doing it. You will surely sense that the faster the pace is, the less "agogical availability" there is. In the first two cases, pulsations seem to project their specific pace forward (that is precisely due to our brain's holistical processing – see above) and thus create a certain inertia, as if we were bound to follow a certain temporal grid that acts like an attractor for the coming pulsations. This is precisely why these IOIs are to be considered "inertial". In the latter case (i.e. IOI 200ms), helas, we finally can be – to a noticeably extent – temporally expressive and this is why IOIs above 200ms will be considered as available for agogics. Please practice this threshold between the last inertial isotempo and the first agogics-specific one for a longer while as it is very important to fix its features into your memory. Good luck! |
| disinventing the wheel > 008 Minimum acton / Minimum rate of attention-shif |
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| Posted: Jun.28.2005 @ 10:18 am |
| At around IOI 200ms two important and related perceptual phenomena
occur. First, this is the minimum timespan in which we can shift our
attention from one object of consciousness to another. Therefore, two
pulsations separated by a 200ms timespan can be processed by our brain
separately (i.e. analytically). Does that contradict what I
mentioned in the previous blog-entry? Completely, but the point
is not yet fully made: the peculiarity of this 200ms attention-shift is
that we can experience it at most once every two pulsations. In other words, 200ms does not represent a sustainable rate of attention-shift. It is just the minimum interval possible in which, upon certain circumstances, we can move our attention from one object of consciousness to another (pulsations in our case). This remotely explains why at IOI 150ms, where our attention cannot be shifted between two neighboring pulsations, we experience the kick-kickback sensation: just because at this pace the two pulsations in no circumstances can belong to different objects of consciousness. That is to be, nonetheless, scientifically proven. Another perceptual phenomenon defined by the 200ms timespan is that of the minimum acton. An acton represents the order given by our brain for a simple motor action along with the fulfillment of the respective order. A certain psychologist discovered that once our brain gives such an order (e.g. strike the G key), we cannot change our mind with regard to the action that has to be accomplished during the first 200ms. This better explains why at IOI 150ms we experience that kick-kickback sensation: the second (arsis, kickback) pulsation comes too quick for our brain to avoid its production. In fact, within a 150ms timespan (or less) our brain is unable to order the thesis, and then the arsis pulsation to be produced as separate actons – whereas at IOI 200ms, sometimes (see above) that is possible and this is why we do not experience a thesis-arsis relationship, at this pace, as a convincing kick-kickback kind of pulsatory structure. |
| disinventing the wheel > 007 The recoil kicks back |
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| Posted: Jun.27.2005 @ 11:54 am |
At around IOI 150ms an interesting perceptual phenomenon takes
place. If you take a thesis-arsis structure and try to seek at which
IOI they sound like a kick-kickback relationship you are likely to spot
a time-interval of about 150ms. That sounds quite impressionistic but
it is nonetheless true. I have tried in vain to find, in books and
publications, a direct scholarly explanation for this perceptual
phenomenon. The fact is that pulsations that are 200ms (or less) apart
are definitely processed by our brain holistically. That explains many
of the perceptual phenomena (e.g. blurring, specific subjective
rhythmization) mustered in the previous entries. Scholars claim that
this type of processing is already functional at IOI 200ms. Yet, if we
try to perceive a kick-kickback relationship at this rate, we will fail
to as we shall feel that the second (arsis) pulsation comes a little
bit too late.
Whenever you feel unsure, start performing this isotempo with a kick-kickback-like thesis-arsis relationship (as described above) and then just continue the thus established pace. If the result of this method will seem to you perceptibly faster than the MIDI example you may have created for IOI 150ms, don't worry: IOIs between 130-140ms are valid instances of the same perceptual phenomenon. You will be able to discriminate them (i.e. 130-140 and 150ms) later on, when your temporal hearing will have become more educated. Another way to grasp this isotempo is to "swing" – or "dot" – it. At 200ms you won't be able to (Nota Bene: 200ms meaning the total of short note + long note; average = 100ms). In other words, at around 300ms (i.e. again, 300ms means short arsis note + long thesis note; average = 150ms) we start being able to swing a melody. Therefore, just produce the fastest "swing-able" pace you can handle, keep in mind the pace of the thesis values and then "un-swing" it to a isotempo by introducing arsis values midway between every two neighboring accents. Voilá! |
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