<![CDATA[zeuxilogy]]> <![CDATA[016 Beats (continued)]]> 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.
]]> <![CDATA[015 DJs love these beats!]]> 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).
]]> <![CDATA[014 IOI around 400ms (continued)]]> "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.
Listen to an example (IOI 425ms)
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.
]]> <![CDATA[013 The zig-zag isotempo]]>
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.
Listen to an example (IOI 400ms)
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:
"In order not to imply in the experiment ocular movements, we shall imagine mentally any similar zig-zag trying then to pass from one point to another (A, B, C, D, E, F, G, H etc.) is such a way that consecutive stops do not create, from a temporal point of view, subjective thesis-arsis relationships (nor binary neither compound) as we should perceive any stop as experientially equal to any other stop. Moreover, we shall make sure that each stop implies a thorough change of the object of consciousness (i.e. a complete transfer of attention). Upon these conditions, the next step is to find out (and measure), from a psychophysical point of view, which would be the maximum rate of passing from one point in the zig-zag to another. The result should indicate an IOI value situated around 420-430ms. The absolute memory (i.e. skipping the experiment just described, for that implies relational memory) for this isochronous tempo can be achieved by practice."
(Quoted from my article A Matter of Perspective)
]]> <![CDATA[012 The slowest "melody specific" isotempo]]> legatissimo performances (see previous blog-entry) is in both cases great.
Listen to an example (IOI 350ms)
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.
]]> <![CDATA[011 IOI 250ms (continued) 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.
]]> <![CDATA[010 On the borderline]]>
Listen to an example (IOI 250ms)
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).
]]> <![CDATA[009 IOI 200ms (continued)]]>
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!
]]> <![CDATA[008 Minimum acton / Minimum rate of attention-shif]]>
Listen to an example (IOI 200ms)
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.
]]> <![CDATA[007 The recoil kicks back]]> 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.

Listen to an example (IOI 150ms)


Untill I  find a documented explanation for this phenomenon, please take it as it is. Perform and listen to as many isochronal melodies at IOI 150ms as you please and try to develop an absolute memory for this particular pace.

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!
]]> <![CDATA[006 Thershold of subjective rhythmization]]>
Listen to an example (IOI 100ms)
Other theories – that successfully passed my personal testing – claim that there can be only one subjective accent within a 200ms timespan. That's true and it implies that, indeed, at IOI 100ms we can imagine binary structures: 100ms + 100ms = 200ms. It follows that it is around IOI 70ms (i.e. 200ms roughly divided by 3) that we can only place thesis accents every third pulsation. Please listen to such an IOI and decide for yourself if that is true. I guess it is and it becomes more apparent at around IOI 75-80ms.

You should become accustomed to these 2 thresholds (i.e. of binary and compound rhythmization) as you will need to recognize and produce their corresponding IOIs by heart. Please do practice them (a lot!) until you seem to have gained a good grasp on their "sond and mood". In so doing, watch carefully the way you place thesis values: if you can do that every third pulsation only, you are performing an isochronal tempo around 70-80ms. Conversely, if you can place accents both every third or second pulsation then you must be performing an isochronal tempo (isotempo) around 100ms (or more, so be careful not to loosen the isotempo too much).

If you are not a good instrumentalist, you might not be able to perform these IOIs due to physiological restraints (i.e. they are too fast for your unexperienced fingers). In this case, what can I say? Praktice, praktice, praktice! Or rest content to recognizing them upon listening. Try out as many isochronal melodies as you can: write them down in Finale NotePad and play them at both 75ms (MM800) and 100ms (MM600) and try to sense the differences by placing subjective accents, as described above).]]> <![CDATA[005 Crepitus]]>
Listen to an example (IOI 50ms)
There is a comprehensive literature dedicated to this phenomenon but here we shall only focus on the practical ways in which we can use it musically.

On the one hand, you will notice that, at this speed, you won't be able to perform instrumentally just any melody that you want, except for some ascending or descending passages. No "do-mi-re-fa-mi-sol..." sequences – only short one-way scales and arpeggios. In fact, I doubt that you can keep the isochronicity stable for more than 5 pulsations – for a fistfull of fingers, so to speak...

On the other hand, while listening to a IOI 50ms melody, try to tell which pulsations are accents (thesis) and which are non-accents (arsis) and you will see how tricky this taxonomy is at this tempo. Usually, we are prone to consider as thesis pulsations those notes that represent melodic peaks (both upper and lower).

These said, you can tell now that you know how to recognize a crepitus-specific IOI. It sonds blurred, you cannot play just any melody that you want at this speed and you do not discern thesis vs. arsis pulsations the way you do it at slower rates, where you generally can tell that a "tick" is followed or preceded by one or two "tocks". At IOI 50ms, if you pay enough attention, you will be able to discern many more "tocks" (arsis values) in a row. Strange, isn't it?

Feel free to practice some short scales and arpeggios and listen to several melodies in this isochronal tempo until you are sure you've got it right so that you won't mistake it for the next IOI.]]> <![CDATA[004 Prerequisites]]>
Please do not expect to find here too many references to the books and articles that I based my theory upon. This is just a blog, not a scholarly lecture. However, if you want to read some of the "academic" stuff that I wrote, e-mail me and I'll gladly send you a few articles and studies that comply with academic standards.

That said, I will start describing perceptual phenomena related to IOIs from 50 to 800 millisecond. As a matter of convenience, I will do that for IOIs which are 50ms apart (i.e. 50, 100, 150, 200, 250ms etc). That does NOT mean that all relevant time-related perceptual phenomena take place at precisely these values, but this "tempered" scale is good for a start. It settles a conventional grid whence we can fine-tune our educated-to-become temporal acuity. Let's go!]]> <![CDATA[003 Jugglers with time torches]]>
But there is still a long way to go before entering the battle against pulsatory inertia. For now we shall just muster a series of isochronal tempi in order for us to see what happens between IOI (inter-onset-interval) 50 milisecond and 1500 milisecond – a fair scope of our ability to assess isochronicity.]]> <![CDATA[002 Pot pourri]]> <![CDATA[001 From Incan wheels to rhythm theory]]> When Pizzaro conquered the Incans he found there over 23,000 km of roads used by a population who had missed to invent the wheel.That made me think of the fact that in music theory we might have missed to invent rhythm and, in consequence, come with another solution for our relationship with discrete time. Most times we switch from one isochronal tempo to another in music we relate durations. We use simple-to-complex ratios to do that and it seems that that's it with musical time. In so doing we miss to cope with our overall temporal competence, which is far more complex than that. So complex that no future, alternative theory, will ever claim to encompass it all. However, what classical rhythm theory does cover is, in my opinion, too narrow to be left unchallenged. The ideea is that classical rhythm theory is like an invented wheel that somehow efaces the emergence of a presumably better alternative. Have you ever wondered why there are so many books, professors and academic interest on pitch theories and – comparatively – so little stuff about musical time theory? Well, I think that's precisely because today rhythm theory is so simple that it does not claim for more widespread academic effort. Two quavers make a crotchet. 1 + 1 = 2. Are you happy with that? Do you need a dedicated course in every music academy to develop for you this principle? I guess not. But what happens if you want to jot down rhytmical surfaces that definitely seem to overpass the constraints of the duration-relational frame? Tag them as "rubato" or, worse, "free rhythm"? Shrug? Let the computer tell you what is there? With this blog I will try to answer these and many other related questions in a "gaia scienza" manner. So, prepare to curse and bless while discovering, along with the blogger, the creative story of "discrete time before the wheel was invented".]]>