Points To Ponder #10

Feel like you are missing out on something?

Most likely you are.

I’ve been noticing a lot lately that there are very many people around with either very bad or very short memory spans. Anyone can have a momentary lapse but it seems that the ability to retain information in our own mind is becoming an ever greater rarity in these days when information is available to us simply by switching on a device and asking for it.

I’m also being made more aware of the simple things we miss or forget about by reason of it’s ‘obviousness’ or familiarity… no..  familiarity is not the right word… prevelance, that’s it. The things we don’t see anymore because we have become so used to them that we no longer think of them or value them or realise their degree of importance to us and to everything (everyone) else.

People who live in or near large cities are likely quite familiar with multi-storied buildings. These are often described as being 10 story’s or 33 story’s or 70 story buildings depending upon how many floors it has, but how often do you actually realise that a 20 story building (barring things like no floor 13 as it’s considered Bad Luck, or ‘secret’ floors with no elevator button number for them) in reality does not have 20 floors but 21? (maybe even 22? or even more!)

Getting into the elevator of such a building you see the buttons for each floor 1 to 20 and assume there are 20 floors as it’s a 20 story building – logical, right?  Wrong! There is the floor you entered into the building on, the ground G floor or Floor Zero. 0 to 20 is in fact 21 not 20. You can rise (or reverse, coming down) 20 levels but you have to count the one you are already on as well for the real total. The one that is so obvious and close to you that you forget it.

Some buildings may have a ‘Mezzanine’ floor and/or basement levels as well accounting for the 22 or more part above, but the real point here is the ‘forgotten’ Floor Zero – the one you start at before going up or down.

Counting the floors we can only count 20 – there are 20 vertical movements in total in the standard 20 story building but they are in between 21 floors, counting the ground floor  – the most important floor arguably, yet the easiest to overlook. Counting will give different results for the same thing (building) depending if we start counting with 0 or with 1 which is the same as if we are counting the floors (start 0) or the rises/drops between floors (start 1).

A similar thing can be observed with the 7 musical notes A B C D E F and G. There are only 7 notes in an octave and yet an octave is a grouping of 8 notes, where successive octaves start and end on the same letter note (but each one is a doubling or halving of the frequency and wavelength of the other).

Starting from a lower A we move up in ‘even’ amounts (frequency rises/drops) through B, C, D, E, F, G and then finally to the higher A, from which we can repeat the process to the next A. From A to A there are 7 ‘steps’ but A to A is 8 notes! the ‘ground’ note (= to floor zero) is the ‘zero frequency’ rising up to the end of the octave in 7 equal stages to the ‘7th’ note which is written the same as the first – ‘A’.

If we write the letters of the white keys on a piano keyboard (some have 11 octaves in range) they look like this:

ABCDEFGABCDEFGABCDEFGABCDEFGABCDEFGABCDEFGABCDEFG
 1234567 1234567 1234567 1234567 1234567 1234567 1234567
Each octave starts and ends with 1 ! Here there are 7 octaves: 7 x 8 = 56 but there are clearly only 7 x 7 = 49 notes?

The more musically astute among you will realise that besides the 7 white keys of a keyboard there are also 5 black ‘half’ notes or tones making a total of 12, and that, as almost impossible as it is to believe or figure out exactly how, all 12 notes are still ‘evenly’ spaced. Just how can 7 notes sound like they move in even jumps to the next when you can somehow ‘fit’ 5 more tones in to those seven and say they are all still evenly spaced??

The answer, which i’ll expand on later should anyone be interested, lies in the ‘obvious’ (by now) fact that there are not a total of 12 tones in an Octave, but  13!

And equally obviously, they all fit evenly around a standard clockface with each tone represented ‘exactly’ by an hour. The 7 notes are distributed perfectly logically and symetrically around the face and on hour marks, as are the sharp and flat half tones!

First hour

love.

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