PHI NOT? How to easily make music with more melodic and chord possibilities than the usual 'major' scale.
What you just heard was an example of the PHITER scale under the PHI tuning. If you think it sounds cool, read on...
If you want to use the PHITER scale in any of your own songs and have a synthesizer of softsynth that supports SCALA tunings, just download the scale in SCALA format HERE
PHI is (1 + the square root of 5) over two or 1.6180339887. Is has a special mathematical property: If you divide a line into two parts, A and B, and make A 1.618 times the size of B then A + B will also be 1.618 times the size of A. I will refer to this relationship as the "folding split"
So what's so beautiful about using the PHI ratio in music that makes it good for the PHI tuning?
The human mind generally likes symmetric ratios...and PHI, as you can see from the example above, is about as symmetric as you can get. This is why Greek architecture and the Egyptian pyramids were both built using PHI as a ratio between parts of their buildings for beauty and that virtually all models, for example, have a lip to nose width ratio of close to 1.618 to 1 and a shoulder to hip size ratio of 1.618. Simply put, PHI is a symbol of beauty ingrained into the human mind from birth and its working well in music makes logical sense.
So what does this have to do with music scales and chords...what does the standard musical scale lack to make it as symmetrical and 'symmetrically beautiful' as a one based on PHI?
The chromatic/"standard" musical scale is based on two ratios, 1.5 and 2, that are symmetrical, but not as much as PHI is. The standard music tuning is really just a series equally spaced notes IE 262hz * (middle C on a piano) * 2^(x/12) where x = 0 to 12. But what is x/12 approximating why are we using 2 (a very symmetrical number) as the octave in the standard tuning?
It turns out 1.5 IE 3/2 is the ratio used to make such a scale and multiplying 1.5 by itself enough times more-or-less creates a power of 2, thus making 2 the octave for the standard tuning. The ratio "1.5" is known as the "5th" in the standard musical tuning. Do 1.5^1 , 1.5^2, 1.5^3...all the way up to 1.5^12 (the octave)...and keep on dividing each result by two until you get results to all fit between or nearly between the numbers 1 and 2. For example 1.5^12 / 2^6 = 2.027287. Now take all those ratios and multiply them by 262hz (which is middle C on a piano).
That is how, roughly, you mathematically create/explain the basic 12 tone tuning (c,c#,d,d#) used in most modern music. The error between 2.027287 and 2/1 (the octave) is called the pythagorean comma. Note also, what we have done by taking all these ratios is worked our way around the circle of 5ths (note 1.5 = a 5th) so emphasized in modern music theory. For those who don't know, the notes c and g represent a 5th as do (g and d) and (d and a)...keep going around and you will get back to C within 12 of these steps.
So, in the end of the day, we have spent hundreds of years beating around the bush teaching people the standard tuning, which is basically just a chain of fifths which tries to intersect the relatively symmetrical ratios 1.5 and 2 to the best of its ability. True, we have made some improvements to how we use the chain of fifths in the standard tuning (IE by using 2^(x/12) to generate the tuning so it is more symmetrical "on the average" than by using 1.5^x)...but we still are using a musical scale very close to the ancient Greek original scale in which we can only use 7 notes at once (IE CDEFGAB AKA the C-Major scale) and adding more to the standard scale makes it sound quite dissonant.
In a nutshell what makes the PHI scale work more cleanly in many cases than the standard tuning , is that taking 1.618^1,1.618^2, 1.618^2 (a "circle of 1.618) will intersect BOTH the equivalent of a 5th (1.618) in the PHITER scale and a ratio that sounds profoundly like an octave to the human brain (1.618). Simply put, the human mind appears built to handle 1.618 as both an octave and a 5th AND think of the PHITER scale equivalent to the "circle of 5ths" in a "folding split" format, thus making the scale "infinitely symmetrical" and very easy for the mind to process.
The problem is...for hundreds of years we have been stuck with the notion that using the above "meantone" way of generating scales by either 1.5/"the 5th" or near approximations is the ONLY way to get good sounding chords. And yes, meantone and tunings that approach the same general notes, such as diatonic just-intonation...also sound pretty good and they do so by trying to eliminate fluctuations/amplitude-modulations in volume of certain frequencies also know as "beating".
Those scales simply revolve around the idea of aligning the overtones of instruments to virtually eliminate dissonant beating between them, while the PHITER scale instead seeks to allow some beating, but in a symmetrical manner that the brain can easily understand. Notice that the overtones in pleasant string instruments beat some while less consonant organ-like sounds do not...and indeed "regulated" beating can be used to make relaxed/consonant sounding scales.
However, diatonic scales like JI and mean-tone scales have their difficulties. Have you tried sitting in front of a piano and making large chords, like a c sus4 13th chord? Realize just how careful you have to be to get all the notes right...and if even one note is wrong it sounds terrible? This is why, unlike something like riding a bike, standard tuning music most often never completely becomes second-nature: unless you are a fantastic musician, you most often end of calculating which notes form "eligible chords" as you play.
Making new chords and melodies quickly and easily with the PHITER scale
With the PHITER scale you have virtually no reason to deal with that issue of looking for good vs. bad chords since virtually all combinations of notes in the scale form relaxed/consonant-sounding chords. With the PHITER scale, you can just sit down and jam and sound like a chord theory buff! The PHITER scale is just one huge 11-note chord (the same one shown in the sound example that plays when you load this page) and just about any set of notes within it will sound like a good chord. So no matter what notes you hit, the PHITER scale will make them approach the purity of chords played by a highly trained musician.
Want to make highly original melodies? The PHITER scale allows 8-notes worth of freedom (per the 2/1 "standard" octave) instead of the usual seven in the standard scale, thus allowing more combinations of notes and more different melodies. Not to mention the fact the PHITER scale uses drastically different tones so each note has a unique feel as compared to the usual major and minor scales.
As a disclaimer the PHITER scale is NOT a "perfect solution to all tuning/musical problems"...it does a lot of things well but nothing "perfectly". Just Intonation may have certain purer intervals and chords deemed more important and "normal" to some people than those in the PHITER scale and so will Lucy Tuning and MOS scales. Also some MOS scales have more notes per octave to play around with (9 instead of the 8 notes of the PHITER scale). Before you decide to use the PHITER scale, make sure to check out these other tunings and decide for yourself which one is best for you.
For those who are inclined with tuning math, the PHITER scale is created from multiples of the the steps L=99.271 and s=69.097 and, being created from such steps, is technically "just" as MOS-type scale with unique harmonic properties (again, as you can hear in the sound clip at the top of the page).
Want to learn more about how to compose with the PHITER scale? Contact me via e-mail HERE