The Seventh Partial

(entry for 12/20/2024)


Two posts ago, we mentioned that the 7th partial of the Series of Partials, that is, the 6th overtone of any fundamental, was not involved in the tuning system used in Western Music, that is, the music of Europe and the Americas.

There are a couple of reasons for this state of affairs, but first I need to clarify something: countries such as Greece, Romania, and Bulgaria are all part of Europe, but it turns out that nowadays their music is heavily influenced by that of Turkey and the other regions of what we call the Middle East. This makes sense, because those areas are ‘right next door.’ So their music is not strictly ‘Western’ in the same way that the music of, say, Germany or France is.

The difference is the importance, or lack of it, of the 7th partial. Now if you think back to the principle of ‘diminishing importance in tone quality’ of each higher partial, where the 6th partial was only 1.5625% of the total sound, we can easily figure out that the 7th partial is only 0.78125% of the total sound, which isn’t much! In Europe and China, where the tempered scale was invented, the 7th partial wasn’t even remotely close to any of the notes in the tempered scale, but we could safely ignore it, since it was such a tiny part of the total sound, less than 1%. (By the way, from here on we’re going to round off and say that the 7th partial is 0.78% of the total.) So as the tempered scale became more and more prevalent in those areas, any influence of the 7th partial became less and less felt.

But the same thing did not happen in the Middle East. For one thing, their musical instruments didn’t have the same tone quality as Western ones did. Their sound was much brighter and therefore much more ‘piercing.’ In other words, the percentage of the total sound made up of higher pitches in the series was more prevalent. In other words, the 7thpartial was more important. (Along with the 9th, 11th, and higher odd-number partials.) The higher partials were still relatively unimportant compared to the fundamental, but they were more important than was true of European instruments.

Here are two of the most important Middle Eastern instruments:



The Oud, ancestor of the guitar.



The Qunan, ancestor of the zither.  The first one was made in the 19th century B.C.!


So, the tempered scale never really caught on in the Middle East, or even father east, such as in India. The tempered notes sounded more ‘out of tune’ to them than they do to us. (On the other hand, some of their pitches sound ‘out of tune’ to us!)

A good example of the difference between Western pitches and Middle Eastern ones is contained in the sound of the Muezzins calling the faithful to prayer in largely Islamic countries. It’s impossible to notate their calls using Western notation, because the pitches don’t fit our scales. Some Western composers have tried to imitate these Middle Eastern pitches by inventing something called ‘quarter tones’ or similar fractional descriptions, but since quarter tones are still based on variations of the tempered scale, this still doesn’t quite fit the situation. A tempered quarter-tone system would divide the octave into twenty-four discrete pitches, that is, a doubling of the twelve tones that we normally use. So ‘Arabian’ music, as Middle Eastern music is often called, does use twenty-four pitches, but they are not tempered! That is, the differences between pitches are not equal. Instead, they conform to the Series of Partials (including the 7th partial), which as we have seen in earlier posts, is ‘pure’ or ‘just’ rather than tempered.

To put it all another way, the pitch system used in the Middle East is much more ‘natural’ than the tempered system that the West uses. This has led many modern composers to rely more and more on ‘Arabian’ sounds in their compositions—the catch being that fretted and keyed instruments are rather ‘stuck’ in the tempered world! But performers have found various ways of ‘bending’ the tempered pitch sounds to make them more similar to the un-tempered ones, so that altered pitches are much more common than they used to be, resulting in greater familiarity (and comfort) for the average listener.

There are several different ways of notating these pitches, but the most common way is to use words plus mathematical symbols to represent the different pitches rather than a system of notes and staves such as the West uses.

But to come back to the reality of Western temperament, some music theoreticians have proposed that our fondness for the dominant seven chord may stem partly to its almost-resemblance to the fourth, fifth, sixth, and seventh partials of the Series of Partials. In other words, the ‘G’ pitch in an ‘A dominant seven’ chord is not quite, but almost, the 7thpartial of the fundamental A. It’s a bit ‘sharper’ than the 7th partial would be. (For those that are mathematically inclined, the ‘pure’ 7th partial of the A110 is 770 beats per second. The ‘G’ at that point is 784.74, which is substantially higher. But our ears are ‘flexible’ enough that we might consider the two pitches to be the same, hence the dominant seven chord ‘sounds’ important. On the other hand, the tempered F-sharp / G-flat would be 740.42, which is even farther away from 770, so the G ‘fits’ our hearing better than the G-flat would. At least that’s the theory!)

The 7th partial is somewhere between F-sharp and G natural.


All of this business about the 7th partial has been a bit of a detour, since the subject of this series of blog posts is music notation as practiced in the West. Next time, we’ll get back on track, covering how important or un-important various intervals are in the overall scheme of things, remembering that the distance from the sixth partial to the seventh one is not a tempered interval and can therefore be ignored. (Unless you live in Turkey or India!)


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To see an index of all of Len’s Music Blog posts, please click HERE.

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