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I did some reading on chord inversions on wikipedia, and there is a quote i'd like to ask about:

Inversions are not restricted to the same number of tones as the original chord, nor to any fixed order of tones except with regard to the interval between the root, or its octave, and the bass note, hence, great variety results.

(Hubbard, William Lines (1908). The American History and Encyclopedia of Music, Vol. 10: Musical Dictionary, p.103. Irving Squire: London)

I am wondering about the exception last in the quote, regarding interval between the root and the bass note. Given that the harmonic interval between root and base note varies for each inversion, what is the actual recommendation for creating variations here?

  • Seems to be a nebulous quote, with no great substantiation. 'Just cos it's on the net...' Dv unsubstantiated too... – Tim Feb 15 '20 at 9:08
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    The quote appears to be from an encyclopedia – Erik Feb 15 '20 at 9:10
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    Albrecht's answer is right ...both the meaning of chord inversion and that this definition you found isn't very good. – Michael Curtis Feb 15 '20 at 23:48
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Inversions are named (1st, 2nd, 3rd, …) from the relation between the bass note and the root of the chord.

So the sentence is a convoluted way of saying absolutely nothing. If the bass note was different, the chord would be a different inversion by definition.

The complete "American History and Encyclopedia of Music" edited by Hubbard is available on Internet Archive. A cursory look shows that it is nothing like any conventional "encyclopedia" - it is mostly a collection of articles on seemingly random topics, arranged in random order. You might expect an encyclopedia to work systematically through the alphabet, but the entire first volume seems to be a random collection of writing about operas.

Why somebody chose to use it as a reference for Wikipedia is strange.

  • The bass note (lowest note in a chord) is the designator of that chord's inversion. It's only called 'root' when the tonic is at the bottom. Where that root comes in any inversions has no reference to the bass note. – Tim Feb 15 '20 at 15:00
  • In thorough bass we number the inversions too - but we also assign the intervals of the bass tone in relation to the root tone. 135,36,46. V7 inversions 1357 = 7, V56, V34, V2 – Albrecht Hügli Feb 15 '20 at 19:11
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Inversion means: the root tone isn’t in the bass! (All the rest is rubbish.) So it’s logical there are many possibilities.

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I think he's making heavy weather out of saying that it's the bass note that determines the inversion, not the arrangement of the upper structure. If a C chord has E - the 3rd of the chord, i.e. a 3rd away from the root, C, it's a first inversion, no matter what disposition of C, E and G notes are above.

In Britain we have 'The Oxford Companion to Music' which seems similar to "The American History and Encyclopedia of Music". It was my school's primary reference book when I studied O and A Level music in the 1960s, largely I suspect because it was considerably cheaper than a set of 'Grove'. I also possess a wonderful, multi-volume 'New Musical Educator' - undated, but as the frontmatter includes 'The Publishers guarantee that the Binding, Printing, Paper and Blocks for Illustrations used in this book are the products of British workers' I'm assuming it was published between the wars. Its stance is that music reached perfection at the end of the Romantic period, earlier styles are described as 'primitive'.

We may be thankful that the Internet enables us to number all of these among our resources, but not as our ONLY resource!

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What I believe he is saying is that you can configure voices above the bass note of the chord inversion in whichever way you want, providing you do indeed stick to the chord's constituents. Or, put it another way, you can place the chord's constituents above the bass note at whatever octave you feel will create the best voicing.

This idea has its roots in figured bass where the keyboard player was permitted to use creativity and improvisation in their chord voicings. The only strict rule would be in a case where the piece's composer already supplied the bass note with a figured bass number to denote the chord inversion, in which case, the keyboard player would indeed use that bass note/chord inversion - the unique voicing was up to the player.

I believe he is also saying that you don't have to use every tone in the chord. For example, some composers will omit the 5th in certain situations. Another example is a case where composers will triple the root. It is good practice to include the 3rd. It is also good practice, in a 4 voice texture, to double the root.

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