Talk:Root (chord)

Please Add

Root chords along a minor scale — Preceding unsigned comment added by Skysong263 (talk • contribs) 03:54, 14 May 2015 (UTC)

Not enough sources

This page lacks sources. I found an interesting one: "R. Parncutt - Music, Gestalt, and Computing: Studies in Cognitive and …", Springer (1997). This book offers an overview of results in cognitive sciences about perception of music, and it has some material on the perception of roots of chords. It might also be a useful source for other pages! Cazort (talk) 16:48, 31 December 2007 (UTC)

What and why does this article need sources? Hyacinth (talk) 06:35, 12 March 2010 (UTC)

Layman's terms needed

I tried looking this up to better understand what a "root" is.....and this article does absolutely nothing to define it in terms that make sense to those who haven't studied music theory. (74.177.37.69 (talk) 05:26, 25 September 2010 (UTC))

Not sure what to suggest. I agree that the lead-in is a little obtuse, but conversely, the idea of a chord's root is intrinsically steeped in music theory. I did find this link that may be helpful, though. --Blehfu (talk) 14:40, 25 September 2010 (UTC)

What does the article lack? A definition? Examples? Clarity? Hyacinth (talk) 18:04, 25 September 2010 (UTC)

As someone quite steeped in music theory I hava a hard time answering that question, however, i think the main problem is that the introduction lacks a connection to the intuitive grasp of the root of a chord that (i belive) most readers have. (i'm sorry if i'm not making myself clear, not a native speaker). I'm unfamilliar with what counts as "layman's terms" in english, but trying to explain this concept to my students i often have to fall back on things like "the note you'd be least surprised to hear the bass play" --Niklas R^Talk_page 02:32, 9 March 2011 (UTC)

Check out the first sentence of section thats supposed to define the concept:

"Although the safest way to recognize a chord's root is, after having reduced the chord to close spacing, to rearrange it as a stack of thirds, there are shortcuts to this: in inverted triads, the root is directly above the interval of a fourth, in inverted sevenths, it is directly above the interval of a second."

The sentence is just abysmal, right? Also across the whole section this is the only attempt at a definition. The rest of the description is just examples and relations to other music theory concepts. This sentence could be elaborated on, describing what does it mean to i.e. "arrange as a stack of thirds" Zaabson (talk) 20:09, 2 May 2023 (UTC)

I tried to clarify this. My formulation probably could be improved, but I hope to have made things clearer. The clarification remains somewhat circular, as I define the root in relation with the "root position," and inversely, but I hope the redundance somehow helps. — Hucbald.SaintAmand (talk) 20:19, 9 May 2023 (UTC)

Confusing or unclear

Why and where is this article confusing or unclear? How should it be cleaned up? Hyacinth (talk) 15:41, 11 December 2011 (UTC)

Psychoacoustic theory

• A more recent psychoacoustic theory of chord roots was offered by Richard Parncutt.<ref>{{cite web|last=Huron|title=Harmony: A Psychoacoustical Approach by Richard Parncutt|url=http://musicog.ohio-state.edu/Huron/Publications/huron.Parncutt.review.html|accessdate=15 February 2012}}</ref>

I removed the above since without context or explanation it doesn't serve much purpose. Hyacinth (talk) 09:59, 28 February 2012 (UTC)

Root of a scale

How about some mention of root in the context of scale and what if any relationship this has to the root of a chord? Thanks.CountMacula (talk) 13:41, 9 May 2012 (UTC)

Perhaps a clearer, more concise definition and better acoustical basis?

When all of the notes of a chord are translated to the range of one octave, the root of an interval will be the lower pitch in an odd numbered interval and the upper pitch of an even numbered interval.

In a chord with three or more notes, the root is the note that meets this criteria the greatest number of times when compared with all other pitches in the chord. For example, in a C major triad in first inversion, with the notes from bottom to top { e, g. c }, we have the following relations:

Note Considered	Comparison I	Comparison II	Analysis	Rating
c	e to c = 6th	g to c = 4th	c top note of even interval in both cases.	+2 It's the root.
e	e to c = 6th	e to g = 3rd	e is bottom of even & bottom of odd.	+1 Not the root.
g	g to c = 4th	e to g = 3rd	g is bottom of even & top of odd.	0 Not the root.

The acoustical basis for this definition of roots is found in the overtone series. Except for electronically generated sine waves, most tones in nature consist of many frequencies. For most musical instruments, the vibrating medium produces tones matching the harmonic overtone series. The first 9 tones in the series consists of the following notes, from low to high, using C.

Note Name	C3	C4	G4	C5	E5	G5	Bb5	C6	D6
Interval above Fundamental	unison	1 octave	1 octave + fifth	2 octaves	2 octaves + major 3rd	2 octaves + 5th	2 octaves + b7th	3 octaves	3 octaves + Major 2nd

There are no intervals in the overtone series until the 8th overtone, D6, where the fundamental is not the root.

Yamex5 (talk) 21:32, 30 March 2013 (UTC)

References

Possible mathematical and scientific basis ?

The section entitled "Possible mathematical and scientific basis" reads as follows:

The concept of root has some basis in the physical properties of harmonic sounds. When two notes or more notes from the harmonic series are played at the same time, people sometimes perceive the fundamental note of the series, even if that note is not present (see Missing fundamental). This property has been used in organ building for the production of low notes by resultant tones. Andreas Werckmeister’s Harmonologia (1702) describes the major triad in root position and in first inversion in terms of the harmonic series, but this description cannot be extended to the minor triad.[7]
Hindemith, who described the chromatic scale as resulting from "the juxtaposition of vibrating units in the proportions of the simple numbers from 1 to 6", i.e. from the intervals corresponding to harmonic partials 1 to 6, called the fundamental of this harmonic series the "root" of the scale.[8] From this root, he then derived a series of notes in diminishing degree of relationship, which he called Series 1 and on which he built a system of composition. This system however has been criticized for being based generically in theory derived rules and not on perception of specific instances.[3]

The first sentence seems to announce what will be found in the section, but what follows fails, IMO, to fulfill the promise.

The two sentences that follow, concerning the missing fundamental and the resultant tones, hardly concern the concept of root. The missing fundamental is that of a single tone, not the root of a chord. And resultant tones, as used in the organs for the production of low tones, are produced as the difference (in frequency) between two tones; in most cases, the resultant tone doubles one of the two tones one or several octaves lower – and masks the two tones: the aim is to produce what is heard as one single low tone.

Andreas Werckmeister, in Harmonologia, does not describe the major triad in terms of harmonic partials, but in terms of ratios of whole numbers (which, it is true, form the harmonic series in the mathematical sense, but not in the musical one). He says for instance that c g c¹ e¹ corresponds to the numbers 2, 3, 4, 5, i.e. that the intervals between them correspond to the ratios 3:2, 4:3 and 5:4. When he describes e g c¹ as corresponding to the numbers 5, 6 ,8, he means that the interval ratios are 6:5 and 8:6. It is very improbable that Werckmeister knew the existence of harmonic partials and of the harmonic series in music, and these ratios do not immediately suggest harmonic partials. He does not mention minor triads, in this context at least, nor does Rivera in the article in article given as reference in footnote.

Hindemith does not describe the chromatic scale "as resulting from the juxtaposition of vibrating units in the proportions of the simple numbers from 1 to 6", he derides that as a medieval conception. He continues: "does not all this seem like a distant echo of the musica mundana of the ancients" [etc.], klingt das nicht wie ein leiser Ton aus der musica mundana der Alten (Mendel's translation, p. 53; the German original is not p. 73, as indicated in the footnote, but p. 75). And Hindemith's own series 1 has no relation with a scale, nor with chords, nor with roots, nor with practical music. It merely indicates a theoretical proximity of tones.

I think that this section should disappear, but I remain somewhat reluctant to remove it immediately. Opinions and advices would be welcome. — Hucbald.SaintAmand (talk) 17:57, 20 September 2019 (UTC)

The new section below (of which I do not understand a word) reminded me that something had to be done to the section "Possible mathematical and scientific basis", as indicated above. I replaced it by a brief section on "Root vs Fundamental", which however lacks references in its present form.

I would be tempted to add a word about what is known in the Paris Conservatoire as "natural chords", including the dominant 7^th, etc., which since Catel in the early 19th century are believed to correspond to the harmonic series – with a very forced assimilation of the 7^th of the chord with the 7^th harmonic partial. But this would require comments that do not really belong to this article.

One may also discuss why the minor triad cannot be included in the discussion of the harmonic fundamental, while it obviously has a root. There would be references about that.

So, the section needs improvement; but I think it had waited long enough. I leave it to others to see what must be done with the section below this one in this Talk page (which, as I said, I utterly fail to understand). — Hucbald.SaintAmand (talk) 06:40, 3 July 2020 (UTC)

Subroots or macrointervals (intervals not in series, but also not the root but smaller; their importance is obvious is some nonclassical scales [but not only] as a means to maintain a balanced mood; usually present many times)

For example on the nonclassical scale Sigil

Sigil (has 3 submodes/tonal shifts)

• do, re♯, mi, sol, sol♯, si
• do, do♯, mi, fa, sol♯, la
• do♯, re, fa, fa♯, la, la♯

semitonal mode: 0, +1, +3, +1, +3, +1, +3

Here the subroot/macrointerval 4 semitones = Major third = diminished fourth is of structural importance (has a dominant role in the mood), but the 3 semitones = minor third = augmented second isn't that crucial structurally even being very common in the scale (because the overall shape of the scale is based on the diminished fourth in series (with other ancillary interlayer/interset intervals which do not define the spacing); the minor third defines the local mood [not the global]).

For example on the nonclassical

Evil Shaolin (has 2 submodes/tonal shifts)

• do, re, re♯, fa, fa♯, sol♯, la, si
• do♯, re, mi, fa, sol, sol♯, la♯, si

semitonal mode: 0, +1, +2, +1, +2, +1, +2, +1, +2

On this scale the minor third defines the global mood (acts like the subroot, because it is present many times).

Assumed root?

In its section on "Assumed root", the article contains this statement which puzzles me:

An assumed root (also absent, or omitted root) is "when a chord does not contain a root ([which is] not unusual)". In any context, it is the unperformed root of a performed chord.

The quotation included in this statement is refered to a Rhythm Guitar Tutor by Charles Chapman (2004). The reason why this puzzles me is that the root is not a property of the chord itself, but of its representation. As the first sentence of the article says,

The concept of root is the idea that a chord can be represented and named by one of its notes.

In other words, the concept of root belongs to an analytic representation of the chord. The "assumed root", therefore, is not "when a chord does not contain a root", but when the analyst considers that the root is not among the notes of the chord.

The musical example supposed to illustrate this puzzles me even more. It shows at the left a chord consisting of the notes B E G C and described as an "A minor ninth chord without root and with B in the bass." Without context, as in the example, such a chord could also be described as a C major seventh chord (C E G B) in third inversion. The caption further claims that what it shown at the right is a "full Am9", but the chord shown there is a mere A minor seventh chord (A C E G) in root position. I would have two questions: (1) why is the chord at the left analyzed as a chord with assumed root? (2) what is the chord at the right supposed to illustrate in this respect?

The article further says that

In jazz and jazz fusion, roots are often omitted from chords when chord-playing musicians [...] are improvising chords in an ensemble that includes a bass player [who] plays the root.

To which could be objected that in any polyphonic ensemble playing chords (say, a string quartet), there usually is only one instrument (at times two) playing the root. There is no reason to believe that the other players think that the root is "assumed" in such a case: it merely is played by others. The lengthy explanation that follows merely states which "additional extensions" could be added to a dominant seventh, but does not seem to concern the root played by the bass player.

I am aware that these sentences may describe practices that are common among guitarists or jazz players. I sympathize with the idea that concepts which may seem obvious for classical musicians must be clearly be explained for others. But the reverse should be true also. To me, what this section tries to explain is by no means clear. I leave it to those who know to clarify ... — Hucbald.SaintAmand (talk) 17:39, 3 July 2020 (UTC)