Intervals in Music

Crazypiano wrote:

To write a melody, which are the most used "intervals," the least dissonant? I would like to have a brief description of all intervals from an acoustic perspective.

I hope it's not complicated

It's not complicated, do you mean tonal melody?

Regarding the "acoustic" part ... you are referring to intervals in a harmonic sense, right?

I had missed the rebuttal.

So, I quote Schoenberg, who divides the world of intervals into three parts: STRONG successions, with ascending fourth intervals (which often indicate a cadence) and descending third intervals (which often indicate a transition from major to minor mode); WEAK successions, with descending fourth intervals (plagal or suspended cadence) and ascending third intervals; VERY STRONG successions, with ascending and descending stepwise intervals.

In reality, Schoenberg refers primarily to the successions of chord roots... this is because, as far as I know, he never explicitly dealt with melody. In fact, studies on melodic profiles are relatively recent in musicology, but since composition studies are still largely dedicated to harmony, it makes sense to reflect on the HARMONIC relationships inherent in intervals. From Rameau onwards, in fact, the role of roots is... fundamental; the relationship between one chord and another is conveyed not so much by the overall structure of the chord as by the relationship between one root and another, i.e., by the interval between the two roots. Even among "presumed" roots, as in chords on the VII or in inversions. Some chordal functions, at least at the "origins" of harmonic theories and practices, are derived solely from melodic-contrapuntal movements. Take the famous augmented sixth chords: their function as dominant of the dominant is "revealed" by the movement of the two notes that form the augmented sixth, which should resolve into an octave. Counterpointally, any augmented sixth should resolve to an octave—for example, C-A# resolves to the octave B-B—because it is taken for granted that there is a leading-tone tension, which is a MELODIC tension.

Many melodies result in being "sensible" if they follow contrapuntal logic, i.e., if they follow the "impulses" of melodic movements. Humming helps to understand:

What follows C-D...? Either an E or a C. And if I add an F? C-D-F... E arrives. And if I add a G? C-D-G... and clearly C. It is a very silly example, but understanding the relationships between intervals often helps one understand the deep meaning of a melody, especially in well-written melodies. Singing Bach is IMPOSSIBLE if you do not understand the contrapuntal profile of his melodies, because some relationships are non-immediate (and not supported by chords!)

thallo wrote:

Singing Bach is IMPOSSIBLE if one does not understand the contrapuntal profile of his melodies, because some relationships are not immediate (and are not supported by chords!)

Could you give me an example regarding Bach?

Don't use the formal 'Lei' with me

my knowledge of Bach is not comparable to that of a pianist; I am a singer and, alas, Bach is still rarely sung in solo teaching, choral settings, and even less so in professional solo and choral performance.

But I want to try an experiment. Instead of trying with Bach arias that I already know, I will download a new one and immediately try to make you understand what I mean.

The first sacred cantata I found in the list of Bach's works on IMSLP: Ach Gott, von Himmel sieh darein http://conquest.imslp.info/files/imglnks/usimg/b/b3/IMSLP24170-PMLP03250-bwv002.pdf

The aria is on page 12, "Tilg, o Gott, die Lehren".

In the first phrase, we almost immediately have a descending minor sixth leap (Bb-D). This leap makes no contrapuntal sense in itself; it has a greater meaning due to the fact that the phrase, harmonically, goes I-IV-I. Melodically, this identifies three important degrees: the first (Bb), the fourth (Eb), and the fifth (F). The final F could have been part of a dominant chord; who knows, melodically what should matter to us is that the Bb-D interval is part of a melodic path that goes Bb-D-Eb-F, which is an ornamentation of a descending fourth interval, Bb-F. For those who sing, interpreting these melodic profiles is fundamental, sometimes, especially when there are "strange" intervals. At the bottom of the page, for example, a long and "tiring" modulation to F begins. This long modulation passes through strange melodic profiles, such as D3-G2-E2-F2-G2-C2. The E-natural MUST be thought of as the leading tone to F, and everything is an embellishment of the G, which in turn is part of the C chord. "Behind" this melodic line, it is as if there were two blocks: one that goes "Bb-C-D-Bb" and one that goes "E-F-G-F-E-D-C". Read this way, its intonation is immediate and very easy because it reveals the harmonic-melodic tensions. Moving forward, it gets even worse; there is a nice descending minor seventh, followed by an ascending sixth (C3-D2-Bb2). The final point of this sequence is A2 (it is not for nothing that it is part of the chord of the key not yet established but already "tonicized"—the F, on which the cadence occurs on the third beat). Without this beacon, all the intervals make no sense, they are difficult to intonate, and the text itself helps with this (the A is at the end of "lehren", at the end of the so-called textual unit).

The aria continues; perhaps I won't analyze it all, but reading its melodic line cannot be done without identifying functions (tonic, dominant, leading tone...).

Thanks Thallo!

Clearly Schoenberg is referring to the tonal realm

@Thallo

> Singing Bach is IMPOSSIBLE if one does not understand the contrapuntal profile of his melodies,

> because some relationships are not immediate (and are not supported by chords!)

But don't the melodies derive from Pietist chants or things of that sort? ... so if they are not singable, are they really sung melodies?

from what I know, the pre-existing melodies used by Bach are mainly in the chorales. I am talking about arias or choruses, complex compositions

Crazypiano wrote:

...what effect do intervals produce?

The only way is to try them; the emotional response is subjective. Therefore, a minor sixth might give certain sensations to me but may give others to you.

Crazypiano wrote:

To write a melody, which are the most used "intervals," the least dissonant?

The festival of subjectivity... "dissonant"?

Crazypiano wrote:

I would like to have a brief description of all intervals on an acoustic level.

I hope it's not complicated

If you are talking about acoustics, you are referring to formants, harmonic spectra, pitch (Hz)... it seems disconnected from the previous questions

In your opinion, how much of Bach is counterpoint and how much is harmony? And how much does the melody "ride" the harmony?