Intervals in Music

In our music theory video courses (at the top of the forum home page in the scrolling slider), they are covered in one lesson...

Lopez wrote:

how were musical intervals explained to you?

Take the major scale as a reference; the major ones are the second, third, sixth, and seventh. The perfect ones are the fourth, fifth, and octave.

Then:

- by lowering major intervals by one semitone, you obtain the respective minor intervals

- by lowering major intervals by two semitones, you obtain the respective diminished intervals

- by lowering perfect intervals by one semitone, you obtain the respective diminished intervals

The difficult part is understanding that the first of the two sounds under consideration is to be considered the tonic, so reasoning begins from its major scale.

Example, if the interval is C Ab.

C is the tonic of C major, so the A in this scale is natural (C-A, major sixth); since the interval is C Ab, precisely the A is lowered by one semitone, so we will speak of a minor interval.

If one knows the scales, perhaps it is the easiest and most intuitive method

Am I saying something stupid, counting the width of intervals in tones and semitones?

TheSimon wrote:

In our music theory video courses (at the top of the forum home page in the scrolling slider) they are covered in one lesson...

...where? Can you provide the direct link?

http://www.pianoconc...teoria-musicale

Lesson 10

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Dilettante wrote:

Am I saying something stupid, counting the width of intervals in tones and semitones?

It seems unmusical to me. What would be the use of knowing that a minor third is composed of one and a half semitones?

Wasting time... I also think it's perfectly useless...

Personally, I find counting the number of tones and semitones useful only in the case of thirds, when analyzing chords.

For all other intervals, and for complex designations (diminished, diminished plus, augmented, and augmented plus), the best point of comparison is the relative scale.

That is,

the intervals that a tonic establishes with the degrees of its scale can be

major

minor

perfect.

The interval of fourths and fifths is always perfect, both in the minor scale and in the major scale.

All other intervals in the MAJOR scale are major (second, third, sixth, and seventh).

In the minor scale, only the interval of the third is always minor; the others (always excluding fourth and fifth) can be major or minor, depending on the type of scale we are in. The problem lies only in these, let's say... and there are many practical ways to solve it. The major second is a tone, the minor second is a semitone (and is found in the Neapolitan minor scale); the major sixth is a tone after the fifth, the minor sixth is a semitone after the fifth; the major seventh is one semitone from the tonic, the minor seventh is one tone from the tonic.

From this, the other complex terms derive.

A diminished interval is a minor or perfect interval, altered by a descending semitone.

An augmented interval is a major or perfect interval, altered by an ascending semitone.

So... the diminished second is enharmonically equivalent to the unison (that is, it would be C-Db)

the diminished third is a minor third with another flat (C-Ebb)

the diminished fourth is a PERFECT fourth with a flat (C-Fb)

the diminished fifth is a PERFECT fifth with a flat (C-Gb)

etc...

for the augmented ones,

an augmented second is a MAJOR second with a sharp (C-D#)

an augmented third is a major third with a sharp (C-E#)

an augmented fourth is a perfect fourth with a sharp (C-F#)

and so on.

But by doing this, one becomes dependent on the tonal system; pretend to explain it to someone who doesn't even know what a major scale is... and then which one, a pentatonic?

...oh my god, the first effects of my teacher's cure 😟

... and this document

http://www.ludovico.net/download/papers/RT_001.pdf

Dante wrote:

However, by doing this one becomes dependent on the tonal system; pretend you are explaining it to someone who doesn't know what a major scale is...

I would start by meditating on why an interval is defined as major/minor and not a distance of one and a half tones. Or equivalently, but based on which factors/parameters?

In my opinion, all the nomenclature refers to the world of scales. A diminished interval is something less than something well-defined, the same goes for the augmented one... augmented relative to what? To a model interval derived from a scale, precisely.

The same classifications: consonant, dissonant, and mixed depend on a well-defined system.

Classical interval names only make sense within the tonal system.

That being said, there are "other" names that are absolute, in a physical sense. If you evaluate the tuning of an interval, you can do so by calling the interval generically by its name (like "fifth") and adding other types of adjectives or ratio of tuning (like "fifth 3:2" or "Pythagorean fifth" or "perfect fifth"). Adjectives like major, minor, augmented, diminished have sense only in a "classical" tonal system. That being said, all the more reason if you find yourself in another system, you will ALWAYS have to refer to a reference tonic or a scale.

The very concept of an interval cannot be separated from a starting point, a tonic in our case, and in practically all modal scales, the tonic creates interval hierarchies.

Exceptions only exist in serial systems... there, in theory, no tonics exist...

thallo wrote:

Exceptions only exist in serial systems... there, in theory, there are no tonics...

Strong in an absolute sense doesn't use F# or anyway the leading tone in a series of not 12 sounds?

I don't understand what you mean, Tiger

thallo wrote:

I don't understand what you mean, Tiger

You are right, I was extremely brief.

I meant to say that when Forte calculates interval vectors, he brings the chord to its prime form... an operation he performs by establishing a sort of tonic, to be clear, by establishing the lowest sound.

Having said that, something which I am certain of, I have noticed that two possible scenarios occur. In the first, F# is at the bottom, in the second B... that little bit I have read mentions, but I don't know in what sense, the leading tone... 😵

That is why I was asking 😉

The issue is complex... and it is worth making a premise, a fundamental premise for EVERY analytical technique: Forte gives his opinions, which are historically contextualized, and his analytical system must be calibrated for each repertoire.

From this, some considerations.

1) For many, the chord has a tonic. And the tonic is generally the bass, whether expressed or unexpressed. This is a theory of chords that dates back to Rameau and gives prominence to the low sound as the principal sound.

2) In theory, Forte should deny this since the concept of a "set" is independent of the distribution of intervals. That is, no matter its position, a set is always itself (in various permutations).

3) However, if you want to analyze the permutations of a set and give MEANING to those permutations, then you must also evaluate the bass and the sonic, historical, "harmonic" role of one bass relative to another. If a chordal permutation of a set is structured as a fifth containing other notes, it makes sense for you to say "the frame of this permutation is a fifth, and it is credible to think that the composer knows this too". Just as it is credible to think that while listening to the piece you perceive the fifth... so what do we do, ignore that the fifth exists just because the composition is dodecaphonic? That would be throwing all of Berg away 😉

4) Everything is resolved by giving weight to things that have weight and removing weight from things that do not. In other words: there are composers who, even in serial music, identify more important degrees, and composers who, even in non-serial music, drastically diminish the role of the tonic (and its related intervals).

I will add a personal experience. I talk about it often now, but having written my thesis on it, it is a subject I am very well-versed in...

La Monte Young writes in natural intonation. There are certain "sets" that he uses, very simple sets made essentially of fourths, fifths, and minor sevenths. These sets, however, always exceed the octave and are configured in precise positions. Simply put, they very often follow the configuration of natural harmonics. Not only that, but they cannot be reduced to a prime form, because Young plays on instruments tuned in a particular way by himself; therefore, that minor seventh there (7/4, septimal minor seventh) exists only in relation to certain "tonics". In this case, I gave up using set theory (even though it would have been convenient because it would have highlighted these recurring intervals very immediately) because it would have distorted the composer's conception.

I will add one more reflection. Series are different from scales also because they do not inherently recognize a linear organization of hierarchies. That is... in theory, dodecaphony eliminates hierarchies. In reality, it reformulates them. The same applies to serialism. The point is that these hierarchies are often imposed in an "unjustified" way. That is, you decide that in your series the most important note is the sixth note of the series, not the first. As happens with the finalis of Gregorian plagal modes, for example. Or again, you can decide that the "tonic" is, in reality, a polyphonic cluster, like a major third, and find a way to communicate this idea. Hypothetically, you could decide to give an "attractive" role to an effect, a noise, a dynamic, or a rhythmic cell. Serialization is this: it is reformulating EVEN the hierarchies. In this sense, I say that the role of the tonic and the intervals is not obvious in serial compositions.

Thank you truly to everyone also for having drawn blood from such a vast topic..apparently.

I'll take advantage of this topic... what effect do intervals produce?

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

I hope it's not too complicated