Harmony and counterpoint

doubts about music theory books

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Fox

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Opening post by Fox

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Hi and sorry if I am always asking you a lot of questions

But books are sometimes unclear and teachers often say so!

There is one thing I really don't understand, and that is why all the books call 4/4 or 2/4 a "fraction"?

My teacher says it is not a fraction! But then why do the texts say fraction?

No, because then the concept of numerator and denominator would also be wrong.

The books call 2 the numerator and 4 the denominator, using 2/4 as an example (but if it's not a fraction, we cannot speak of numerator and denominator)

And if 4/4 is not a fraction as the books say, then what is it? It's certainly not the tempo, which is the speed of the piece (like Allegro - 120 bpm for a quarter note)

Then the concept of "movement" is also wrong. For example, 4/4 consists of two movements on the downbeat and two on the upbeat (that's how books write it), but in reality, these are not movements but accents. So why don't they say 2 accents on the downbeat and two on the upbeat?

I have understood that 4/4 is the meter, the metric (the unit of measurement) of the piece, which can then change (indicating a different meter during the course of the piece, obviously).... I don't know, if the piece starts in 4/4 it can change to 2/4 and then return to 4/4... etc.

According to the classification in textbooks, speaking of simple and compound meters, it explains that for example, the fraction 2/4 indicates 2 as the numerator and 4 as the denominator, meaning 2 indicates the number of beats (that are in the measure) and 4 the value of the beats (1/4), but it is wrong to say it like that!

It would be correct instead to say that: 2 is the number of accents and 4 the value of the single accent (referring to the 2/4 meter)

For example, this sentence: The simple binary meter is formed by two beats in which the first beat (of the first movement) will be strong and the second weak. E.g., 2/2, 2/4, 2/8.

is wrong according to what I am studying; it is correct instead to say: The simple binary meter is formed by two accents in which the first accent will be strong and the second accent weak. E.g., 2/2, 2/4, 2/8.

Did I do well, friends?

Thank you and sorry for the doubts, but as you can see, it is sometimes the books that are wrong

PS: In the sentences where I increased the size, I did so to better highlight the importance of the matter

To summarize

In the end, what they teach as a fraction is the meter (example 4/4) - where the first (4) is the number of accents we will find in the measure and the second (4) is the value of each single accent, which will be: first accent strong, second weak, third mezzo-forte, fourth weak in the case of 4/4

Then, the movements on the downbeat and upbeat are always the accents; in the case of 4/4, two accents on the downbeat and two on the upbeat..

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Reply 2 by Valchiria

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For basic information, you can turn to Luigi Rossi. Clear, organized, and educational. I'm not preaching the Gospel, but for someone starting from zero, it represents a good overview.

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Reply 3 by Fox

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Valchiria wrote:

For basic information, you can turn to Luigi Rossi. Clear, organized, and educational. I'm not preaching the Gospel, but for someone starting from zero, it represents a good overview.

Thanks, for me it would be enough if the instructions were correct and I'd already be happy

Believe me, I have studied a lot to understand these things and I have compared myself with various music teachers and I have read many texts and handouts

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Reply 4 by Thesimon

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In my opinion, we need to talk about Time Signatures, beats, and subdivisions. The time signature is represented by a fraction in which: in simple time, the numerator expresses the number of beats and the denominator, the value of a beat. In compound time, the numerator instructs us on the number of subdivisions and the denominator on the value of a subdivision.

In simple time, one beat is composed of two subdivisions; in compound time, it is composed of three subdivisions. This explains why 6/8 is a binary meter, precisely because it is made up of two beats and six subdivisions (2 x 3 = 6) and comes from its relative simple meter 2/4.

In particular, for every time signature we could perform an analysis by asking ourselves:

- whether it is a simple or compound meter

- whether it is a binary meter (2 beats), ternary (3 beats), quaternary (4 beats), quinary (5 beats), etc.

- how many beats does it have?

- how many subdivisions?

- what is the unit of beat?

- what is the unit of subdivision?

- what is the unit of measure?

- what is its relative simple/compound meter?

Let's take 3/4 as an example:

- Simple or compound meter? SIMPLE

- Binary, ternary, quaternary... ? TERNARY

- How many beats does it have? THREE

- How many subdivisions? SIX

- What is the unit of beat? THE MINIM (HALF NOTE)

- What is the unit of subdivision? THE EIGHTH NOTE

- What is the unit of measure? THE DOTTED MINIM

- What is its relative compound meter? 9/8

This reasoning can obviously be applied to all time signatures.

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Reply 5 by Valchiria

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Fox wrote:

as far for me, it would be enough if the indications were correct and I'd already be happy

And what better way to understand it than by using a good text?

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Reply 6 by Fox

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TheSimon wrote:

In my opinion, we need to talk about Time Signatures, beats, and subdivisions. The time signature is represented by a fraction in which: in simple time, the numerator expresses the number of beats and the denominator, the value of a beat. In compound time, the numerator instructs us on the number of subdivisions and the denominator on the value of a subdivision.

In simple time, one beat is composed of two subdivisions; in compound time, it is composed of three subdivisions. This explains why 6/8 is a binary meter, precisely because it is made up of two beats and six subdivisions (2 x 3 = 6) and comes from the relative simple meter 2/4.

In particular, for every time signature we could perform an analysis by asking ourselves:

- whether it is a simple or compound meter

- whether it is a binary meter (2 beats), ternary (3 beats), quaternary (4 beats), quinary (5 beats), etc.

- how many beats does it have?

- how many subdivisions?

- what is the beat unit?

- what is the subdivision unit?

- what is the time signature unit?

- what is its relative simple/compound meter?

Let's take 3/4 as an example:

- Simple or compound meter? SIMPLE

- Binary, ternary, quaternary... ? TERNARY

- How many beats does it have? THREE

- How many subdivisions? SIX

- What is the beat unit? THE MINIM (HALF NOTE)

- What is the subdivision unit? THE EIGHTH NOTE

- What is the time signature unit? THE DOTTED MINIM

- What is its relative compound meter? 9/8

This reasoning can obviously be applied to all time signatures.

Thank you so much; in fact, textbooks explain it exactly the way you wrote... actually, for me, you wrote it better than the books! Now I will copy your scheme into my notes :) however, my doubts remain, because I am studying that beats are actually accents and that even the movements within a measure are accents, and that dividing by movements is wrong just as much as dividing by beats. Anyway, thank you for the scheme, it will be very useful to me. One thing is certain: the words change, but the procedure is the same!

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Reply 7 by Fox

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TheSimon wrote:

In my opinion, we need to talk about Time Signatures, beats, and subdivisions. The time signature is represented by a fraction in which: in simple meters, the numerator expresses the number of beats and the denominator, the value of a beat. In compound meter, the numerator instructs us on the number of subdivisions and the denominator on the value of a subdivision.

In a simple meter, one beat is composed of two subdivisions; in a compound meter, it is composed of three subdivisions. This explains why 6/8 is a binary meter, precisely because it is made up of two beats and six subdivisions (2 x 3 = 6) and comes from its relative simple meter 2/4.

In particular, for every meter we could perform an analysis by asking ourselves:

- whether it is a simple or compound meter

- whether it is a binary meter (2 beats), ternary (3 beats), quaternary (4 beats), quinary (5 beats), etc.

- how many beats does it have?

- how many subdivisions?

- what is the beat unit?

- what is the subdivision unit?

- what is the time signature unit?

- what is its relative simple/compound meter?

Let's take 3/4 as an example:

- Simple or compound meter? SIMPLE

- Binary, ternary, quaternary... ? TERNARY

- How many beats does it have? THREE

- How many subdivisions? SIX

- What is the beat unit? THE MINIM (HALF NOTE)

- What is the subdivision unit? THE EIGHTH NOTE

- What is the time signature unit? THE DOTTED MINIM

- What is its relative compound meter? 9/8

This discussion can obviously be applied to all meters.

Can I paste here, regarding tempo, a part of a wiki page that explains exactly what you are saying? In essence, tempo has different meanings and is not intended only as the speed of a piece.... now everything is clear.

CONCEPT OF EXTENDED TEMPO

Tempo is a term that has several meanings, depending on the subject being discussed.

From a metrical point of view, tempo refers to the time signature and the numerical fraction.

In fact, as we have seen, the numerical fraction indicates in its numerator the number of beats present in each measure

and in the denominator the value to be assigned to each of them.

The classification of beats is the other area where this term is used, regarding simple beats and compound beats.

Tempo can also indicate the pace or agogic indication (Adagio, Andante, Allegretto, Allegro, etc.)

placed at the beginning of a piece, as well as the metronome indication.

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Reply 10 by pianoexpert

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Who knows why they are called simple meters and compound meters. It doesn't seem to me, if I'm not mistaken from having read it....Let's see who tells me

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Reply 12 by Fox

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I read that 7/4 = 3/4 + 4/4

but how do I divide it if I want to sight-sing it? 3 movements on the downbeat and 4 on the upbeat?

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Reply 14 by Fox

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TheSimon wrote:

on the contrary

Thanks, can I also beat 4/4 + 3/4? That is to say, one on the downbeat and three on the upbeat, and then one on the downbeat and two on the upbeat, putting the strong accent only on the first note of each measure?

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Reply 15 by Fox

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What I would also like to understand is why the mixed meter 5/4 is composed of a simple 2/4 duple meter and a simple 3/4 triple meter, or vice versa? And how do I distribute the accents? Can you please help me? Thanks everyone

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Reply 16 by Thesimon

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5/4 - The first two beats on the downbeat, third, fourth and fifth on the upbeat.

7/4 - The first 4 beats on the downbeat, fifth, sixth and seventh on the upbeat.

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Reply 17 by Marzapane

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5/4 can be understood as 2+3 or 3+2

7/4 can be understood as 3+4 or 4+3

There is an implicit notation (the note values are distributed according to the 2+3, 3+4 patterns or vice versa), an explicit one where in the meter you find for example 2+3/4, and a more graphic (very effective) one widespread in the '1900s' that prescribes the type of "decomposition" of the 5 or 7 quarter notes

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Reply 18 by Fox

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Marzapane wrote:

5/4 can be understood as 2+3 or 3+2

7/4 can be understood as 3+4 or 4+3

hi thanks

so if I divide the movements for example 2+3 (1 beat 1 upbeat and then 1 beat and two upbeats) does the strong accent fall on the first and on the 3?

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Reply 19 by DrJellyfish

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Fox wrote:

hi thanks

so if I divide the beats, for example 2+3 (1 downbeat 1 upbeat and then 1 downbeat and two upbeats), does the strong accent fall on the first and on the 3?

Rather than thinking about accents, I would try to understand the melodic and rhythmic development.

Anyway, if it is a matter of solfeggio, I would do as Simone says, leaving (generally speaking) the 3 at the end. If you have to conduct the discourse, it changes.

I am amazed by the discussion about fractions: if 4/4 is not a fraction, what is?

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Reply 20 by Fox

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DrJellyfish wrote:

It amazes me, this talk about fractions: if 4/4 is not a fraction, what is it?

Hi, thanks for the answer

4/4 is not a fraction but just a time signature, that's how I studied it.. then they call it a metric fraction, but it isn't right (according to teachers)

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