Beginner theory Looking for information on understanding some fundamentals of music theory

In 4/4 time there are 4 beats in the bar. Pronounced Misissippi
Any of these beats may be subdivided into two 8th notes - Doobe Doobe Doobe Doobe

In 6/8 there are two beats in the bar, but each of them is subdivided into three eighth notes. Pronounced Apricot Apricot.
 
Since the note durations are made explicit this way, why even specify it in the time signature?

Because the first bar might not contain 6 eighth notes.
These bars are also in 6/8

Screen Shot 2018-09-16 at 00.01.31.webp
 
3. When listening to non-classical music, should you be able to identify (a) the number of beats per measure-ie, the lower number in the TS (8 in the case above), by counting beats from the rhythm backing; (b) the start of each measure?

You should be able to tell how many beats there are in a bar, and that should normally tell you the top number in the time signature, but it does not necessarily tell you what the bottom number is. For example, a piece with 2 beats in the bar could be in 2/4 or 2/2.

And sometimes the time signature is just plain confusing. For example, the second movement of Beethoven's 4th Piano concerto is written as 2/4, but there are actually 4 quite slow 8th note beats in the bar.
 
AHA! Thank you-my Theory Manual does not mention this, at least in the introduction to the topic. Since the note durations are made explicit this way, why even specify it in the time signature?
Different time signatures can have different "feels," which in part is where emphasis is placed in a measure. Is also effects how notes are connected in the way that confused you- in 4/4 it would be 2 eighth notes sharing a connecting bar as opposed to the three that share a bar in 6/8. The begining of a grouping represents a downbeat.
Amendum: didn't realize there was another page, sorry for redundancy
 
If you're starting off learning both a new instrument and written music, your Teacher will set you appropriate pieces of music to learn, which will gradually increase your knowledge and understanding. Simple Time signatures and Keys to start off with. A well constructed student book, which your Teacher should suggest, will be laid out to introduce new aspects over a period of time,

Whilst it's perfectly reasonable to want to get answers to questions about music theory at any point, learning the fundamentals will provide the blocks for understanding more complex examples, like the one in this post.
 
OK. In 'simple' or 'duplex' time signatures, the unit of the beat can be sub-divided into two - hence 'duplex'. So, a crotchet (quarter note) can be split into two quavers (eighth notes), a quaver (eighth note) can be split into two semi-quavers (sixteenth note).
In compound time, each unit of the beat can be split into three. So, a dotted crotchet (the "." (dot) after the note lengthens it by 50%) can be sub-divided into 3 quavers/eighth notes (aka 'triplets') etc.
You know you're dealing with 'compound' time (i.e. stuff that is split into thirds instead of halves) by the top number being divisible by 3.
It's a somewhat contrived system, but no-one has come up with anything better that's widely accepted as an alternative.
 
You should be able to tell how many beats there are in a bar, and that should normally tell you the top number in the time signature, but it does not necessarily tell you what the bottom number is. For example, a piece with 2 beats in the bar could be in 2/4 or 2/2.

And sometimes the time signature is just plain confusing. For example, the second movement of Beethoven's 4th Piano concerto is written as 2/4, but there are actually 4 quite slow 8th note beats in the bar.
Interesting. And clearly above my pay grade.
 
If you're starting off learning both a new instrument and written music, your Teacher will set you appropriate pieces of music to learn, which will gradually increase your knowledge and understanding. Simple Time signatures and Keys to start off with. A well constructed student book, which your Teacher should suggest, will be laid out to introduce new aspects over a period of time,

Whilst it's perfectly reasonable to want to get answers to questions about music theory at any point, learning the fundamentals will provide the blocks for understanding more complex examples, like the one in this post.

I'n not studying MT in and of itself. My teacher has advised me to learn to become conversant with notes, intervals and rests, the G Major and time signatures in order to widen the range of music I eventually hope to play. However, this question came purely from me since it appeared to be covered by the yopics above. I have no intention of going any farther as I since that MT is hopelessly, convolute,e and unintuitive!
 
I have no intention of going any farther as I since that MT is hopelessly, convolute,e and unintuitive!

Any new subject seems complicated at first. Music theory is simply trying to describe what people do when they create music. Over the years a shared notation has been developed to describe note pitches, note lengths, underlying rhythms and underlying harmonies of western music.

So a time signature tries to describe the rhythm. Nowadays we usually divide music up into bars, with a strong beat at the start of the bar. This makes it easier to dance to the music or to play and sing along in a group. Most European pieces of music have quite simple rhythms with 2, 3 or 4 equal beats: 2/4, 3/4 and 4/4. (Latin American music can have more complex rhythms.)

In Compound Time, each of the beats in the bar is subdivided into three - Diddely Diddely Diddely Doo. A standard way has evolved to represent this: 6/8, 9/8 and 12/8 - representing 2, 3 and 4 beats in the bar. The tails of the 8th notes are also joined together in threes to make the rhythm clearer. The last movement of the Horn Concerto is in 6/8; it's rhythm is Diddely diddely.
 
Much of what you asked has been answered here already, and I won't muddy the waters by adding anything.

As time goes on and you learn to play more saxophone, more music theory should be inherently introduced into your lessons (it sounds as though your teacher is already suggesting relevant pieces of theory)

I don't think learning to play the piano will offer any support to your music theory knowledge at this stage in your journey.

If you haven't come across it already, this web-site : MyMusicTheory. Free online music theory lessons following the ABRSM syllabus offers a steady progression in the knowledge of music theory. It is based around the ABRSM music theory grade exams (originating from the UK, but the exams are taken around the world by those who choose to take them)

If you have any further questions, or require any further clarification, just ask.
 
AHA! Thank you-my Theory Manual does not mention this, at least in the introduction to the topic. Since the note durations are made explicit this way, why even specify it in the time signature?

One reason is so that you can tell the difference between 3/4 and 6/8. 3/4 has three quarter note beats per bar. 6/8 has 2 beats per bar each lasting for 3 eighth notes. You are right though, it is usually obvious from the note groupings. In some cases it isn't e.g. a bar with just a dotted minim..
 

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