Learning Music Theory Part 2 (Dotted Notes and Rests)

In this blog post, I discuss what I’ve learned about dotted musical notes.  A musical note that is accompanying with a dot usually means a length of a musical note is being extended.  Being extended by how much?  Usually, a dot represents half of a parent note’s length.  So, for an example, a dot of a dotted whole note is half of a whole note, and so this means the length of this dot is 2 in 4/4 time signature staff (or in any other x/4 time signature staff).  Furthermore, I think we can visualize a dot in sound by imagining a parent note’s sound is being sustained for a bit longer by the length of a dot.

Dotted whole note isn’t common.  Nonetheless there are other dotted notes.  On the top of my head and from what I’ve learned about the dotted notes, the other dotted notes are dotted half, quarter, and eighth notes.  Furthermore, rests (silences) can also be dotted.  Thus we also have dotted whole, half, quarter, and eighth rests.

It’s easy to count dotted whole and half notes in writing and voice.  For an example, counting dotted whole note in writing we got 1-2-3-4.

Counting dotted quarter note can be tricky.  Let’s try to count a dotted quarter note shall we?  We can visualize a dot to the right of a quarter note as an eighth note, because half of a quarter note is an eighth note.  Since a dot can be visualized as an eighth note, by using the counting system for eighth notes we can easily count the dotted quarter note.  So, there are 2 eighth notes in a quarter and 1 eighth note in a dot; in total we got 3 eighth notes.  Usually, there will be an additional eighth note to be added right after the dotted quarter note so 2 full beats can be formed.  This means now we have 4 eighth notes in total.  Counting this in writing should be like 1-+-2 +.

Counting dotted eighth note can also be just as tricky as counting dotted quarter note.  Let’s try to count a dotted eighth note shall we?  We can visualize a dot to the right of an eighth note as sixteenth note, because half of an eighth note is a sixteenth note.  Since a dot can be visualized as a sixteenth note, by using the counting system for sixteenth notes we can easily count the dotted eighth note.  So there are 2 sixteenth notes in an eighth and 1 sixteenth note in a dot; in total we got 3 sixteenth notes.  By adding one more sixteenth note to a dotted eighth note (3 sixteenth notes), we got 4 sixteenth notes to round up everything as 1 full beat in a x/4 time signature staff.  How?  4 sixteenth notes = 2 eighth notes = 1 quarter note = 1 beat in x/4 time signature staff.  We can count the dotted eighth note and a sixteenth note together in writing as 1-e-+ a.

We can use the same counting methods of dotted notes to count the dotted rests (silences).  As always, counting the rests in writing should be inside parentheses.  As always, counting the rests in voice should be in lower audible tones.

Anyhow, it’s hard to visualize notes and length of notes in writing, and so I’d made couple images to help you visualize what I’d mentioned earlier.  Click on the images below to enlarge them.

Dotted Notes six four time dotted whole half quarter

Dotted Notes four four time dotted eighth

Dotted Notes six four time dotted rests

Here is a little test that I’d done.  First, the question is what is the length of a dotted eighth note in 4/4 time signature staff (in arithmetic)?  To answer this, we have to do a little math.  First, we ask ourselves, what is half of a quarter?  Half of a quarter is an eighth note we know, but in arithmetic, it’s 1/2.  Since the dot to the right of an eighth note is a 16th note — a dot is half of an eighth note — we can simplify everything down to 16th notes to make things simple to count and what-not.  So we have to ask ourselves what is half of an eighth note in arithmetic?  1/2 of 1/2 = 1/4 or (16th note).  Since we can visualize there are 3 16th notes in a dotted quarter note, and so 3 of 1/4 = 3/4 (as in 3 * 1/4 = 3/1 * 1/4 = 3/4).  So the answer to our question of what is the length of a dotted eight note in 4/4 time signature staff is 3/4 (in arithmetic).

Learning Music Theory Part 1

My love for making music began with Cakewalk’s Music Creator software which I bought on Steam a year or two back if my memory is correct.  From Music Creator, I saw how easy it was for me to produce sounds from MIDI controller devices such as M-Audio’s AXIOM AIR 25 MIDI Keyboard controller.  Furthermore, Music Creator allowed me to record audio and piece audios together with ease.  From Music Creator, I graduated to Sonar X2 Studio and eventually Sonar X3 Studio.  Right now I’m using Sonar X3 Studio with various third party VSTs (Virtual Studio Technology).  With different specific VSTs, I was able to produce wide variety of sounds and musics.

Anyhow, I was not able to read music and write music in music language, because I was lacking in music theory knowledge.  Instead, I was making music with my hearing only.  I used my ears and my love for feeling a new tune to come up with music that I was able to record through Sonar X2 and Sonar X3 Studio software (and various VSTs).  Sometimes, I used loops and samples too!

Nonetheless, as my love for making music expands each day, now I begin to see my lacking of music theory knowledge is a drawback.  I want to be able to write music and read music without the help of a software.  For your information, software such as Sonar X3 Studio does provide Staff view, and this view automatically writes out the musical notes that you play from your MIDI controller.  Although software can obviously write out the musical notes and keep musical notes on records, the records of musical notes would be no good for me in the future if I can’t read these musical notes, right?  Furthermore, I think developing insight into reading and writing music and knowing more of musical theory might help me in creating better music in the future.  Nonetheless, music is all about sounds, and so sounds do come before theory!

At the moment, I’m reading a musical theory book, “Basic Music Theory: How to Read, Write, and Understand Written Music (4th ed.)” by Jonathan Harnum, on Kindle software.  It’s a wonderful beginner book for musicians who want to start learning music theory.  It’s so easy to understand that I think I’m being blessed for being able to read this book in this time.  I’ve gotten only to Chapter 9 — each chapter is very precise and thoughtfully brief to the point of keeping things easy to understand and digest — and yet I’m able to decipher what are musical notes, time signatures (or meters), musical rests, importances of musical staffs (one line and five lines staff or staves),  musical bars, musical measures, and counting music.  This is a lot of materials to digest, and yet this book helps me digest so much music theory knowledge in couple hours.  Of course, how much music theory knowledge I will retain over time can only be told by my perseverance of staying in touch with music theory for some times to come.

Without musical beats and silences and pitches, tunes will hard to come by.  With good tunes, sounds from beautiful instruments, and good lyrics, good music can be achieved.  Of course, good music doesn’t necessarily need to include lyrics, but with good lyrics music can become another fascination.  I’m no expert in making music, and I’m a student of music as long as I breathe, I think.  This is why I intend to write blog posts on some of the music theory I’ve learned, and only in this way that I can record what music theory I’ve learned.  In this very way, I can ensure my effort of learning music theory can be revisited by me in the future through my blog posts.  Perhaps, I may need to rekindle my music theory knowledge somehow in the near or distant future, because of bad memory or whatever.  In addition to my own benefits, hopefully these coming blog posts of mine on music theory will also help others whose desire is to learn music theory.

I won’t be able to do a good job in capturing music theory knowledge as the book I’d mentioned in this blog post earlier, and so I advise you to check out the book if you are wanting to pick up on basic music theory essentials.  Nonetheless, here let me mention few basic music theory essentials.

From what I’ve retained of reading on music theory so far, it seems that learning music theory is to facilitate one’s knowledge into reading, writing and understanding music language.  Although music is all about sounds and patterns of sounds, only with certain music theories (because there are different theories of how to form music in readable symbols and numbers and words) that we can really capture music in records that can be passed onto others for reading and replaying the same music.  Furthermore, I’ve the feeling of music theory is far beyond in just forming music language, but it’s more of tricks and what-not that can enhance one’s music production.

The trick to be able to read and write music is definitely beginning with familiarizing musical notes.  Musical notes represent musical beats.  Musical beats are steady sound pulses that can form patterns, thus we have musical tunes and music in general.  According to what I’ve read, common musical notes are quarter, half, and whole notes.  Commonly, a quarter note represents one beat, a half note represents two beats, and a whole note represents four beats on common staffs such as 4/4 time signature staff (or four four as in 4 beats per measure and quarter note per beat).  These notes can be written on one line or five line staff.  One line staff was the easiest to read, but cannot represent the sophistication of intricate musical instruments and sound patterns, I think.  Thus, we have five line staff that allows us humans to record music with greater sophistication.  Five line staff is more complex and harder to read, but it’s more common today.  According from what I’ve read in the book I mentioned earlier, one line staff is commonly used with recording musical notes made by percussion instruments.  Five line staff is commonly used with music instruments that have greater sophistication in sound pitches and so forth.

Each staff can be divided into measures.  These measures can be represented by single musical bar (or bar-line) and double musical bar (or double bar-line).  The measures are there for making reading music easier.  Thus, each measure divides group of musical notes into a section within a five line staff.  A double musical bar signifies the end of a section, movement, or entire song.  Let’s backtrack a bit, a five line staff has five lines and four spaces, and each line and space has to be counted from bottom up.  The very bottom line is line 1 and counting up from here.  This means the very top line is line 5.  The between of line 1 and line two forms space 1, and we can count the upward from here (up to space 4).  The musical bars I mentioned can also be called bar-lines (e.g., single bar-line, double bar-line).

You can tell a musical note is a whole note when a symbol of emptied elliptical circle is being drawn onto a staff (whether that would be a single or five line staff).  You can tell a musical note is a half note when a symbol of emptied elliptical circle attaches to a stem which either goes up or down.  You can tell a musical note is a quarter note when a symbol of filled-in elliptical circle attaches to a stem which either goes up or down.

Musical note with stem goes up needs to be positioned either directly on the third line of the five line staff or below the third line of the five line staff.  A half note with stem goes down needs to be positioned either directly on the third line of the five line staff or above the third line of the five line staff.  Don’t you notice how strange that a third line of the five line staff allows the stems of musical notes to either go up or down?  It’s because the third line allows musical notes with stems to conform to the direction of the stem of the next musical note.  A musical note with stem goes down needs to have a stem attaches to the left of the elliptical (either filled in or emptied) circle.  A musical note with stem goes up needs to have a stem attaches to the right of the elliptical (either filled in or emptied) circle.  Easy to remember trick is imagining note with stem down as letter d for (down) and note with stem up as letter p for (up).

Musical Five Line Staff JPEG By Vinh Nguyen

Silence in music is known as rest, and there are various rests.  Rests can be represented in various symbols, but the way we count the rests in beats are comparable to the non-rest counterparts.  For an example, in the picture above, we can see a hat looking icon represents a half rest (non-rest would be half note in four four time signature), and this half rest can only be sit upon the third line in the five line staff.  The upside down hat looking icon represents the whole rest (non rest would be whole note in four four time signature), and this whole rest can only be hanging from the fourth line in the five line staff.

Besides knowing how to read the basic notes in common time signature staves, we need to know how to count the beats.  Counting the beats help one in knowing how the beat would play out and how long the beat would last and so forth.  Silents/rests can be counted with a whisper or in a lower audible tone.   Counting 8 (eighth) note would require an and in voice counting or + in writing, and whenever an and or + is met one needs to know this is an up beat, thus a foot goes up if one is foot tapping to the beats.  Counting 16 (sixteenth) note would require e and a in voice counting and writing (e.g., 1 e + a, 2 e + a, 3 e + a, 4 e + a).  When writing out silences or rests, the counting of writing needs to be in parentheses, and an example would be (1-2).

Eighth note (8) will have a flag, sixteenth note (16) will have 2 flags, and adding another flag indicate cutting down more of the lasting time of a beat by previous count by half.  When grouping same flag notes together, they form flag bar.  Single flag notes in group such as (a group of eighth notes) form a single horizontal bar above or below the notes’ stems according to the stems’ direction.  Double flag notes in group such as (a group of sixteenth notes) form a double horizontal bar above or below the notes’ stems according to the stems’ direction.

Eighth and Sixteenth Notes With Flags by Vinh Nguyen


Eighth Notes and Sixteenth Notes With Flags In Group


And then there is an eighth rest which looks like a number 7 with a small circle growing to the left and on the top of the horizontal line of the number 7.  I’m too lazy to draw it out and post a picture for this, but you will know what I mean when you see one, I think.  Eighth rest needs to be positioned in the middle of the staff.  Sixteenth rest has one more flag to the seven looking alike eighth rest.  So instead of one strange looking tip that attaches to the eighth rest, 16th rest has two strange looking tips as if a mini and bigger number sevens combine into one.

Let’s try to count in 2/4 time signature (meter) of 16th notes in a group OK?  If I’m not wrong, this is how it should be… This means we have to visualize beats in 16th notes, but the maximum we can group 16th notes into group is to have the 16th notes adding up to 2 quarter notes per measure.  How come?  2/4 time signature tells us that 2 can only have 2 beats per measure, but the secret code #4 tells us that #4 is a quarter note type beat.  So, basically we need four 16th notes for a quarter note.  Nonetheless, 2/4 time signature tells us that we can have 2 quarter notes in a measure, and so we need eight 16th notes for a measure.  By visualizing this we got the counting in writing for eight 16notes in a measure as 1 e + a,  2 e + a.  If there is a silence/rest in a counting somewhere, then we should add in the parentheses.  An example would be 1 e + (a), 2 e (+) a.  I think to understand this better, one needs to know how short a time of a beat is.  With this in mind, I guess we can imagine it takes four 16th beats/notes to make up a quarter beat/note, thus the 16th beat/note is 4 times shorter in duration than a quarter beat/note.

Let’s try to count in 4/4 time signature (meter) for 8th notes in a group OK?  If I’m not wrong, this is how it should be in writing… 1+2+3+4+.  If there is a silence/rest in a counting somewhere, then we should add in parentheses.  An example would be 1(+)2+3+4(+).

I also learn that familiarizing with the symbols of the notes allows you to facilitate the visualization of the counting of notes in writing or in silence.  For an example, in 4/4 time signature, if we need to write the counts of the eighth notes out fast, all we need to remember is that 2 symbols of eighth notes equal to one quarter note.  Since 4/4 time dictates 4 quarter beat type per measure, we know we need eight eighth symbol notes for the measure.  Of course, to make the picture even simpler, we can visualize that a pair of eighth symbol notes equal to a quarter, and so we need 4 pairs of eighth symbol notes.  Thus it goes 1+2+3+4+.  Of course, you have to count the + as and when you read it out.  + or and equal an eighth beat if we’re talking about eighth notes in 4/4 time signature (meter).

It’s sort of confusing the way I describe — in writing and images in this blog post — of what I can remember on the top of my head so far in term of my music theory learning progress.  Nonetheless, hopefully what I describe in this blog post will be useful for anyone who wants to learn some music theory’s basic essentials.  As I try to learn more stuffs from music theory from all reputable sources, I will try to post more of what I will know on music theory on this blog of mine.  Until then…





Blender: My First Blender Project And Experience, A Coffee Cup Is A Lot More Than Hello World Kind Of Things

I’ve known of Blender, open-source/free 3D rendering software, for a long time and installed the latest version onto my PC whenever the opportune moment arrived, but I have never really tried to learn and use it.  Today, I committed some of my time to try to create my first Blender’s 3D rendered image.  By following the “Blender Tutorial For Beginners: Coffee Cup” videos (there are 2 parts), I was able to render a very nice coffee cup.  I did not follow the tutorial videos I mentioned to the letter, because I scaled the middle part of my coffee cup a bit bigger and outward.  Basically, what I meant was that my coffee cup is more round in the overall shape.  Moreover, I rendered the coffee cup with 1000 samplers and .98 clamp.  The tutorial videos rendered the coffee cup with 250 samplers and .98 clamp.  According to the tutorial videos, the higher the number for the samplers of a rendered image, the better the image will look.  I guess, it’s also true for the clamp.  I think the higher the clamp number between 0 and 1, the less fireflies there will be.  The tutorial videos explained that the fireflies are those white pixels that appear in unwanted place when the image gets rendered.  I guess .98 clamp meant 98% for clamp, but please do correct me if I’m wrong on this.

Anyhow, after following the tutorial videos, I got myself a very nice 3D rendered coffee cup image.  Check out the cup right after the break.

Blender 3D rendered cup 01 with 1000 samplers and .98 clamp

You can download the Blender project files that I created for this very image by clicking on this link -> Blender 3D rendered Coffee Cup Project Files By Vinh Nguyen.  I used Blender 2.7 version to render this very 3D coffee cup image.

Right after the break, you can check out the YouTube tutorial videos that I watched and learned to create the coffee cup.