Notating Tunes as Numbers from the Major Scale

In David Reed's book Improvise for Real he uses a numeric method to notate melodies based on the major scale.  This method of writing out music doesn't require a key signature or sharps or flats; it sees all scales as relative, as equals. (The only time a sharp or flat is needed is when a note lies outside the major scale and is therefore "sharper" or "flatter" than the 7 notes of the major scale).

When you write out a melody this way it shows where the notes are found within the (universal) major scale, making it easier to play it in any key on your instrument.  It also allows you to notice patterns or commonalities that you might not otherwise notice when you segregate tunes by key.

For example, I noticed the occurrence of a sharpened 5th note in several of the Caribbean melodies I've been learning, especially those with a minorish sound.  This may be an indication of a dominant 3rd chord which creates tension that is ultimately released by the 6 chord (a minor chord), in much the same way that the naturally dominant chord (the 5 chord) creates tension that is then resolved when it goes to the 1 chord.  In other words, 5 is to 1 as 3 is to 6.

To provide an example of this numeric notating I have chosen Old Joe Clark because it is both simple enough and weird enough to be good fodder for analysis.  Old Joe Clark is what old-timers call a "modal" tune, which basically means that its tonal center is based on a note other than note 1 of the major scale.  However, the notes of the major scale are still 100% present in Old Joe Clark...it just places more emphasis on notes 2 and notes 5 of the major scale than note 1, as you can see in the numeric transcription below.

Old Joe Clark numeric transcription

The melody to Old Joe Clark begins with notes 2, 3, 4, 3 and 2, 1, 7 of the major scale.  If you were placing this in the G-major scale (which is where Old Joe Clark typically resides, believe it or not) those notes would be A, B, C, A and A, G, F#.  I interpreted the melody as starting on note 2 of the major scale because that interpretation allows for all the notes to lie within the major scale.  The height of the number shows whether the melody is going up or down.  As Reed says, this helps avoid confusion when the melody crosses the octave line.

The brilliant thing about notating the melody in this way is that it makes all keys relative, so with a little practice you could just as easily play Old Joe Clark in any of the 12 keys simply by knowing where the notes of each of the major scales fall - in any position - on your instrument.  I am thinking of adopting this notation method for many of the tunes I am learning.  It provides significant insight into the construction of melodies.

Ear Training: 13 Ways To Improve Your Aural Skills by Tom Hess

More and more I’m realizing that aural skills are the most important aspect of playing music.  It’s as simple as hearing a sound on a recording and then finding that sound on your instrument.  Studying theory and being able to read music can make you more knowledgeable, but it won’t necessarily make you a better or more natural player.  Whereas, someone who has worked stuff out by ear by listening to records can usually play pretty well, even if he doesn’t know the theory behind what it is that he's doing. (source: justinguitar.com - Why Transcribing Is So Important) With that in mind, I'd like to share this list by Tom Hess.  13 Ways to improve your aural skills (by Tom Hess) There are lots of ways in which you can improve your aural skills. I've listed many of them below. The idea here is NOT to pick just one of these ideas from the list and expect miracles. Do as many of these things as you can, as often as you can. Activities to practice: 1. Transcribing (figuring out by ear) songs, chords, melodies, solos, etc. using your instrument. 2. Transcribing without using your instrument (write the music down on paper and then when you think you have it as close to accurate as you can get it check your work with your instrument. Notice what errors you made and look to see if a pattern forms in your errors. For example, if you realize that you always think that minor chords sound major chords then you can see that this is something you will need to focus your practice time on. 3. Sing (yes sing out loud) scales. Start with singing the major scale, later add the natural minor scale, harmonic minor scale, pentatonic scale, blues scale, etc. 4. Sing intervals (two notes at varying distances). 5. Sing arpeggios (chords - one note at a time) start with major triads and then move on to minor triads. 6. Sight singing (you will need to have a basic understanding of reading music to do this) You can use any piece of sheet music for this. There are sight singing books that you can buy if you want. 7. Transcribe rhythms. this is just like transcribing a melody, but the focus here is on writing down on paper the rhythm only. 8. Improvising melodies, solos, etc. over chords. This is great thing to do anyway. 9. Imagine a 3 or 4 note melody in your mind and then try to play it on your instrument. 10. Record yourself playing lots of different chords (just major and minor triads for now). Try not to repeat the same chord very often. play back your recording and then try to identify whether the chords you hear are major or minor. 11. For those of you living in the United States, your local community college or university that has a music department typically offers basic aural skills classes that may be open to the general public. Community colleges often charge a very low fee for this class. I am not familiar with how this works in other parts of the world, so non US citizens should check this out with your local colleges. 12. There are ear training software programs available that can be found on the internet. The one I used in college was called Practica Musica by Ars Nova. (Note: This is not an endorsement for practica musica or Ars Nova, I'm just letting you know that this and other aural skills software do exist and can be a valuable resource.) Tom Hess 13. For those of you who may not be able to enroll in an aural skills class, I strongly recommend to seek out a private music teacher. The good thing about seeking a private teacher is that the teacher does not need to be a teacher of your chosen instrument. Any competent music teacher (no matter what instrument the teacher plays) can teach you aural skills. The key is to find a competent teacher though, there are a lot of incompetent teachers out there. Ear training is critical to any musician's development as musician. Remember to persevere and be patient with yourself as your ear develops. Expect progress to be like your physical instrument playing, slow but steadily moving forward each day. Your ear needs constant practicing just like your hands do, so don't neglect the most crucial tool that you have...... your ears! Tom Hess is a successful recording artist and composer. He is also a very dedicated music teacher, mentor, and coach.

Numeric Solfege - Another Way of Naming the Notes in a Scale

What is easier to grasp musically?  The notion of "three, five, one" or "mi, sol, re"?

Numbers seem more innate than the do re mi solfege syllables, especially when trying to recite the do ti, la backwards or remember the one-syllable solfege terms for the five accidental notes that - when added to the major scale - make up the chromatic scale.  Some type of numeric solfege could make the names of the 12 potential notes in a scale more easily understood.

The nice thing about solfege is that it consists one-syllable sounds that roll off the tongue for singing and ear training.  Numbers may not be quite as singable, but all numbers between 1 and 8 are also one syllable except for seven, but you can drop the second syllable and make that number “sev” to keep with the one syllable consistency.  But, what names do you use for the five accidental notes  Obviously, flattened-third and flat-five won't do.

Try this.  All accidentals in the major scale can be thought of as flattened notes.  The word “diminished” is kind of another word for “flat”.  So, to keep the one syllable numeric theme, instead of saying flattened-third (b3) or flat-five (b5), you can simply say “dee” for flat-third (diminished three) and “dive” for flat-five (diminished five).  There is no “D” sound in any of the numbers between one and sev, so by adding a “D” sound to the name of the flattened note it makes it clear that it is a flattened version of the number it rhymes with.

By that logic, the whole chromatic numeric scale looks like this:

one, doo, two, dee, three, four, dive, five, dix, six, dev, sev, eight*

*Or one again instead of eight, if you prefer.  
The "one" would always be the note that you've identified as the root/tonal center.

If you were to start with C as your one, it would look like this:

One	C
Doo	C#
Two	D
Dee	Eb
Three	E
Four	F
Dive	F#
Five	G
Dix	G#
Six	A
Dev	A#
Sev	B
Eight	C

This numeric system is built around the major scale, but because it provides a recognizable name for any possible note in relation to the “one”, you can use it for any scale.  For example, the minor pentatonic scale is 1, b3, 4, 5, b7, 1.  

If you use solfege, you might think of the minor pentatonic scale as la, do, re, mi, sol, la (and , actually, there are benefits to this way of thinking).  But, based on the system described above, the minor pentatonic scale would be considered one, dee, four, five, dev.  Using one-syllable numbers does not seem as abstract as other alternatives.  

An Excerpt from Matt Glaser's Ear Training for Instrumentalists

This week I've been listening to Matt Glaser's Ear Training for Instrumentalists in the car while driving.  Disc Three of this 6-CD Homespun Tapes "audiobook" is where it really gets interesting.  Glaser starts that disc by taking a short phrase and playing it in all twelve keys, while traveling in 4ths, pausing between each key so that you can play it back with him.  First he plays the phrase in C, then F, then Bb, then Eb, then G#, then C#, then F#, then B, then E, then A, then D, then G.  Very cool.

When I got home last night I gave this a shot on mandolin and it sure is an ear and finger buster!  I had to use some extra brain power to get through it, although some of it came surprisingly easy.  The phrase is do - la - sol, la - sol - mi, sol - mi - re, do.  Numerically, this is 1 - 6 - 5, 6 - 5 - 3, 5 - 3 - 2, 8.  Listen to the audio sample below and then try this out for yourself!

Matt Glaser

Matt Glaser is the Artistic Director of the American Roots Program at Berklee College of Music, so yeah he knows his stuff and this is a really well thought out teaching of Ear Training.  It is a few years old (published in 1999?), but the information it contains is of course timeless.  As you might expect, the ear training study overlaps with theory and improvisation.  Since it's mostly audio, with only a few printed pages in the booklet, the six disc set is a nice mix of the intellectual and the intuitive.  

There are many great tips along the way, including what Matt calls "internal hearing", and I haven't even gotten to the last two CDs yet.  This is definitely one of the better music practice book/CD sets I've come across.  What a novel concept - a music instruction book that is actually almost 100% audio!  

At $60 suggested retail, it's a little expensive, but there are some used copies on Amazon for under $25.  Well worth it, considering the content within is as valuable as several lessons with an instructor.  You can also download the audio from Homespun Tapes.  

The Importance of Ear Training in Learning Music

Painting by my Mom

I've been playing stringed instruments for about 8 years now, off and on.  Since I didn't have any prior music experience when I started - no singing in a choir or piano lessons as a kid - I didn't really know how to go about learning it.  I've tried private in-person lessons, Skype lessons, workshops, a music camp.  I've looked at numerous instruction books, videos, blogs, and forums.  I've memorized tunes and practiced scales and arpeggios, and I've regularly attended many oldtime jams and Irish sessions.

All of that helps, especially the one-on-one lessons, daily focused practice, and getting out to play with others.  But over the last 3 weeks since I've been taking two free online music courses*, I feel like the advice I would now give to someone just learning to play music has changed.  Now I would say that the single most important aspect to learning music is Ear Training.

*The two free online classes are "Fundamentals of Music Theory" by the University of Edinburgh Reid School of Music and "Developing Your Musicianship" by Berklee College of Music.

Ear Training is not the same as playing by ear.  You sometimes hear people say stuff like I don't know anything about theory, I just play by ear.  That's only one aspect of it.  To me, a broad understanding of music theory also plays a big part in ear training.  You should know what a minor 3rd interval is compared to a major 3rd.

You should know the names of all the intervals (all 12 within one octave).  Not just the interval names but also the sound that goes with it.  So if someone asked you to play a perfect 4th you could do it.  And vice versa if someone played a perfect fourth on piano you should be able to recognize it.  You should know that a perfect 4th is 5 semitones (or half-steps).  For that matter, you should know what a semitone is! Developing a musical vocabulary (theory) allows you to define what it is you're hearing (ear training).

If I could have had the knowledge, patience and perseverance starting out to devote my first few years explicitly on ear training, then I feel like I'd be a lot more advanced than I am now.  Here's a comment by a person named Chang that I saw on the I Was Doing All Right jazz Ear Training blog that helps illustrate this importance:

I think a good way to think of theory is like grammar. Grammar gives you a structure for understanding language-based communication.
How does a child learn a language? It is not by learning grammar!
A child learns by LISTENING carefully over and over to others who speak the language. Eventually the child learns to hear the words and each word begins to have a unique signature sound as well as a unique meaning. Then the child tries to mimic the words through his instrument (the vocal apparatus). It can take a while to get it right. (Ever hear a young child trying to say words with Rs?) Then the child learns to combine words in a way that more effectively allows him to communicate what he needs. (eg, "MY toy!")
All of this happens way before any grammar is learned!
If you think about it, if you imagine a CAT in your head and can't think of the word CAT, all the grammar in the world will not enable you to express the idea of a CAT! No knowledge of parts of speech, verb conjugations, or sentence construction will get you to the word CAT!
This is exactly the problem in musical education. The correct place to start is to hear lots and lots of INTERVALS and associate each one with a name. We must be able to tell each one of them apart because each one conveys a different musical idea. This is like learning elementary words like YES, NO, ME, DOG, HOUSE, MOMMY, FOOD, etc.
Then we must learn to hear the difference between unique interval combos (scales, licks, riffs, simple melodies, and simple harmonies). This is equivalent to learning idioms, phrases, and simple sentences (eg, "I AM HUNGRY!"). It is only at that point that theory becomes very useful in helping us arrange our musical 'vocabulary' in much the same way that grammar helps us organize the words we speak or write. If one doesn't have a basic vocabulary, then grammar is absolutely useless! Similarly if you can't hear the difference between the M6 and m7 intervals, or you can't pick out the notes which distinguish the minor from the major scale, then music theory will not be nearly as enriching as it could be.

Using Common Songs to Hear Intervals

There's a lot of information online regarding the use of song associations for interval training.  So, I set out to find ascending and descending examples for all the intervals from a minor 2nd through an octave.  Here's what I came up with:

Minor 2nd (one half step)
Ascending:  Jaws Theme
Descending:  Joy to the World

Major 2nd (2 half steps or semitones)
Ascending:  Happy Birthday or Frere Jacques/Fray Felipe
Descending:  Mary Had a Little Lamb

Minor 3rd (3 half steps or semitones)
Ascending:  So Long, Farewell (Sound of Music)
Descending:  Frosty the Snowman

Major 3rd (4 half steps or semitones)
Ascending:  Have Yourself a Merry Little Christmas
Descending:  Swing Low, Sweet Chariot

Perfect 4th (5 half steps or semitones)
Ascending:  Here Comes the Bride or Oh Christmas Tree
Descending:  Old MacDonald Had a Farm

Augmented 4th/Tritone (6 half steps or semitones)
Ascending:  The Simpsons theme
Descending:  Black Sabbath Black Sabbath

Perfect 5th (7 half steps or semitones)
Ascending:  Twinkle Twinkle Little Star
Descending:  Flintstones

Minor 6th (8 half steps or semitones)
Ascending:  The Entertainer (3rd and 4th notes)
Descending:  no example found ("doh-mee" descending solfege)

Major 6th (9 half steps or semitones)
Ascending:  old NBC theme or Hush Little Baby
Descending:  Nobody Knows the Trouble I've Seen

Minor 7th (10 half steps or semitones)
Ascending:  Star Trek theme
Descending:  no example found - please help

Major 7th (11 half steps or semitones)
Ascending:  Take On Me
Descending:  no example found - please help

Octave/Perfect 8th (12 half steps or semitones)
Ascending:  Somewhere Over the Rainbow
Descending:  There's No Business Like Show Business (2nd and 3rd notes)

Some of these song associations are so ingrained that they are super easy to hear.  In other cases I struggled to find familiar examples; as in I can't really imagine the Star Trek theme for an ascending minor 7th.  Some of the wider descending intervals must not be very common at all, because I found no usable examples for a descending minor 6th, descending minor 7th or descending major 7th.  

If you know of other intervals examples, especially any that might be found in Grateful Dead or Phish songs, please share them.