So far everything has been derived from the Major Scale, but now I have some new scales to introduce. These are foreign and exotic scales with fascinating new sounds!

After RM1 as a proof of concept, RM2 introduced the Major modes and RM3 explained how they work. Now RM4 will introduce new scales and–guess what?–RM5 will explain how they work. This episode also includes a bit more information on chords.

TO THE SCALES!

(They have been right justified for easy comparison)

Symmetrical Scales:

These scales are not generally pleasing, but can be very cool to play with. They are called symmetrical because the scale formulas allow multiple degrees to be identified as the root.

Chromatic: x x x x x x x x x x x x

Whole Tone: x – x – x – x – x – x -

Diminished: x – x x – x x – x x – x

Six Tone Symmetrical: x x – - x x – - x x – -

Modified Symmetrical Scales:

Altered: x x – x x – x – x – x -

Leading Whole Tone: x – x – x – x – x x x -

Common Scales:

These are some popular western scales that make up most music nowadays.

Major: x – x – x x – x – x – x

Major Pentatonic: x – x – x – - x – x – -

Blues: x – - x x x x x – - x -

Minor Pentatonic: x – - x – x – x – - x -

Natural Minor (Aeolian): x – x x – x – x x – x -

Melodic Minor: x – x x – x – x – x – x

Harmonic Minor: x – x x – x – x x – - x

Modified Common Scales:

Lydian Flat-Seven: x – x – x – x x – x x -

Lydian Minor: x – x – x – x x x – x -

Lydian Diminished: x – x x – - x x x – x -

Overtone (Lydian Dominant): x – x – x – x x – x x -

Major Locrian: x – x – x x x – x – x -

Super Locrian: x x – x x – x – x – x -

Double Harmonic: x x – - x x – x x – - x

Nine Tone: x – x x x – x x x x – x

Auxiliary Diminished: x – x x – x x – x x – x

Auxiliary Augmented: x – x – x – x – x – x -

Auxiliary Diminished Blues: x x – x x – x x – x x -

Ethnic Scales:

These scales are a bit more rare. They tend to be tonally powerful and emphasize some interesting notes. Play in these scales and, like magic, you sound like you’re playing music from their countries of origin (more or less–mimicking the ethnic rhythm helps).

Roumanian: x – x x – - x x – x x -

Spanish Gypsy: x x – - x x – x x – x -

Eight Tone Spanish: x x – - x – x – x – x x

Neopolitan Major: x x – x – x – x – x – x

Prometheus: x – x – x – x – - x x -

Prometheus Neopolitan: x x – - x – x – - x x – -

Pelog: x x – x – - x – - – x x

Oriental: x x – x x x x – x – x -

Hungarian Major: x – - x x – x x – x x -

Iwato: x – - – x x – - – x – x

Hirajoshi: x – x x – - – x x – - -

Hindu: x – x – x x – x x – x -

Arabian: x – x – x x x – x – x -

Gypsy: x x – - x x – x x – - x

Mohammedan: x – x x – x – x x – - x

Javanese: x x – x – x – x – x – x

Persian: x x – - x x x – x – - x

Byzantine: x x – - x x – x x – - x

Hawaiian: x – x x – - – x – x – x

Mongolian: x – x – x – - x – x – -

Egyptian: x – x – - x – x – - x -

Chinese: x – - – x – x x – - – x

Scale Names and Relativity

Many scales have names that describe them relative to other scales. For example, compare the Locrian and the Major Locrian.

Locrian: x x - x - x x – x – x -

Major Locrian: x - x - x x x – x – x -

The Locrian is transformed into a Major Locrian by sharpening the 2nd and 3rd degrees (raising them 1 half-step). That change results in a scale that seems to combine the Locrian and the Unison. It combines the Locrian sound with a very “Major” sound, hence it is called the Major Locrian.

A similar modification of the Locrian mode generates the Super Locrian.

Locrian: x x – x - x x – x – x -

Super Locrian: x x – x x - x – x – x -

Every note in the Locrian mode is 1 half-step off of the Major scale (Unison mode) except for the 1st and 4th degrees which remain. By flattening the 4th, the scale is then considered Super Locrian. As you can see, the names themselves are unimportant, but help to convey the design of the scale. The Super Locrian can also be seen as equal to the Melodic Minor scale from the 7th degree.

Melodic Minor: x – x x – x – x – x – x

Super Locrian: x x – x x – x – x – x -

Robot Implementation

Just as we replaced the Major Pentatonic in RM1 with the full Major scale in RM2, we can replace the Major scale with any of these others and apply the same logic.

Where modes of the Major scale explored different sensations within that scale, these scales can explore brand new areas that don’t exist within the limitations of the Major formula. Furthermore, each of these scales has its own set of modes that emphasizes its different facets.

It’s not hard to find other scales out in the wild, but you’ll probably see that most of them are not much different from some that are already on this list. In the next installment we can go into generating our own scales so having a long list will be unnecessary. However, it’s worth playing with these scales so you have a better feel for what’s coming up. You’ll also want to be comfortable with the terminology of scales.

Scale and Chord Terminology

(Chords are described according to the scales they encompass, so this section applies to both subjects)

You’ve probably picked up on some of the terminology being thrown around. If you understand these terms, you can decipher scales and chords based on their names very easily. You can also begin describing scales and chords more accurately, including those you invent yourself.

Here are some common terms:

Triad: A chord made up of the 1st, 3rd, and 5th degrees. Generally this refers to the Major Triad (a triad in the Major Scale).

Flat: If a degree is flattened, it is lowered by 1 half-step. An example of this is the Lydian Flat-Seven Scale, which is the same as the Lydian mode, but with a flattened 7th degree.

Diminished: This refers to a degree being lowered (flattened) by 1 half-step. Generally this is in regards to the 5th degree. In other cases, the degree being diminished will be stated (e.g. Diminished 7th). In a diminished triad, the 3rd and 5th degrees are both flattened.

Major Triad: x – - - x – - x – - – -

Diminished Triad: x – - x - - x - – - – -

Augmented: An augmented interval is the opposite of a diminished one; it has been raised (sharpened) by 1 half-step. An augmented triad is the same as a Major triad but with a sharpened 5th.

Major Triad: x – - – x – - x - – - -

Augmented Triad: x – - – x – - - x – - -

Major: Major tends to mean “like the Major scale.” As mentioned above, the Major Locrian is basically a combination of the Major and Locrian scales.

Minor: Minor is usually synonymous with “flattened.” This is true in the case of the minor 2nd interval (m2, as in Cm2) where the interval is actually composed of a flattened 2nd degree (AKA a semitone). Other times it may mean “like the Minor Scale” as in the Lydian Minor Scale which is a combination of the Lydian and Minor scales. Generally the “Minor” sound is associated with a minor 3rd interval (as contained in the Minor scale). The Minor scale is sometimes called the Natural Minor to differentiate it from the Melodic Minor and Harmonic Minor, which are also characterized by a flattened 3rd degree.

Dominant: The dominant is the 5th degree. A scale or chord with the word dominant in its name may contain the 5th degree and/or be based upon the Myxolydian mode (the 5th mode) as in the case of the Lydian Dominant.

Seventh, 7, or vii: The 7th degree is an exception to some rules because when a scale or chord has a 7, that usually means it has a flat 7 (AKA minor 7). However, if a scale or chord is meant to contain the 7th degree as in the Major Scale (Unison), it will be called a Major 7. These two triads demonstrate the difference between the C7 (Cm7, Cmin7) and the C Major 7 (CM7, Cmaj7) chords:

C7: C – - – E – - G – - Bâ™­ -

C Major 7: C – - – E – - G – - - B_

The minor 7 is characteristic of the Myxolydian mode. Therefore, another name for the minor 7th interval is the Dominant 7th. Since the plain old 7th usually refers to a flat 7, saying Diminished 7th is really saying “Diminished flat 7th” which equals a double-flat 7 or the 6th interval. Yes, it’s all very confusing and stupid.

Leading: A leading tone is 1 half-step lower than the note it “leads” to (the Major 7th interval). The Leading Whole Tone Scale adds a leading note between the augmented 5th and 6th degrees. Apparently the major and minor 3rds also have “latent tendencies.”

Pentatonic, Hexatonic, etc: Names like these are often using latin to describe the number of notes in the scale. Penta means 5, so a Pentatonic scale contains 5 notes. Hex means 6 so the Hexatonic contains 6 notes. This is not true in the case of the Diatonic which actually means “Progressing tones” (another name for the Major Scale).

No experiment this time around, but look forward to one in Robot Music 5, when we’ll finally start breaking some rules. We gotta teach our Robot to improvise!

-Christopher J. Rock

Notes:

http://www.musisindo.com/e107/guitarchord.htm: This is a great website for examining chords and scales on piano keys. Just enter in the chord or scale you want to see and it highlights the right keys. You can even enter in formulas for your own custom scales.

Naming Scale Degrees

As discussed in previous chapters, the names of notes are not relevant to our Robots. For that reason, I haven’t bothered to name the “accidentals” properly.

Accidentals are all the sharps and flats not included in the C Major scale. When these came up I started out using only the sharp symbol (♯) and then switched to flat (b) for scale degrees. I’ll quote wikipedia for the correct way to name scale degrees:

In naming the notes of a scale, it is customary that each scale degree be assigned its own letter name: for example, the A diatonic scale is written A – B – C♯ – D – E – F♯ – G♯ rather than A – B – Dâ™­ – D – Fâ™­ – E♯♯ – G♯. However, it is impossible to do this with scales containing more than seven notes.

That’s all well n’ good for some old European guy, but if you ask me it’s just making things look more complicated than they need to be. That’s why I prefer to stick to degree numbers with flats when necessary.

Accidentals, pfft. . . . Who says they were an accident?

New logo baby.

Robot Music I proved that a pleasing song can be randomly generated under the right guidelines. Those guidelines stuck to a 4/4 rhythm and the C Major Pentatonic Scale.

Robot Music II proved that the C key could be replaced with any other (changing the root). It also showed that the Major Pentatonic Scale (5 notes) could be expanded to the Major Scale (7 notes) without harming our method. And most importantly, this section covered modes and demonstrated that shifting a song’s mode can significantly change its tone. Knowing that the tone can be changed, how can we control it?

Robot Music III introduces the Circle of Fifths. It is a basic musical tool that will help us predict the impact of a mode of the Major Scale. With it, our Robot can place notes along 2 dimensions (Consonance vs. Dissonance, Dominance vs. Sub-Dominance) and estimate the emotional impact of a note according to an arbitrary algorithm based on personal tastes.

This installment is the first to go into the perception of music. To begin, we must discuss aural perception and some musical fundamentals. That technical information will be related to our previous musical concepts by the use of the Circle of Fifths. And finally, a demonstration of mode relationships and some discussion of their popular uses.

You probably already know some of this, so I’ll try to move fast.

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How Sound is Felt

The sensation of sound is created by waves of varying pressure in the air. When a guitar string is plucked, it smacks against air molecules, smashing them together on one side while pulling them apart on the other. Then the string swings back the other way, pulling apart the air on the first side and smashing it on the second. That vibration continues, creating a pattern of high and low pressure ripples in the air that flow out from the string, just like if you splash in water, you see ripples spreading out from your hand. The more quickly the string vibrates, or the hand splashes, the more ripples are created in a short time. That raises the frequency of the ripples. The ripples in the air hit your ear and vibrate your ear drum, just like the ribbon in a microphone. Your inner-ear converts that to an electrical signal (just like a microphone does) and transmits it to the brain. The brain then interprets that data, filtering it and deciphering its meaning.

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Technical Terms

A sound is characterized by the shape of its wave. To better understand waves and a couple other musical concepts, you’ll have to understand these terms:

Pitch and Frequency: The frequency of a wave is interpreted as pitch, or how “high” or “low” a note is. Higher frequencies create a higher pitched sound and lower frequencies, a lower one.

Wavelength: The length of a ripple (1 cycle) is the wavelength. Waves with high frequencies are made of ripples that are very close together so they have shorter wavelengths.

Period: The period is the time it takes for 1 cycle to pass. In regards to sound waves, a shorter period is related to a shorter wavelength.

Amplitude: The height of a wave is its amplitude. It is the “loudness.”

Interval: 2 notes played at the same time.

Chord: 3 or more notes played at the same time.

Beat: When an interval is played, the two waves combine, and they interfere with each other. Sometimes the waves amplify each other (become louder), sometimes they cancel out and become quieter. Most of the time, the waves go back and forth between loud and quiet. The “going back and forth” is a beat. When you hear a guitar or piano chord ring out, listen for the beat going “woOowoOowoOowoOowoOow.”

Consonance and Dissonance: Wave combinations that create an extremely tiny or very long beat are considered consonant while waves that create a short beat are called dissonant.* Consonance is generally considered beautiful, if not boring, and dissonance can be interesting, but very harsh.

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Creating Consonance or Dissonance

To be consonant, waves must be able to “fit together” neatly. This means, that if you tried to fill the space of one wave with another wave, you could do it with as few remainders as possible. Yes, I mean remainders like in math; division. If you have a remainder, the beat will be equal to the number of cycles necessary for the remainder to add up to 1 (more or less).

Illustration of Waves A, B, and C

For example, if Wave B has 3/2 the frequency of Wave A, they share a lot of qualities. Waves A and B will both loop at the same points. Wave B will loop 3 times for every 2 loops of A, but every time that A’s cycle ends and begins again, so does B’s. These two waves are extremely consonant and will amplify each other. Wave C, however, has 11/10 the frequency of Wave A. If both waves start at the same time, the ending/beginning point of their cycles won’t meet again until Wave A has looped 10 times and Wave C has looped 11 times.

The time it takes for the two waves to begin and meet again is the length of their beat. The beat created by Waves A and B is so short (equal to twice the period of Wave A) it cannot be heard.** The beat created by Waves A and C would be much more distinct, it would sound very rough.

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Note Ratios

These are the ratios of the popular 12 notes (multiply a note’s ratio by the frequency of C to discover the frequency of that note–Or look at this chart):

Note: These are the ratios according to Just Intonation. In fact, modern instruments are generally tuned to Equal Temperament. Equal Temperament involves a different set of ratios that were developed to allow musicians to easily change keys, but to come as close to Just Intonation as possible.

You can probably tell that some of these ratios will fit together better than others (3/2 creates a beat of 2 cycles; 16/15 is 15 cycles). In Robot Music I, we used the half-step as a basic unit of measure for notes. It places them in order of frequency from lowest to highest. Now, by comparing the consonance and dissonance of different intervals, we can create a new sequence of notes; the Circle of Fifths.

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The Circle of Fifths

This is the circle of fifths:

Here it is written in notes, then again in degree numbers and in ratios.***

Note: I’ve begun using “b” to mean flat instead of “#” to mean sharp. You should know that an A# is equal to a Bb; they are the same note. # means “+1 half-step” and b means “-1 half-step.” In the case of degrees using b is more common.

Each note is the 5th degree (the dominant) of the note before it and the 4th degree (the sub-dominant) of the note after it in the sequence. In other words, G is the 5th of C and F is the 4th of C. Or if you look at the E note, you know that B is the 5th of E and A is the 4th of E.

C – D – _E _F – G – A – _B

E – F# – G# A – B – C# – D#

1 - 2 – _3 _4 – 5 – 6 – _7

The greater the distance between any two notes in the sequence; the more dissonant they are as an interval. Therefore 2 intervals of equal distance from the root are equally consonant or dissonant. Furthermore, 2 notes of nearly equal distance in the sequence have a nearly equal consonance or dissonance.

In addition to consonance and dissonance, the circle of fifths illustrates dominance and sub-dominance.

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Dominance and Sub-Dominance

Disclaimer: I am making these comments on dominance and sub-dominance not because I have learned of it elsewhere, but because I have felt them to be accurate and useful. Elsewhere, the term dominant is used synonymously with the 5th degree and the sub-dominant with the 4th degree. This concept will be readdressed later.

Dominance and Sub-Dominance involve which note is established as the root in a chord or riff. If you don’t know which note is the root, you don’t know what perspective your scale is being played from so you can’t control its effects. Here the circle is divided into dominant and sub-dominant halves.

You can consider everything on the left side to be dominant, everything on the right to be sub-dominant, and the blue 5b to be completely neutral. I find that playing the intervals on the dominant side clearly establishes the interval’s 1st degree as the root of your riff or chord. The sub-dominant intervals may be less clear or even establish themselves as the root.

For example, in rock songs you often hear a 5th interval (1 and 5) like the C and G notes being strummed at the same time. The 4th interval is equally popular (1 and 4), like C and F strummed at the same time. The difference between the two is that between C and G, C will be established as the root note, but between C and F, F will take control.**** Often sub-dominant notes can obscure your root. That’s not necessarily bad, but it must be known. The closer the interval gets to the neutral 5b, the less dominant or sub-dominant effects they have and the more neutral they become.

The first note played and the lowest note played also are more likely to be established as the root, but the dominance/sub-dominance effects won’t really come in until chords and inverses are being used. We won’t get into that yet.

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A Spectrum

As you can see, the general effects or what you might call the “meanings” of notes are accurately mapped out by the Circle of Fifths. It presents notes on a continuous spectrum according to their similarity as the ear and brain perceive them.

The Circle of Fifths is often compared to the color spectrum and remarkably similar to it. Coincidence? I don’t know, but I doubt it (there are theories). The important thing is that you recognize the sound of the 1st degree as very similar to the 4 and 5. Somewhat less similar to 2 and 7b. Less similar to 6 and 3b. And so on down the list.

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Modes Over the Circle

You should remember modes from Robot Music II. Now we can marry those ideas to the Circle of Fifths.

A mode of the Major Scale is defined by its root degree. Each one has a unique tone about it, but we haven’t yet discussed the relationships of the different tones. In fact, just as the Circle of Fifths maps out perceived similarities in notes, it also maps out similarities in the modes of those notes in the Major Scale.

For example, the 1st Degree’s mode (Unison) is almost identical to the mode of the 5th degree (Myxolydian):

1st Mode/Unison:
x – x – x x – x – x - x

5th Mode/Myxolydian:
x – x – x x – x – x x -

The only difference is the placement of a single note. The same goes when you compare the Unison to the mode of the 4th Degree (Lydian):

1st Mode/Unison:
x – x – x x - x – x – x

4th Mode/Lydian:
x – x – x - x x – x – x

However, the Unison is very different from the mode of the 7th Degree (Locrian):

1st Mode/Unison:
x - x - x x - x - x - x

7th Mode/Locrian:
x x - x - x x - x - x -

The Unison and the Locrian only share 2 notes. That’s still 1 more note than is shared between the Lydian and Locrian which are complete opposites (as they are on the circle):

4th Mode/Lydian:
x - x - x - x x - x - x

7th Mode/Locrian:
x x - x - x x - x - x -

The relationship between the mode of each degree is analogous to the relationship between the placement of each degree on the Circle of Fifths. Since the modes themselves are related in this way, the tones they generate are related as well. This is how the Circle of Fifths can allow our robot to control mood changes by shifting modes.

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A Tone Spectrum

Often the words used to describe the tones of the opposing ends of the modal spectrum are “Light” and “Dark.” You can also say “Consonant” and “Dissonant” which would be somewhat more accurate. Or you can use the chromatic analogy of “Warm” and “Cool.” Regardless of semantics, the effects are the same. There is a general feeling produced by modes in the direction of the Lydian, Unison, and Myxolydian that is significantly different from that of the Locrian, Phrygian, and Aeolian. Your job is to listen to each mode and learn those differences, then you can provide your Robot with an algorithm that selects and changes modes according to your tastes.

Ideally you would listen to each mode in a variety of uses, but it would be a bit too much work for me to record several songs for each mode. If you have access to an instrument, try improvising in the different modes to get a better feel for them. Here are the modes themselves, played in C (try to play different modes back to back):

4th Mode/Lydian:
x – x – x – x x – x – x

I always found it odd that this mode was considered “Bright” because it’s only 1 of 2 modes with the highly dissonant Devil’s Interval (1 + 5b). Still, it shows up often in upbeat music.

1st Mode/Unison:
x – x – x x – x – x – x

Your standard Major Scale. This winds up in all kinds of music these days. You can bet that anything poppy is in the Unison Mode.

5th Mode/Myxolydian:
x – x – x x – x – x x -

The Myxolydian is popular because it’s the same as the Unison, but with a distinctive flat 7 interval (1 – 7b). The flat seven is big in Blues, Jazz and much of Rock.

2nd Mode/Dorian:
x – x x – x – x – x x -

The Dorian seems to be the least popular of modes, though it contains an interesting mixture of the Major and Minor sounds. I’ve heard it played by some recent Rock bands (maybe Post-Rock).

6th Mode/Aeolian:
x – x x – x – x x – x -

The Aeolian is best known as the famous Minor Scale. You’ll find it in any song that means to take a somber tone.

3rd Mode/Phrygian:
x x – x – x – x x – x -

I’ve always liked the Phrygian. It’s rarely used, but it has an interesting sound.

7th Mode/Locrian:
x x – x – x x – x – x -

The Locrian shows up in a lot of what you would expect to be “darker” music: Death Metal, Hardcore, etc.

Jazz musicians after Bebop explored all of these. Of particular note is Miles Davis’ experimentation with Modal Jazz.

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That sums up the 3rd session of Robot Music. Next we’ll go over brand new scales, some exotic, and completely different from the Major Scale. Our Robot will have much to choose from.

-Christopher J. Rock

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*Waves that are exactly the same have an infinitely long beat, they are perfectly consonant and create perfect amplification. Waves that are extremely close in frequency have a beat so small it cannot be heard, but they also have a very long beat that can be heard. Waves with a small difference in frequency have an audible and short beat; a lot of dissonance. Waves with more distant frequencies can have varying beats or none at all.

**If Waves A and B were slightly out of tune, they might generate a very long beat that would also qualify as consonant.

***Another term to know is Inverse. As you move from the 1st degree left or right on the circle of fifths, you’ll find the numbers to the left to be twice the inverse of the numbers to the right (except for the 5b in the middle with a ratio of 7/5). That is because the intervals to the left are the inverse of the intervals to the right. Playing a 4th interval is the same as playing a 5th interval, but from the perspective of the opposite note (a different root). Besides that, the intervals are equal.

****Resulting in an inversed 5th interval.
_

Notes

Relativity and Proportion in Perception

Most of our judgment is based on relativity. It’s difficult to judge a person’s height, but you can always tell how tall they were compared to you. It’s bright outside because you’ve been in the dark all day. I can’t see you because the sun is in my eyes. How old is she? I don’t know, but she’s older than I am.

Part of using relativity in our judgment is recognizing proportions. I’m just as big to my little brother as he is to our little sister. How fast was the red car going? I don’t know, about twice as fast as the blue car. A mouse is to a cat as a cat is to a dog. The Moon has 1/3 the gravity of the Earth.

How do these apply to music? When a tenor sings a song and a baritone sings the same song, the difference in pitches is obvious, but it’s also obvious that the songs are identical. Your mind recognizes the relationships of the notes sung by the tenor as proportionate to the relationships of the notes sung by the baritone, even when the notes themselves are completely different. Perception of notes is then contextual (dependent on surrounding notes).

Context is the reason we pay attention to scales. The scale is the general context of a note. The mode (defined by the starting point; the root) modifies the meaning of that context.

Series: Robot Music I, Robot Music II: Modes, Robot Music III: The Circle of Fifths, Robot Music IV: Scales of the World

It’s been a long while, but response to the last music post was enough to get me revved up again. Now it’s time to continue with the Robot Music series on procedurally written music.

I wanted this tutorial to be simple, but educational enough that if you wanted to study more, you would know where to look. For that reason, there is a lot of music vocabulary in here. I’ve done my best to explain each term as it comes up, but if any remain confusing, don’t hesitate to look them up elsewhere or even skip them. You can probably forget all of the fancy words and still understand the important concepts being discussed.

In the last session we rolled a die to generate riffs in a Major Pentatonic Scale. Sticking to that one scale limits the sound of your music a lot, so now we’ll mix up our technique by exploring modes. We’ll be replacing the Major Pentatonic Scale with the full Major Scale. The pentatonic only has 5 notes, while the entire Major Scale has 7. Those last two notes can be seen as bothersome* which is why they were left out last time.

Most people’s first musical revelation is the amazing power of switching between a Major scale and a Minor scale. It’s often generalized that when a song is in the Major scale it sounds happy and when it’s in a Minor scale it sounds sad. That is the effect we will be looking into to change the emotional impact of robot songs.

As mentioned in the last post, popular music is limited to 12 notes (C, C#, D, D#, E, F, F#, G, G#, A, B — then loop to the next octave; C’, etc). Each of these letters is an arbitrary name for an arbitrary frequency of air waves. The only thing that is not arbitrary about each note is its relationship to all of the other notes. The relationships between notes are really what is important; and that’s where scales come in.

A scale is a list of notes used for part or all of a composition. However, to grasp the significance of a scale, you are better off ignoring the “notes” within it and focusing on its form; the pattern of the scale or the kind of note relationships it involves.

To discuss relationships, we’ll use the “half-step” as one basic unit. A half-step is the difference in pitch between two adjacent keys on a piano or a difference of 1 fret on a guitar. It is the distance between any one note and its neighbor (C and C# or E and F). The 12 notes of common music span 12 half-steps.

Let’s use half-steps to create a method for describing note relationships without specifying note names (because all we want is the scale’s pattern). First we’ll look at the relationships between notes in the Major Scale:

-We’ll represent all of our possible notes with 12 dashes:

C, C#, D, D#, E, F, F#, G, G#, A, A#, B

- – - – - – - – - – - -

-Now we can describe the C Major Scale by representing each of its notes with an x:

C, C#, D, D#, E, F, F#, G, G#, A, A#, B

x – x – x x – x – x – x

Notice that the dashes between each x represent a note that is not included in the Major Scale.

-With this pattern, we can figure out which notes exist in keys other than C, such as D Major, E Major, G# Major or any other:

Pattern:

x – x – x x – x – x – x

C Major:

C, C#, D, D#, E, F, F#, G, G#, A, A#, B

D Major:

D, D#, E, F, F#, G, G#, A, A#, B, C, C#

E Major:

E, F, F#, G, G#, A, A#, B, C, C#, D, D#

~

G# Major:

G#, A, A#, B, C, C#, D, D#, E, F, F#, G

Etc.

As you can see, the names of the notes are irrelevant if you know the pattern. Memorize that pattern and visualize it transposed over the keys of a piano or the frets of guitar (the pattern can begin on any key or fret). Play only those keys or frets where the x’s go and you will be playing a Major Scale. Most pop music is completely limited to this one scale. You’d be surprised at how easy it is to play along with many songs once you’ve learned this pattern.

Each x in a scale is called a degree. The Major Scale has 7 degrees (e.g. the 2nd Degree of the C Major Scale is the D note).

The difference between the 1st degree and the 2nd degree in the Major Scale is 2 half-steps. You can also describe the distance between them as 1 scale step. The distance between each degree in a scale and the next highest degree is 1 scale step, but it can be any number of half-steps! For example, C is the 1st degree of the C Major Scale and F is the 4th degree. They are separated by 3 scale steps, but they are also separated by 5 half-steps (C-D-EF-G-A-B).

Now that you know the pattern in the Major Scale, you must have realized there can be tons of others too. You’re right!

The Minor Scale and Modes

The pattern you use is the scale you are in, and changing scales can completely change the emotional charge of your music. So now let’s look at the Minor Scale.

The most common Minor Scale uses this pattern:

Pattern:

x – x x – x – x – x x -

C Minor:

C, C#, D, D#, E, F, F#, G, G#, A, A#, B

Look at the differences between the Major Scale and Minor Scale:

Major: x – x - x x – x – x - x

Minor: x – x x - x – x – x x -

Notice that the 3rd and 7th x’s of the Major Scale are lowered by 1 half-step (or flattened) in the Minor Scale.

You have to wonder, what led some age old musical wizard to discover such a slight modification to the Major Scale that could completely shift its emotional meaning? Maybe we can figure that out. . . . (This might get tricky, so go slowly if you must.)

-Let’s look at the Major Scale in 1 octave:

x – x – x x – x – x – x

-There are obviously more than 12 keys on a piano and that is because there are multiple octaves. Octaves are created because the pattern of a scale loops every 12 half-steps. If we extend the Major Scale over 2 octaves, it looks like this:

x – x – x x – x – x – x|x – x – x x – x – x – x

-Now, let’s start from the 1st x and count our way to the 6th x in the 1st octave, then highlight it:

x – x – x x – x - x - x|x – x – x x – x – x – x

-Do the same thing to the 6th x in the 2nd octave:

x – x – x x – x - x - x|x – x – x x – x – x – x

-What if we took all the notes starting with that 6th x and ending before the 6th x of the next octave? Here they are all highlighted:

x – x – x x – x - x – x|x – x – x x – x - x – x

-Let’s clean it up by getting rid of all the other notes:

x – x|x – x – x x – x -

-Remove the octave separator and, look at that, it’s the Minor Scale:

x – x x – x – x x – x -

In other words, the Minor Scale is equal to the Major Scale from the perspective of the 6th x, or the 6th Degree. That’s what a Mode is. A mode of a scale is its pattern when described from the “perspective” of one of the degrees in a scale (a degree = an x). In music lingo, no one says perspective though; you would call it the root. The 6th Mode of the Major Scale is also called the Aeolian, but most of us just call it the Minor Scale.

Here is a list of all the modes of the Major Scale (the first and last degrees of the 1st mode have been highlighted to emphasize the differences between each subsequent mode):

1st Mode/Unison:
x – x – x x – x – x – x

2nd Mode/Dorian:
x – x x – x – x – x x -

3rd Mode/Phrygian:
x x – x – x – x x – x -

4th Mode/Lydian:
x – x – x – x x – x – x

5th Mode/Myxolydian:
x – x – x x – x – x x -

6th Mode/Aeolian:
x – x x – x – x x – x -

7th Mode/Locrian:
x x – x – x x – x – x -

Notice that the 1st mode is just the normal Major Scale. The 2nd mode is the same as the 1st one, but all the x’s are bumped to the left by 2 half-steps (1 scale step). The third mode is bumped by a total of 4 half-steps (2 scale steps) and the 4th mode is bumped by 5 half-steps (3 scale steps). They are all the same basic pattern as the Major Scale, but slid over to one side. The difference between each one is how far they are slid.

Each mode has a distinctly different feeling; some more radical than others.

Defining Your Mode

So the question remains, when you’re writing a song using the Major Scale, how do you define your mode? This is actually a complicated question, but for now I’ll keep it simple. Generally, the first note played is the root. All the notes after that determine your scale and mode depending on how they forge a pattern.

Let’s say you make a riff out of this sequence of notes: C, E, G. C is the root note because you played it first, then the scale and mode are determined by E and G’s relationship with C. Let’s look at that relationship compared to the pattern of the Major Scale (1st Mode):

C C# D D# E F F# G G# A A# B C’

x – x – x x – x – x – x x’

Those notes are a perfect match for the Major Scale in the 1st Mode! What’s more, is that those notes are very characteristic of the Major Scale’s 1st Mode; they are a strong part its distinctive feeling.

What if you played a slightly different sequence of notes?

C C# D D# E F F# G G# A A# B C’

x – x x - x – x – x x – x’

Now your notes describe the Major Scale’s 6th Mode, also known as the Minor Scale. Play the first sequence and you get a happy tune, play the second and it’s sad.

Overview

First, scales showed us that a note’s impact is dependent on its context (the pattern of other notes played near it). Modes showed us that the impact of a pattern depends on the root, the “starting point.” When you start with the 1st degree in the Major scale, you get the “happy” sound. When you start with the 6th degree in the Major scale, you get the “sad” sound. In many cases the root is the first note played in a riff.

Experiment

Let’s try using the same randomly generated song (with the help of a di) of Robot Music I, played in different modes.

This is the original song (click to listen):

C, C, G, G – C, C, G, G – C, C, G, G – C, C, G, G

C, E, D, G – C, E, D, G – _C, E, D, G – C, E, D, G

–

C, C, G, G – C, C, G, G – C, C, G, G – C, C, G, G

C, E, D, G – C, E, D, G – _C, E, D, G – C, E, D, G

–

C, C, C, C – G, G, G, G – E, E, E, E_ – C, C, C, C

C, C, C, C – G, G, G, G – E, E, E, E_ – C, C, C, C

Now we want to play the same song, but we will replace the Major Pentatonic Scale of Robot Music I with one of our modes of the Major Scale. Here it is, the same song, in the 6th Mode or the Minor Scale:

C, C, _G, G – C, C, _G, G – C, C, __G, G – C, C, _G, G

C, D#, D, G – C, D#, D, G – C, D#, D, G – C, D#, D, G

–

C, C, _G, G – C, C, _G, G – C, C, __G, G – C, C, _G, G

C, D#, D, G – C, D#, D, G – C, D#, D, G – C, D#, D, G

–

C, C, C, C – G, G, G, G – D#, D#, D#, D# – C, C, C, C

C, C, C, C – G, G, G, G – D#, D#, D#, D# – C, C, C, C

It’s darker than the original, somber.

How about something stranger? This is the same thing in the 7th Mode:

C, C, _A#, A# – C, _C, _A#, A# – C, _C, _A#, A# – C, C, _A#, A#

C, D#, C#, A# – C, _D#, C#, A# – C, D#, C#, A# – C, D#, C#, A#

–

C, C, _A#, A# – C, _C, _A#, A# – C, _C, _A#, A# – C, C, _A#, A#

C, D#, C#, A# – C, _D#, C#, A# – C, D#, C#, A# – C, D#, C#, A#

–

C, C, _C, _C _- A#, A#, A#, A# – D#, D#, D#, D# – C, C, _C, _C

C, C, _C, _C _- A#, A#, A#, A# – D#, D#, D#, D# – C, C, _C, _C

This one is very dark, somewhat distressing. Such is the Locrian Mode! A mysterious she-devil!

Now you know how modes can change the emotional impact of your music, but we haven’t yet discussed how you control that impact. How can you predict the feeling that will be created by a given mode? What is the meaning of a given note? That will be the topic of the next episode of Robot Music: The Circle of Fifths. Finally, we will begin quantizing music! (And I’ll get it up sooner this time)

-Christopher J. Rock

*This is the pattern of the Major Pentatonic Scale: x-x-x--x-x--. This is the pattern of the entire Major Scale: x-x-xx-x-x-x. As you can see, the 4th and 7th degrees used in the entire major scale are not included in the major pentatonic scale. Those two notes can be very beautiful, but when played together or in sequence they form what is called “The Devil’s Interval.” This interval is equal to 6 half-steps (C and F#) and earned its name in classical music because it was found to be so grotesquely dissonant that it was forbidden. Use of this interval was later popularized in Jazz, especially Bebop and later experimental forms. In more recent musical trends it can be found in much of hardcore and other genres that aim to inspire a sense of darkness, anger or anxiety. You can say that in modern times, we have lowered the status of the Devil’s interval from “sinful” to “ill-advised.” The point of all this is to say that in Robot Music I, I chose to use the Pentatonic Scale to raise the chances that you would be happy with the music generated by that system. However, it’s about time you face the real world and realize that a little dissonance never hurt anyone. If you prefer the major pentatonic scale, you can easily apply all of the concepts herein to that instead of the entire major scale. However, the emotional variation between modes of the pentatonic scale will not be nearly as radical as those of the entire major scale. That being said, Blues and Rock are generally played in the pentatonic so if you prefer that sound, you may find it beneficial. The 7th Mode (Locrian) of the Major Scale includes a Devil’s Interval between the 1st and 5th degrees. In fact, you can hear it in the recording of our generated song in the 7th Mode (as linked above).

Other Song Information

In case you’re curious, here is the original song written in the form of half-steps from the root:

0, 0, 7, 7 – 0, 0, 7, 7 – 0, 0, 7, 7 – 0, 0, 7, 7

0, 4, 2, 7 – 0, 4, 2, 7 – 0, 4, 2, 7 – 0, 4, 2, 7

–

0, 0, 7, 7 – 0, 0, 7, 7 – 0, 0, 7, 7 – 0, 0, 7, 7

0, 4, 2, 7 – 0, 4, 2, 7 – 0, 4, 2, 7 – 0, 4, 2, 7

–

0, 0, 0, 0 – 7, 7, 7, 7 – 4, 4, 4, 4 – 0, 0, 0, 0

0, 0, 0, 0 – 7, 7, 7, 7 – 4, 4, 4, 4 – 0, 0, 0, 0

You can use these numbers as fret distances on a guitar or key distances on a piano if you include the black keys.

And here is the original song written in the form of degree numbers:

1, 1, 5, 5 – 1, 1, 5, 5 – 1, 1, 5, 5 – 1, 1, 5, 5

1, 3, 2, 5 – 1, 3, 2, 5 – 1, 3, 2, 5 – 1, 3, 2, 5

–

1, 1, 5, 5 – 1, 1, 5, 5 – 1, 1, 5, 5 – 1, 1, 5, 5

1, 3, 2, 5 – 1, 3, 2, 5 – 1, 3, 2, 5 – 1, 3, 2, 5

–

1, 1, 1, 1 – 5, 5, 5, 5 – 3, 3, 3, 3 – 1, 1, 1, 1

1, 1, 1, 1 – 5, 5, 5, 5 – 3, 3, 3, 3 – 1, 1, 1, 1

You can use these to number the white keys on a piano, starting from the C key. This sequence of numbers is the essence of the song. Knowing these numbers, you can play in any key or mode with ease.

(This post features the hip guitar stylings of none other than ME! I’ll play some real life, randomly generated, Robot Music! The link is at the end.)

I’ve wanted to see more procedural music in games for a long time, but the most we see are pretty sorry attempts. I’m not just talking about “shifting volume on pre-recorded riffs” procedural, I mean “the game is writing its own live soundtrack” procedural.

“But Chris, that doesn’t even happen on consoles! We can’t do it in flash, no way!” Sounds difficult or even impossible, but it isn’t. The only problem is it takes an understanding of tricky programming concepts and tricky musical concepts. Without programmers that also study music theory, we just don’t see procedurally written music.

Well, I’d like to help change that. I know a thing or two about music and a thing or two about programming so in this article I’m going to do my best to tip off any programmers interested in putting together a simple music generator. Today’s generator won’t be truly procedural, but it’ll start things off in that direction.

And if you play a little music, but don’t know how to write a song, maybe this article can help you out too.

For the sake of this exercise, let’s limit our music to looping riffs. Let’s also limit ourselves to a 4/4 time (4 quarter notes per measure, 1, 2, 3, 4 – 1, 2, 3, 4 – 1, 2, 3, 4). We’ll be using random note selection, so there won’t be any regard for tone, but don’t worry, it’ll all work out. There will still be a tone, we just won’t be manipulating it in this experiment. Later we can get into controlling tone, but not all in one post.

Any common instrument uses a grand total of 12 notes: C, C#, D, D#, E, F, F#, G, G#, A, A#, B. You can play those notes randomly and no one can tell you you’re not playing music, but most people won’t want to listen to it. If you want to make something a little prettier, I suggest you limit yourself to a Pentatonic scale (5 note scale). C Major Pentatonic looks like this: C, D, E, G, A. In my opinion, any of those notes can be played in sequence or together to produce what anyone can call a pleasing sound. We can limit ourselves further by only playing in a single octave so that our root note, C, is the lowest note we play.

Now let’s generate a riff.

In 4/4 we need to generate a minimum of 4 notes for our riff. We’ll make our first note in the riff equal to the key we’re playing in (in this case, C). That leaves 3 more notes to generate. So we take 3 random numbers from 1 to 5 where each number equals a note; 1 = C, 2 = D, 3 = E, 4=G, and 5 = A.

I just rolled a die and wrote down the first set of numbers that fulfilled our requirements. I got 1, 5, 5 as our sequence. We add 1 to beginning to get 1, 1, 5, 5. Those numbers correspond with the notes C, C, G, G.

I’ve gone ahead and generated a second riff so we can switch back and forth between the two for some variety, to sound a little more “song-like.” The second one came out to 1, 3, 2, 5 or C, E, D, G. Now we try playing them. We can play the first riff 4 times, then play the second one 4 times and start over (4 measures each).

I’m playing along on my guitar;

C, C, G, G – C, C, G, G – C, C, G, G – C, C, G, G

C, E, D, G – C, E, D, G – C, E, D, G – C, E, D, G

This is an interesting pair of riffs because the first one has a really simple rock feel, but the second one bounces around kinda funny. It’s a unique little tune, especially for one written by a die (or was it? Must discuss later . . .).

Let’s go one more step to make it a full song. I’ll generate another set of notes: 1, 5, 3, 1 or C, G, E, C

We’re going to play this last one slower to break up the other two. We play each note 4 times before moving to the next one:

C, C, C, C – G, G, G, G – E, E, E, E – C, C, C, C

Now we have 3 pieces to our song that we can arrange however we want. Let’s stick to simplicity. We play the first riff 4 times, the second riff 4 times, do the first and second 4 times again, then play the third riff 2 times and start over (Our song can loop. Why not?).

This is the final product:

C, C, G, G – C, C, G, G – C, C, G, G – C, C, G, G

C, E, D, G – C, E, D, G – C, E, D, G – C, E, D, G

–

C, C, G, G – C, C, G, G – C, C, G, G – C, C, G, G

C, E, D, G – C, E, D, G – C, E, D, G – C, E, D, G

–

C, C, C, C – G, G, G, G – E, E, E, E – C, C, C, C

C, C, C, C – G, G, G, G – E, E, E, E – C, C, C, C

And start over. But those letters don’t mean much, so you should probably take a listen: Robot Music – Song 1

Pretty simple right?

1. Pentatonic Scale (C, D, E, G, A) in 4/4.

2. The root note is the first note of the riff.

3. The last 3 notes are randomly generated, where numbers correspond with notes (1 = C, 2 = D, 3 = E, 4=G, and 5 = A)

4. Arrange multiple riffs for some variety.

5. End on the same note that you started with (C).

Of course, you can make your own modifications to this logic. For example, I find that it’s usually a bad idea to make the end of a riff blur too much with the beginning of the next riff. This is a small problem when we play the slow part of our song and all the C notes just mash together into one long sequence. You can fix your algorithm so that the last note will always be different from the first one, or so that no note will ever be played right after itself.

If you’re using this method to help you write your own music, you can modify the notes yourself. I think the slow part of our song sounds a lot better as C, G, E, D instead of C, G, E, C, but you can switch any of them out however you want. And don’t be afraid to ignore the rules we set up today.

You can also add in chords, like exchanging each single note for a power chord (C+G, D+A, E+A#, etc). Many other chords can be used, but they may not be so easy to just slap in (and still sound nice all the time).

The point is, you’ll have to experiment. Try a lot of stuff. There are no real rules to music and if anyone tells you you’re doing it wrong, slap them in the face and tell them they don’t know a damn thing about it. Music is whatever you say it is and if they don’t like it, then tough!

Next time, we’ll modify the logic to recognize different modes of the pentatonic scale, so that we have better control over our song’s tone, but this will do for now.

Hope you enjoyed the subject.

-Christopher J. Rock