(We are now working in European Equal Temperament.)
A scale is any sequence of intervals (notice: not notes) that adds up to 12 semitones. Think of any bonkers combination, and someone somewhere will have a guitar tutorial explaining why it should be the very next thing you learn.
A key or mode is a scale plus a starting note (the "tonic") that then defines a sequence of notes. We say "the key of G-Major" scale or "the Major scale". (Musical speech is sloppy, so we also say "the Major key" or "the G-Major scale".) Two keys are equivalent if they have the same scale. “Scale” = intervals; key = notes.
There are a number of well-known seven-note scales:
Major / Ionian Mode: Tone-Tone-Semitone-Tone-Tone-Tone-Semitone
Natural Minor / Aeolian Mode: Tone-Semitone-Tone-Tone-Tone-Semitone-Tone
Harmonic Minor: Tone-Semitone-Tone-Tone-Tone-Tone-Semitone
Lydian Mode: Tone-Tone-Tone-Semitone-Tone-Tone-Semitone
Mixolydian Mode; Tone-Tone-Semitone-Tone-Tone-Semitone-Tone
Dorian Mode: Tone-Semitone-Tone-Tone-Tone-Semitone-Tone
Phrygian Mode: Semitone-Tone-Tone-Tone-Semitone-Tone-Tone
The Ionian, Aeolian, Lydian, Mixolydian, Dorian, Phrygian modes are often called Church Modes, as they were used in early choral singing.
There are two well-known five note (pentatonic) scales:
Major Pentatonic: Tone-Tone-Minor Third-Tone-Minor Third
Minor Pentatonic: Minor Third-Tone-Tone-Minor Third-Tone
Two well-known six note scales:
Major Blues: Tone-Tone-Semitone-Minor Third-Tone-Minor Third
Minor Blues: Minor Third-Tone-Tone-Semitone-Minor Third-Tone
(Minor Third = 3 semitones)
Exactly one scale of only tones: Whole-Tone: Tone-Tone-Tone-Tone-Tone-Tone
(There are two keys: C and C♯. After that the notes repeat, so starting on D gives the same notes as starting on C.)
Exactly one scale of only semitones: Chromatic: Semitone (x12)
If you want to see something truly out of control, look at the eight-note diminished scale.
Friday, 12 January 2024
Tuesday, 9 January 2024
Intervals
This is the first of a series of posts about music notation and associated ideas. The world does not need this, but I do, to make my own sense of it. There is a lot of notation in music, and it's not all part of one coherent whole. It's a bunch of tools for specific tasks.
Let's start at the beginning.
A note is a name for a given frequency. The most well-known note is "middle C" (or C4) , followed by "A440", which is the frequency 440 Hz assigned to the A above middle C, A4.
The human auditory system regards two notes whose frequencies are in the ratio 2:1 as very harmonious. This is because musical instruments do not produce pure sine wave tones, but a sound that is a mixture of the fundamental frequency and many others, called “overtones”. Playing A440 will usually also generate an "overtone" of A880, and so it sounds pleasantly matching when played against A880 as a note. This is so much so that two notes related by double frequency are regarded as "the same but higher".
This splits the range of audible frequencies into ranges called octaves. Pick a starting position, say A4 = 440, and we have octaves as follows:
A7 = 3620 (almost the highest note on the piano)
A6 = 1760
A5 = 880
A4 = 440 (“tuning A”)
A3 = 220
A2 = 110
A1 = 55
A0 = 27.5 (lowest note on the piano)
(Why is it the lowest? There are pianos which go even lower, but below about 25Hz, the human ear stops hearing a continuous sound and starts to hear the individual beats. The highest note on the piano is 4120Hz and it's very difficult to produce an acoustic instrument that can produce that with significant volume.
The octaves are not the same size in terms of the range of frequencies, but the ratios of the frequencies are all the same. Each octave is double the previous one.
Each musical culture picks a different number of different frequencies within an octave to be its "notes". European music eventually settled on a series of frequencies, each one related to the previous one by the same ratio, the 12-th root of 2 (roughly 1.05946). This is called Equal Temperament, and it makes manufacturing and learning to play musical instruments way easier than the other European system did.
The "distance" between two notes is not measured in hertz (the ear doesn't work like that), but in powers of the 12-th root of 2 (roughly 1.05946). A power of the 12-th root of 2 is called a semitone. (Mathematicians can prove this is indeed a distance function as an exercise.)
Let's start at the beginning.
A note is a name for a given frequency. The most well-known note is "middle C" (or C4) , followed by "A440", which is the frequency 440 Hz assigned to the A above middle C, A4.
The human auditory system regards two notes whose frequencies are in the ratio 2:1 as very harmonious. This is because musical instruments do not produce pure sine wave tones, but a sound that is a mixture of the fundamental frequency and many others, called “overtones”. Playing A440 will usually also generate an "overtone" of A880, and so it sounds pleasantly matching when played against A880 as a note. This is so much so that two notes related by double frequency are regarded as "the same but higher".
This splits the range of audible frequencies into ranges called octaves. Pick a starting position, say A4 = 440, and we have octaves as follows:
A7 = 3620 (almost the highest note on the piano)
A6 = 1760
A5 = 880
A4 = 440 (“tuning A”)
A3 = 220
A2 = 110
A1 = 55
A0 = 27.5 (lowest note on the piano)
(Why is it the lowest? There are pianos which go even lower, but below about 25Hz, the human ear stops hearing a continuous sound and starts to hear the individual beats. The highest note on the piano is 4120Hz and it's very difficult to produce an acoustic instrument that can produce that with significant volume.
The octaves are not the same size in terms of the range of frequencies, but the ratios of the frequencies are all the same. Each octave is double the previous one.
Each musical culture picks a different number of different frequencies within an octave to be its "notes". European music eventually settled on a series of frequencies, each one related to the previous one by the same ratio, the 12-th root of 2 (roughly 1.05946). This is called Equal Temperament, and it makes manufacturing and learning to play musical instruments way easier than the other European system did.
The "distance" between two notes is not measured in hertz (the ear doesn't work like that), but in powers of the 12-th root of 2 (roughly 1.05946). A power of the 12-th root of 2 is called a semitone. (Mathematicians can prove this is indeed a distance function as an exercise.)
Given a note X, the note one semitone up is X♯ and the note one semitone below is X♭. Replacing a note by the flat or the sharp is called flattening or sharpening the note. Under Equal Temperament, (X-1)♯ is the same note as X♭ - these are called enharmonic equivalents.
For more details, see the excellent and best-selling Your Brain on Music.
For more details, see the excellent and best-selling Your Brain on Music.
Friday, 5 January 2024
Ear Training
One of the many skills academically-trained musicians have is being able to identify an interval - the distance between two notes. There are twelve in an octave, from the minor second - 6% increase in frequency) - to the octave - a 100% increase in frequency.
There is of course an app for that. Several. I tried Earpeggio, which offers a wide range of tests. I passed the test of identifying which of two intervals was greater, and I can reliably spot a unison (same note, no difference) and an octave.
You’d think anyone could tell the difference between a minor third and a major sixth, seeing as how they are different ends of the octave, but nope. Major thirds went unidentified. If I’d been guessing, I would have got about two out of the twenty examples right, so even 50% isn’t awful. I noticed that as soon as I had two succeeding intervals close together, I was much more accurate, since I was relying on the memory of the previous note. But an interval on its own… ouch.
However, I’ve never done this before, so it’s not hopeless.
My quick foray into identifying chords was much less impressive.
It’s a neat thing to do when you have twenty minutes to spare in a quiet place, or with headphones.
There is of course an app for that. Several. I tried Earpeggio, which offers a wide range of tests. I passed the test of identifying which of two intervals was greater, and I can reliably spot a unison (same note, no difference) and an octave.
You’d think anyone could tell the difference between a minor third and a major sixth, seeing as how they are different ends of the octave, but nope. Major thirds went unidentified. If I’d been guessing, I would have got about two out of the twenty examples right, so even 50% isn’t awful. I noticed that as soon as I had two succeeding intervals close together, I was much more accurate, since I was relying on the memory of the previous note. But an interval on its own… ouch.
However, I’ve never done this before, so it’s not hopeless.
My quick foray into identifying chords was much less impressive.
It’s a neat thing to do when you have twenty minutes to spare in a quiet place, or with headphones.
Monday, 1 January 2024
Happy New Year and A Prosperous 2024 To You All
Nothing says "Happy New Year" like three abandoned boats on Dungeness beach.
Friday, 22 December 2023
Cafeteria
Charing Cross Road. Do not ask the price of egg and chips and a cappucino. It's not 2015 anymore.
Tuesday, 19 December 2023
People Who Need To Feel... Anything
There are two views of the Good Life.
The first is that a good life is full of good works: what matters are the kind, useful, constructive, healing, things we do.
The second is that a good life is full of feelings and relationships, and it does not matter what those feelings and relationships are: what matters is to feel and relate intensely.
It's binary: your temperament is one or the other.
You may, however, believe one, while living the other. Believing that life is for the feeling, but living sensibly, is very common amongst former drunks, junkies, coke-heads, divorcees, and the like, not all of whom enjoyed the ups and downs of their chaos. Chaos is not emotion. You can have emotions and still have a clean and neat kitchen. People who live for feelings often do good works, but for them it's a by-product not a goal.
The people who live for feelings don't just want rainbows and candy-floss. Emotions need to be sweet and sour. Anger, disappointment, frustration, grudges, revenge, contempt, resentment, are just as good.
Football fans are like this. They would like their team to win, but what they really don't want is a nil-nil draw after ninety minutes of faultless defensive play on both sides. They want the roller-coaster. It's the same as gambling: losses work the emotions as much as wins.
Any emotion is better than no emotion. Any relationship is better than no relationship.
This is only dysfunctional from the point of view of Stoicism, Protestantism, and other such fun-sucking approaches to life, many of which on closer examination turn out to be associated with aristocracy and established wealth. In many societies, vigorous, engaged, volatile, emotion-based action and reaction is prized and honoured by the masses, and is thus highly functional, providing the emotional roller-coaster ride that makes living, well, Life.
Therapists who emphasise having "good" emotions and "good" relationships , or at least removing the bad stuff, dumping the users, losers and abusers, are in fact closet Good Works people. Emotions and relationships can only be "good" and "bad" relative to some goal or purpose. Whereas to the emotion-centric emotions and relationships have intrinsic value for good or ill.
Understand that "sour" emotions are as satisfying, if not more so, than "sweet" emotions, and many puzzling things become clear. Especially why people stay in so-called "dysfunctional" relationships, or take stupid risks, or believe daft things: it's all about the emotions. Take away those and their lives become empty, no matter what good things they may also be doing.
When emotion-centric people get older they can often seem to flip. Suddenly they don't like drama, and aren't interested in people who cause problems. This isn't because they have suddenly acquired a goal in life: it's because the rewards they get from the emotions are not worth the energy it takes to create and maintain those high-cost emotional states. The same cost-benefit calculations that kept them in and around chaos, drama, users and losers, now make them choose to live a quieter life, because the costs don't go down, but the benefits do.
The first is that a good life is full of good works: what matters are the kind, useful, constructive, healing, things we do.
The second is that a good life is full of feelings and relationships, and it does not matter what those feelings and relationships are: what matters is to feel and relate intensely.
It's binary: your temperament is one or the other.
You may, however, believe one, while living the other. Believing that life is for the feeling, but living sensibly, is very common amongst former drunks, junkies, coke-heads, divorcees, and the like, not all of whom enjoyed the ups and downs of their chaos. Chaos is not emotion. You can have emotions and still have a clean and neat kitchen. People who live for feelings often do good works, but for them it's a by-product not a goal.
The people who live for feelings don't just want rainbows and candy-floss. Emotions need to be sweet and sour. Anger, disappointment, frustration, grudges, revenge, contempt, resentment, are just as good.
Football fans are like this. They would like their team to win, but what they really don't want is a nil-nil draw after ninety minutes of faultless defensive play on both sides. They want the roller-coaster. It's the same as gambling: losses work the emotions as much as wins.
Any emotion is better than no emotion. Any relationship is better than no relationship.
This is only dysfunctional from the point of view of Stoicism, Protestantism, and other such fun-sucking approaches to life, many of which on closer examination turn out to be associated with aristocracy and established wealth. In many societies, vigorous, engaged, volatile, emotion-based action and reaction is prized and honoured by the masses, and is thus highly functional, providing the emotional roller-coaster ride that makes living, well, Life.
Therapists who emphasise having "good" emotions and "good" relationships , or at least removing the bad stuff, dumping the users, losers and abusers, are in fact closet Good Works people. Emotions and relationships can only be "good" and "bad" relative to some goal or purpose. Whereas to the emotion-centric emotions and relationships have intrinsic value for good or ill.
Understand that "sour" emotions are as satisfying, if not more so, than "sweet" emotions, and many puzzling things become clear. Especially why people stay in so-called "dysfunctional" relationships, or take stupid risks, or believe daft things: it's all about the emotions. Take away those and their lives become empty, no matter what good things they may also be doing.
When emotion-centric people get older they can often seem to flip. Suddenly they don't like drama, and aren't interested in people who cause problems. This isn't because they have suddenly acquired a goal in life: it's because the rewards they get from the emotions are not worth the energy it takes to create and maintain those high-cost emotional states. The same cost-benefit calculations that kept them in and around chaos, drama, users and losers, now make them choose to live a quieter life, because the costs don't go down, but the benefits do.
Friday, 15 December 2023
Decisions, Decisions
So here I am at the wrong end of the age range, seemingly attempting to do something I don't really have the temperament to do. Which means, I need to adjust what it is I think I'm going to be doing and expecting of myself, if I'm not going to be wasting my time. If such adjustments are possible.
At this point, I want to remind you that I totally do not mind doing spider-walks (look it up on You Tube) for minutes on end. I have something to build on.
Most people studying music academically pass the next Grade, then the BMus, or whatever, then to get a gig somewhere. Others may want to find a bunch of guys to play with, and then get a gig somewhere, while picking up what they need to know along the way. It's the gig somewhere that's the end goal. These days, that "gig" might be a TikTok channel on which they demonstrate preposterous virtuosity.
Here's what I could aim for: be able to create a loop of chords that have a sense of direction and some harmonic spice, and solo over it.
Creating a loop with a Looper pedal is nowhere near as easy as people make it look. Putting together some chords isn't just some random thing either. Neither is soloing, if it's done with any taste. The chords could come from other people's songs.
In support of this, there is...
Musical Literacy: reading music, making sense of what is in the score, identifying chords etc
Sight-reading: a) connecting the notes in the score with the notes on the instrument; b) playing those notes in a musical and fluent manner. (if the notes come from a bunch of Miles Davis solos, so much the better!)
Basic Composition: how do chords go together? what creates a sense of direction? How do solos fit over the chords (aka "playing the changes")?
Familiarity with the instrument: where are the notes? Where are the chords? (Electric: where are the tones and effects?)
And in support of that, there is...
Technique: a) getting the fingers where they need to be when they need to be there, and no more (no going down shredding rabbit holes); b) learning to use a Looper pedal, and how to set up the gear to do so.
What about genre?
Classical / Flamenco / Folk / Acoustic Blues / Jazz Solo. Fingerpicking is beyond me.
Metal. Horrible un-musical shredding.
Rock / Funk / Soul / Jazz-funk. The guitar is basically an accompanying instrument. I'd need to be in a band.
Jazz. I'll have a post about jazz, but in summary: chord-scale is no more musical than shredding; cocktail / lounge jazz is cringe; Older styles, fine.
Ambient. Possible, but as a secondary subject.
Noise (Sonic Youth etc). Pass.
Playing classical pieces for solo cello and violin: do-able, but short on self-expression!
Electric Blues / Blues-Rock. This is what I imagine myself playing to an audience if I imagine myself playing to an audience.
So, yeah. Looks like I'm going to learn to play the Blues.
And you will get progress reports.
At this point, I want to remind you that I totally do not mind doing spider-walks (look it up on You Tube) for minutes on end. I have something to build on.
Most people studying music academically pass the next Grade, then the BMus, or whatever, then to get a gig somewhere. Others may want to find a bunch of guys to play with, and then get a gig somewhere, while picking up what they need to know along the way. It's the gig somewhere that's the end goal. These days, that "gig" might be a TikTok channel on which they demonstrate preposterous virtuosity.
Here's what I could aim for: be able to create a loop of chords that have a sense of direction and some harmonic spice, and solo over it.
Creating a loop with a Looper pedal is nowhere near as easy as people make it look. Putting together some chords isn't just some random thing either. Neither is soloing, if it's done with any taste. The chords could come from other people's songs.
In support of this, there is...
Musical Literacy: reading music, making sense of what is in the score, identifying chords etc
Sight-reading: a) connecting the notes in the score with the notes on the instrument; b) playing those notes in a musical and fluent manner. (if the notes come from a bunch of Miles Davis solos, so much the better!)
Basic Composition: how do chords go together? what creates a sense of direction? How do solos fit over the chords (aka "playing the changes")?
Familiarity with the instrument: where are the notes? Where are the chords? (Electric: where are the tones and effects?)
And in support of that, there is...
Technique: a) getting the fingers where they need to be when they need to be there, and no more (no going down shredding rabbit holes); b) learning to use a Looper pedal, and how to set up the gear to do so.
What about genre?
Classical / Flamenco / Folk / Acoustic Blues / Jazz Solo. Fingerpicking is beyond me.
Metal. Horrible un-musical shredding.
Rock / Funk / Soul / Jazz-funk. The guitar is basically an accompanying instrument. I'd need to be in a band.
Jazz. I'll have a post about jazz, but in summary: chord-scale is no more musical than shredding; cocktail / lounge jazz is cringe; Older styles, fine.
Ambient. Possible, but as a secondary subject.
Noise (Sonic Youth etc). Pass.
Playing classical pieces for solo cello and violin: do-able, but short on self-expression!
Electric Blues / Blues-Rock. This is what I imagine myself playing to an audience if I imagine myself playing to an audience.
So, yeah. Looks like I'm going to learn to play the Blues.
And you will get progress reports.
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