Thinking About Music III

There are 29 prior discussions on Thinking About Music and Thinking About Music II

★★✔★★

Music 30 – Olga Kern – ♥ ♪ http://bit.ly/eud38N ♪ ♥ – (Dec31-Jan4, 2010)

Olga Kern

Olga Kern – ♥ ♪ – Our Lovely Tour Guide – ♪ ♥

Ms Kern is the latest in a series of special guest tour guides to the world of music, a roster which has included luminaries such as Ed Rafalko (my rock guitar builder wizard pal who introduced us to the idea of diatonic modes and pitch axis theory, which led us many places including Joe Satriani, Bela Bartok, and the world of evolving ways of thinking about and creating different types of traditional and other music tonality), Jung Lin (who took us many places that were very good including Chopin’s Etudes, Godowsky’s Studies of Chopin’s Etudes, the role of sustain and sustenuto functions on grand pianos, Raff, Albeniz, and an exciting return to Liszt’s Hungarian Rhapsody No 2), and Valentina Lisitsa who left us breathless.  Breathless?  I practically passed out.

In the previous discussions, we figured out what romantic era music is, how it came to be, and why it’s useful to think of it as a reference point and baseline for thinking about all of classical music.  Once we reached that point of “having our arms around it” (around music in general), our theory has been that it’s helpful to have smart people like our tour guides give us advice about which aspects to focus on.  The lovely and talented Ms Lin, Ms Kern, and Ms Lisitsa have been giving us very helpful advice in the form of the works they have selected to invest time in to study, prepare, practice, and perform.

On this page and playlist, we have the … pleasure … of having the advice of the lovely Ms Olga Kern.  We first met Ms Kern on the previous page playing Rachmaninoff’s 3rd Piano Concerto.  Our first experience of Ms Kern on this playlist is being with her as she brings the Shostakovich Piano Concerto No 1 to a powerful conclusion.  Olga’s work in the second video with the GSO is pretty powerful and inspiring as well.  Her playing has inspired us to explore aspects of music theory such as making effective use of a new key.  She has also inspired a remarkable new concept in classical music theory called, The Baseball Diamond of Chromatic Fifths.  More later about these exciting developments.

Olga’s New Key

We became interested in her new key and have discussed key signatures in general …

Key Signatures

I was working on working out key signatures this morning.  How they work.  Which ones are which.  The general issue of key signatures had come up the other day in the discussions about comparing Godovsky’s Studies with Chopin’s Etudes. It was in the guessing about why Godovsky chose Chopin’s “Butterfly” and “Black Key” Etudes as the basis for his “Badinage” Study. (It turned out they all had the same time and key signatures, while all the other Chopin Etudes that were spot-checked had different signature combinations).  And key signatures and how to read and use them came up again in the attempts begun to read some of the recognizable audible and visual note patterns.  They were all had key signatures with 6 flats, 6♭s.  We wanted to figure out which Chopin phrases from which hands (left or right) were showing up in which hands of Godovsky’s phrases.

Anyway, I already knew a few things from my prior junior high school era guitar melody line sight-reading efforts.  I knew, for example, when there’s no sharps or flats in the treble and bass clefs, that’s the key of C.  When there’s 2 sharps, it’s D.  But I don’t really know the rest.  Like what is the key when there’s 3, 4, 5, 6, or even 7 sharps or  1 through 5 or even 6 or 7 flats.  Having 6 or 7 of either is interesting since there are only 5 black keys on the piano keyboard (which corresponds to there being only 5 of the 12-note “chromatic scale” pitch levels that need the idea of “sharps” and “flats” in order to have names and in order to be written down on sheet music).

Another Lovely Tour Guide

Oh, great.  Another tour guide!  While searching for more Olga Kern videos, found the lovely Ms Edwina P.  Her Hungarian Rhapsody No 2 caught my eye.  Love it and her and found she’s invested time in some other interesting pieces.  More DeBussy, more Chopin, and more.  They’re on the Olga playlist.  More later.

Examples of Key Signatures

Ok, so, in the discussion on the Jung Lin page, Thinking About Music II, we were looking into the key signatures and time signatures of the Chopin Etudes and the Godovsky Studies.  Here are some of them:

“Butterfly“and “Black Key” (and also Godovsky’s “Badinage”) are all in 2/4 time with 6 flats.  [As discussed below, it turns out that a piece of music with a time signature showing 6 flats is the key of G Flat major.]

“Aeolian Harp” and “Bees” Etudes (Opus 25 No 1 and 2) are written in 4/4 time and in a key with 4 flats.  [That turns out to be the key of A flat major.]

“The Horsemen” (Opus 25 No 3) is written in 3/4 time and in a key with 1 flat.  “Wrong Note” Etude (Opus 25 No 5) is in 3/4 with one sharp.  [That’s G sharp major.]

“Thirds” (25-6) is 4/4 and a key with 5 sharps — and is very cool.  5 sharps is the key of B major.  [By the way, I’m adding these key names to these paragraphs in a later editing pass through this page.  I’m using the mnemonic image in my mind of the now-famous Baseball Diamond of Chromatic Fifths (an exciting new development in classical music theory, developed and discussed below) to figure out what these flats and sharps in the time signatures mean for what keys the Etudes are written and played in.]

“Cello” (25-7) is 4/4, slow play, 5 min long,  and the key with 4 sharps (kind of sounds “minor key” … i don’t get how that works really, to have a relative major and its relative minor key have same scale notes, same sharps or flats, playing same notes, but get the different major and minor kind of sound).  [Uh oh … I forgot about that issue.  4 sharps can be the key of E major of the key of … hm … the relative minor key could have either of two names … the note three c-steps down from E is either C sharp or D flat.  The Circle of Fifths diagram and the Baseball Diamond of Chromatic Fifths diagram, discussed below, tell us the music world uses C sharp minor.  Which is ok to just know (i.e., become used to, i.e., memorize), but I wonder if there’s some reason to use C sharp instead of D flat?)]

“Sixths” (Opus 25 No 8)” is also very cool with its unbelievable long fast ascending chord sequence at the end.  Also the several  stylish dramatic strokes a few times in the left hand.  And in the middle, a less, but still really great, ascending and descending phrase.  Only 59 seconds and simply fabulous!  It’s written in 4/4 and in the key with 5 flats.  [5 flats is D flat major]

“Octave” (25-10) very cool dramatic engaging fast first section with 4/4 and 2 sharps and changes to a very lovely slower section in 3/4 and 5 sharps … and wow, back to first key, time, and emotion for gorgeous close.  What a wonderful piece.  [5 sharps is B major]

Relative Major and Minor Keys

I also sort of know that the key of C is also the “relative minor” key of A minor.  C major’s relative minor key is A minor.  A minor’s relative major key is C major.  The two keys are “related” because their scale notes are the same.  Neither C major nor A minor have sharps or flats in their scale notes.  C major’s scale (it’s do re me fa so la ti) is: C D E F G A B.  A minor’s scale is the same notes:  A B C D E F G.  No sharps or flats.

In the “diatonic modes” concept, the C Major scale is the C Ionian diatonic mode.  The same notes, as A minor’s scale, are the A Aeolian diatonic mode.

I’m focusing on treble clef time signatures first since I’m faster with it.  When I was teaching myself a little bit of piano in the 4th grade, with a little help from my grandmom and aunt, and in junior high years, when I was self-teaching on guitar  (i.e., no real lessons and very little music theory or scales work), I got reasonably quick and easy at using treble clef notes.  Bass clef remained a mystery for some reason.  Didn’t know what it was for, who to use it, how many lines between clefs.  Knew it was f-clef with little clef sign indicating F.  But didn’t know that was all I needed to know about it.

Anyway, I’ve seen on the pages of my 100 Beatles songs and other 60s sheet music lots of different groups of sharps and flats in the treble clef indicating the key the song’s written in.  I never really — and still don’t — know for sure what the concept of a “song” “being in a key” means.  It often seems to go with having the letter of the key be the letter of the chord the song starts and ends with.  But not always.  It also, in simpler songs, seems to create a set of expected chords to be used as the progression in the song. Like Louie Louie’s in the key of E, so we’ll see chords like:  E E E, A A, B7 B7 B7.  Or all the I IV V (“1 4 5”) songs have their I be their letter.  For example, to play all the gazillion I IV V songs in the “key” of G, use G C D.  Key of C, use C F G.  Key of D: use D G A.   And so forth for all the 12 possible keys:  C Csharp/Dflat D Dsharp/Eflat E F Fsharp/Gflat G Gshart/Aflat A Asharp/Bflat B.  Some songs change keys in the middle.  The discussion in these pages about atonal music indicates that the idea of “key” has a range of validity and only applies for the vast majority of songs that limit themselves to using mostly the notes and chords of that key’s scale (or scales?  not sure).  The atonal folks, instead of switching keys, work at ensuring distribution of notes doesn’t match a pattern within a key’s scales.  Schoenberg, in fact, had a famous method of composing atonal music that ensured all notes were used with equal frequency so no “key” or “tonic” (like “tone-ic”) could be found in a musical work.  Not sure why that was considered a good thing, an objective, maybe just to show it could be done to defy the traditional people who said it couldn’t be done.

Anyway, in music, the idea of “key” isn’t usually as complicated as I just made it.  Usually, like me with my Beatles song book, when something tells you the key is G, you go, ok, and play it and think of it in G.  For that, we have key signatures on treble and bass clefs to just tell us right away what key our song is in.

So what’s a “key signature?”

It’s the writer of the sheet music, the score, writing marks called “sharps” and “flats” on some of the spaces and lines of the treble and bass clefs to indicate “key.”

No sharps or flats indicated, that’s the key of C.  That’s the equivalent of using only the white keys on a piano.  In the simplest use of the idea of “key,” all — or at least most — of the notes in the song will be from the 7-note diatonic scale (do re mi fa so la ti) that starts on the note with the same letter name as the key.  For C, that’s C D E F G A B, with no sharps or flats.  A sharp raises the pitch of a note by an amount that has several names including one I made up called, “chromatic scale step”  or “c-step.”  Others will call it a “half step”.  You can ask them why.  They’ll say, because everybody else does.  And they’ll be right.  But I’ll use c-step since it’s like “1 fret” on a guitar and any one key on a piano and since it avoids certain imprecision and confusion problems I won’t get into again here.

Anyway, here’s a pretty good image that summarizes key signatures:

“Circle of Fifths”

I don’t know why that image from wikipedia is called, Circle of Fifths.  Yes I do.  Going counter-clockwise, C’s fifth is F, F’s fifth is Bflat (aka Asharp), and so forth around the circle.  Not sure why they chose that format, stepping around the circle through the 12 possible keys by fifths (they could have just moved around in chromatic scale steps (counter-clockwise again, C then B, then Bflat, and so forth), but it’s an interesting and useful image.

The outer circle shows the relative major keys (upper case letters) and the inner circle is their relative minor keys (lower case letters).

One of the questions I have is, why do thay use Dflat instead of Csharp for the name for the upper case major scale note at 7 oclock position on the circle and then use Csharp in lower case for the minor over at 5 o’clock?  Same for Aflat vs. Gsharp.  And they don’t ever use Asharp?  In other words, what rules do they use for when to use which name when a sharp/flat note (black key on piano) always has two possible names?

NOTES

Note 1 – The Keys With 6 or 7 Sharps or Flats

Ok, the reason for 6 and 7 sharps or flats is easy now that I see it.  I’ll work out the 7 sharps or flats first.

There are a total of 5 notes that can possibly need sharping or flatting.  At least one key may need all five.  Some of them will appear as 5 flats or sharps on the clef.  One will show as 6.

The treble and bass clefs each have 5 lines and 4 spaces.  The treble clef has an E on the bottom line and another E on the top space.  There’s an F on the bottom space and another F on the top line.  There’s a one c-step (aka, “one half-step”) between E and F and between E# and F#.  No wait wait wait wait.  Hold the phone.  E# (Esharp) is F.

Too bad.  Thought I had the 7 sharps or flats case nailed.

Should still have the 6 case here though, 2 of them, with the E and the F situation on the treble clef.  Let’s see … We’re working with E and F.  There’s no Esharp or Flat, but there is Eflat and Fsharp.  So we’re looking at keys that have Eflat or Fsharp in them.  Every note is in about 6 keys, since, if you shift the “do re mi” forward or backward a c-step (half-step, 1 key) at a time, the note either hits two times in a row (3rd-4th interval) 7th-8th interval) or ships once then hits (all the other intervals).  Let’s just do trial and error.

Let’s try the Eflat major scale:  Eflat, F, G, Aflat, Bflat, C, D, Eflat (3 different flats, but 4 on the treble clef).  That’s the 4-flat key.  I’m not going to look at the Circle of Fifths to check this until I’ve found the 6-flat key from trial and error.

Ok.  I just tried the Gflat major key using a picture in my head of the piano keys.  Picture the piano’s black keys grouped in 3s and 2s.  We’re looking for a key that uses all of them and includes the Eflat key.  Gflat is the leftmost in the group of 3.  Whole step to the next black one (A flat), whole step to third black one (B flat) … good so far for I II and III degrees (steps) on the scale … half step to IV, that’s a white key (B “natural”) … whole step (2 keys) to V (D flat), whole step to VI (there’s our E flat that shows up twice in the treble clef), whole step to … wait … so that’s all five black keys and one of them is Eflat … so we found our key for 6 flats … anyway, that whole step to VII white key F, which is half step from VIII Gflat.

great!  so, when we look up at that circle of fifths, we’ll see that Gflat major shows as having 6 flats, and Eflat major will have 4 flats.

1/2 right.  Gflat major is right for 6 flats.  but Eflat shows as 3 flats.  and that’s right.  i’m remembering something now from my guitar sight-reading the treble clef days … that, when I saw sharps and flats in the key signature in the clef, only one note for each effected letter was shown as sharped or flatted.  you just had to know and remember that, for the example of Eflat major, all the E notes anywhere inside, above, or below the clefs had to be flatted (or sharped).  that was always the case for the simpler keys (1 or 2 sharps or flats) that i was able and willing to extract melody lines from.  when key signatures with three or more sharps or flats showed up, i just moved on to the next song or already knew the melody or guessed at it a lot.

so what we’re seeing here in action is the assumptions and rules the music world uses when assigning keys to song, writing the sharps and flats of the key signatures on the g- treble clefs and f- bass clefs of sheet music, and reading and playing music.

we have one key Eflat that does not double-mark the flatted E. marks it only at the top space.  but we’re assuming — we don’t really know yet — the Gflat major key signature puts a flat mark on both the top space and bottom line of the clef.  let’s look at the one in the circle of fifths …

wow … way off … that’s not how it works at all … it appears that, on the keys with larger number of flats or sharps, they don’t even try to show the right notes marked … apparently, you just have to know that 6 flats is Gflat … and how do we know?  well, one thing is just memorize it, but we actually already worked out why that’s true …

so that’s a good outcome … we know that, when they show 6 flats, even though the flat marks aren’t shown on the right notes … oh man … you know what? … i’m remembering now from guitar days … the reason i didn’t keep working with the keys with higher numbers of flats is I thought the sharps and flats were on the correct lines and spaces and could never get the melody for say, norwegian wood, to come out right … so, if i was sight reading melody to practice sight reading melodies, i just moved onto the next song … most of the melodies i played — other than practicing sight reading (which means, by the way, just reading and playing the melody right away from the written sheet music (vs from memory), when i worked out a melody to play a song i liked, i did it by “figuring it out” by humming it and getting what i played to match my humming.  that’s one of the things people mean when they say “play by ear”  (the other thing is something i could never do, except for just chords of the simplest I IV V songs, is just start playing a song from you or somebody else humming it).

so the way 6 flats works is you just know it’s Gflat key, know from working through it that it’s all the black keys, and proceed accordingly.

i’m realizing some without music experience might be a little lost in this.  here’s the missing fact.  the note in the sheet music might be a quarter note shown on the E line.  If the key you’re in does not “flat” or “sharp” the note, you just play the E note as shown.  If the key you’re in has E flatted, then, when you see the E, you have to remember to flat it.  If the key you’re in has E sharped, when you see the E in the music, you have to “sharp” it (raise it a half step, 1 key or fret).

Why The “Circle of Fifths”?

The Wikipedia article explains why the “circle of fifths” concept and diagram are used.  And it makes a LOT of sense.  This is the kind of thing that would have helped me a lot  back when I was teaching myself music basics without lessons and without reading the right books.  I just didn’t ask my grandmom and aunt the right questions and didn’t check the right book out of the public library.  Lessons would have made it really efficient, but things like this circle of fifths would have been in books.  No big problem.  I had a BLAST playing by ear, playing from records, and a few basic guitar songbooks.

Anyway, Circle of Fifths is cool.  They chose to have the keys along the outside and inside differ by “fifth  intervals” …

[ hm … i better come back to explaining “fifths” … i can now see why they use the idea of “fifth intervals” rather than the other equivalent ways of saying it (that’s 7 frets on a guitar, 7 keys on a piano, 7 c-steps, 2 1/2 whole notes, 5 half steps, 4 of 8 “do re mi fa so” scale steps or 7 of 12 octave half steps in “forward” “do re mi” direction, or scale steps in forward “do re mi fa so” direction, 5 of 12 octave or scale steps in backward “do ti la so” direction ) ]

… why?  because, if you do it that way, the number of sharps or flats goes up by one each time! … that’s great! … that’s wonderful … it’s an intrinsic reason, a reason based on a “natural fact”, not an arbitrary made-up thing … love it …

5 Flats is also Seven Sharps? … and 5 Sharps is also Seven Flats?

That’s what the Circle of Fifths diagram shows.  That’s interesting.

“Seven” from what point of view?  There are only five black keys on the piano that need flat or sharp to have names.  And we figured out earlier, you can’t get seven of either sharps or flats in a single clef.  So that must be some kind of signalling or symbol idea.  Ok the wikipedia article says when raising above … nope … thought i understood what wikipedia said … but, when i tried to put it into my own words here, i found i didn’t understand what they said … gotta go back for more clues …

One thing I’m realizing is the “number of flats” basis isn’t what i thought — the number that show in the clef — for zero through five sharps or flats, it’s the actual number of black keys … the Eflat example shows that … we found 3, but i thought that the two Es in the clef would make it four … it’s three in the Circle of Fifths …

we’ve arrived to the limitations of working up from Mother Nature, from the natural facts … from here, we have to just find out what the music world has agreed to for dealing with these key signatures … wikipedia, here we come again

oh, here’s the page i’m working from – http://en.wikipedia.org/wiki/Key_signature

hm … there’s something wrong here … i’ve been assuming this 6 flats and 7 flats concept makes sense since it’s part of mainstream music theory, but — here we go again maybe  — finding a problem with standard expert stuff that needs adjusting …

because i incorrectly thought that, based on my experience with some small number of sharps/flats keys, the sharps and flats in the signature were the actual sharps and flats, I thought one could work through the 12 possible keys and find the ones that put 6 and 7 sharps or flats into the clefs.  all wrong.  they’re basically forcing the “circle of fifths process” to work beyond its range of validity by inventing fictitious extra sharps and flats.  at least that’s what i think so far.

enough for now.

what a day.  happy new year.

Starting Over Again

There are quite a few very useful mistakes in the discussion above about key signatures.  So I’m starting over.  The first step is to consolidating the parts that were right, along with the corrections, into an adjusted version of the Circle of Fifths to create a brand new mnemonic called …

The Baseball Diamond of Chromatic Fifths

There are 12 base runners on the infield of a baseball diamond.  One on each base and two stuck between bases on each of the baselines.  The base runner’s are the 12 possible chromatic keys.  All the base runners are stuck like glue in their positions.  When we later speakof going from one base runner to the next, in either the clockwise or counter-clockwise direction, we’ll be envisioning ourselves or another runner going from one of the 12 base runners that are fixed/glued in their places.  Later on, we’ll add 12 more base runners, the 12 possible chromatic minor keys.

At the top, the key of C major’s on second base.  At the right, A major’s on first.  At the left, Eflat major’s on third.  And Gflat/Fsharp major’s covering home plate.

Along each baseline are two keys, the upper base runner and the lower base runner.

On the northeast baseline (the one between 1st and 2nd base), the upper runner is the key of G major.  The lower runner is the key of D major.

On the southeast baseline (the one between 1st and home), the upper base runner is the key of E major.  The lower base runner is the key of B major.

On the northwest baseline, the upper base runner is the key of F major.  The lower base runner is the key of Bflat major.

On the southwest baseline, the upper base runner is the key of Aflat major.  The lower base runner is the key of Dflat major.

I’ll use the words, “key” and “base runner” interchangeably.

The base runners around and on first and second base are the guitar strings keys.  Slash Hudson would tell us, if we take them in order from the runner just below first clockwise to the runner to the left of second base, the names of the keys are pretty easy to remember for guys and gals who play 6-string guitar.  That’s E A D G — which is exactly like the first four thicker strings on the guitar — and then C and F — which is like the next two strings, B and E, visualized as special-tuned up one fret or as held on their first frets.  So the mnemonic is “E A D B C-tuned B and F-tuned E.”  If you don’t play guitar, that may seem more trouble to remember than the keys themselves, but, for guitar players, it’s a pretty clear, cool, and helpful coincidence.  Rock n roll.

Two Different Kinds of  Fifths

Chromatic scale fifths vs. diatonic scale fifths.  As a guitar player, that’s a distinction and clarification I needed to make to understand and accept the Circle of “Fifths” concept and diagram.

The circle is described as being based on “fifth” steps of the scale.  True, but it’s the 5th step (or music experts sometimes call a scale “step”, a scale “degree”) on the 12-step chromatic scale, not the 5th of 7 steps on a diatonic scale.  That was important to me as a guitar player because I was thinking of the guitar world’s and the piano/organ world’s and blues jamming world’s familiar I IV V (pronounced, “1 4 5”) group of notes, steps, and chords and their note and barre-chord positions on the guitar’s fretboard.  Those I, IV, and V letters are roman numerals for 1, 4, and 5.  They represent steps/degrees on 7-step diatonic (do re mi fa so la ti) scales.  So, for a guitar player who plays lots of simple, folk, and easy rock n roll songs and also blues jams using I IV V chords, it’s quick and easy to visualize the sequence of keys around the “circle of fifths” by visualizing the I IV V chords they use.  All guitar players who have graduated to barre chords know the shapes  of the I I I – IV IV – V V V – IV IV chord progression, using E-shaped and A-shaped barre chords, for the 1950s and 60s song, “Louie Louie.”  A barre-chord-playing guitarist doesn’t have to know a bit of music theory to play the chords for “Louie Louie” from any place on the guitar’s fretboard (which is the same as saying, starting from any one of the possible chromatic scale beginning notes).  Moving clockwise from any key (base runner) on the Baseball Diamond of Chromatic Fifths to the next key (base runner) is like playing the first two chords of the chord progression for “Louie Louie.”  That makes it easy and clear for any barre-chord-playing guitarist, as the lovely and talented Orianthi could verify for us.

Barre chords.  Pronounced “bar chords.”  The meaning of “bar” is pressing your index finger of your left hand across all six strings of the guitar as if the finger were a steel bar shortening all six strings at once.  The guitarist then uses the other three fingers to make different chords in front of that bar.  Barre chords are “movable chords” because they let the guitarist change individual chords, or clusters of chords, by just moving the bar — the barre, the index finger — up and down the fretboard without changing fingering.  It also allows the guitarist to create movable visual/physical chord progression/combination shapes.  The “shape” can be learned in one location on the guitar neck and moved up or down the neck to change the key (to “transpose” the song) without learning new finger/hand moves.  Here’s Wikipedia on barre chords.  There are lots of videos teaching the basics of barre chords on guitar.  Here’s a good one.

My guitar-building buddy, Ed, would tell me something else that’s guitar-centric, “I IV V”-centric, and “Louie Louie”-centric about the Baseball Diamond of Chromatic Fifths and the Circle of Fifths it’s based on.  He would agree that, moving one step/key/runner in the clockwise direction is like the first two chords in the “Louie Louie” progression, but add the interesting point that then going back in the clockwise direction two steps, jumping over the first I note, is the third chord in the “Louie Louie” set, the V (five) chord.  For example, “I I I – IV IV – V V V” becomes “C C C – F F – G G G” or “EEE AA BBB” or “DDD GG AAA” that all the barre-chord players know by name.  An example of one all the barre-chord players know immediately by visual shape and sight, but many (including me) wouldn’t know by name without stopping a while to think about it, is …  I’m going to read one off of the Baseball Diamond and Circle … Gflat B Dflat.  Very cool.

The oldies tune, “Wild Thing”, is another of the gazillion songs that use just three chords, the I IV V of any of the 12 chromatic scales and keys.  : )

Clockwise and Counter-Clockwise Whole Note (2 c-step) Base Running

Another useful way to move around in the Baseball Diamond of Chromatic Fifths (or also the more traditional equivalent music theoretical tool, the Circle of Fifths) is to notice that, if you start on any one of the base runners (notes, keys), and go in either the clockwise or counter-clockwise direction — and skip or jump over the next-door runner — then the next runners name (note, key) is a one-whole-note pitch interval (also known as, “one whole note” or “one whole step” or “2 half steps” or — and I like this one best — “2 c-steps” which means “2 chromatic scale steps”) away.

In other words, if you start on A (first base) and go clockwise, skip a runner, next one is B, skip another, next is Dflat, skip one, next is Eflat, skip one, next is F, skip one, next is G, skip one, you’re back to A.  Or start at C, to clockwise again, skip one, next is D, skip, next is E, skip, next is Gflat, skip, next is Aflat, skip, next is B, skip, back to C.

Cool.

I was using this idea during the revision/edit pass I was making through this page where I [in square brackets like these] added the names of the keys to the Chopin Etude examples further up in the page.

B Major is also C flat Major?  i.e., 5 Sharps is also 7 Flats?

Some of Olga Kern’s music was playing when understanding arrived about another one of the little statements, another of the little puzzles, on the Circle of Fifths diagram and its equivalent Baseball Diamond of Chromatic Fifths.

The puzzle is:  Why do the Circle and Baseball Diamond show the key of B major as being either 5 sharps or 7 flats, or both?  That’s the key just to the right of home plate at the bottom of the baseball diamond.

Let’s look at the notes in the B major scale.  The intervals, in terms of c-steps (frets, individual white or black piano keys) are:  2 c-steps, 2, 1, 2, 2, 2, 1.   So, starting at B:  B, C#, D#, E, F#, G#, A#, B.  That confirms that all the black keys are used.  That list gives the black keys their “sharped” names.

Those black keys could also be given their “flatted” names:  B, D♭, E♭, E, G♭, A♭, B♭, B.  Notice that’s 5 flats.

When you consider that B is C♭ and E is F♭, you could rewrite that as B (C♭), D♭, E♭, E (F♭), G♭, A♭, B♭, B (C♭).  Seven flats!  That’s the answer to the earlier questions about what the Circle of Fifths means by 7 flats.  What abou 7 sharps?

Nomenclature:  (# means sharp, by the way, for those who might not know that.  flat has a symbol too, a backwards b, but it’s not on the keyboard easy to type.  wait, it’s not a backwards b, it’s just a teardrop with a stem, sort of like a b.  i can just use b for flats.  ok.  Csharp is C# and Bflat is Bb.  but that only works when its major chords with capital letters.  Bflat minor would become bbminor.  not great.  the real b flat minor, if lower case letter b is used, looks like b♭ minor.  B♭ major.  b♭ minor.  Now that I’ve googled to find, copy, and paste the ♭, may as well just use it and # and drop a lot of Csharp and Bflat stuff.  Although, for people new to thinking in music terms, those spelled-out versions were probably helpful in getting started.)

What About 7 Sharps?  Same as 5 Flats?

We can do the same for the key (base runner) to the left of home plate on the baseball diamond, the one that shows either 5 flats, or 7 sharps, or both.  It’s the D♭ major key (base runner).

Applying the usual diatonic (do re mi fa so la ti) 2-2-1-2-2-2-1 c-step pitch intervals beginning on the D♭ note gives us:  D♭, E♭, F, G♭, A♭, B♭, C, D♭.  Five flats.  Five ♭s.  The flatted notes could also be given their sharped note names.  The same scale would be:  C# (D♭), D#, F, F#, G#, A#, C, C# (D♭).  Five sharps.  Except F can be written as E# and C can be written as B# which gives:  C# (D♭), D#, E# (F), F#, G#, A#, B# (C), C# (D♭).  Seven sharps!  That’s where the idea of “7 sharps” comes from.

Six Sharps.  Six Flats.  Same key.  Two different names.

We can use the same process for seeing how 6 sharps or flats works as a key signature in the Baseball Diamond of Chromatic Fifths.  Gflat,which is the same as Fsharp, will have a B or C and a E or F.  When sharps are used, one of them will be the 6th sharp.  When flats are used, one of them will be the 6th flat.  Let’s work it through.

Building the G♭ diatonic (do re mi fa so la ti) scale:  G♭,

Building the F# diatonic scale:  F# G# A# B C# D# F F#.  Five sharps.  But the problem for time signatures would be potential confusion with B major with its 5 sharps.  So, I get it now.  They just consider F to be E# and call F# major the key with 6 sharps.  As for the question of how you play it, I bet an entire dollar and twenty-four cents (ie, big money) that an E on the sheet music is played as an E, not as an F, despite the sharp on E in the key signature.  I bet the sharp on E in the key signature is just there to make it easy, instant, and error-free to pick up a sheet of music and not confuse key of B major with key of F# (or G♭ major).

Building the G♭ diatonic (do re mi fa so la ti) scale:  G♭, A♭, B♭, B, D♭, E♭, F, G♭ with B being C♭ for the “6th flat” …  something interesting is coming out here … the F# is more natural than the G♭ version.

Although the Circle of Fifths diagram shows F# major and G♭ major to be equivalent names, I would say, based on these findings, that F# should be the preferred name for this key at the bottom, home plate, of the Circle of Fifths and the Baseball Diamond of Chromatic Fifths.

Given the symmetry that’s been showing up all over the place, I bet the minor scale turns out the other way.

And that’s turning out to be right.  You often hear of F# major, but not usually G♭ major.  You also often hear e♭ minor, but i don’t think i’ve ever heard d# minor.

Cool.

Another Set of Guitar Strings in the Baseball Diamond

Guitar wiz, Slash Hudson, could tell us that, in fact, the 11 of the 12 base runner notes and keys on our Baseball Diamond of Chromatic Fifths can be viewed as being like two sets of 6 notes in patterns similar to the tuning notes on guitar strings.

As discussed earlier, the first set runs counter-clockwise from the runner on the right of first base (the “big” E string) to the runner to the left of second base (F as the re-tuned or first-fretted little E string).  That’s E, A, D, G, C (re-tuned B), F (re-tuned little E string).

The other set of six guitar strings are as if the thickest four strings had been down-tuned by one fret.  That’s E♭, A♭, D♭, G♭, B, E.  Very cool.

The two sets of guitar strings overlap on the E base runner.  The B♭ base runner isn’t used.

Calling Things Sharp or Flat:   Flip of Coin? or Good Reason?

There are several places in music where I’ve wondered why, when they have the choice of calling a note, key, or chord a sharped note or a flatted note, that they pretty much pick one and use it consistently.  I’ve wondered if these are arbitrary decisions that just have to memorized or if they’re the lovely kind of “natural fact” that can be derived and shown to be the inevitable right choice based on other clear and unavoidable “natural facts.” : )  TOC.  Science of Anything.  Philosophy of Anything.

The traditional Circle of Fifths and the remarkable new and exciting Baseball Diamond of Chromatic Fifths places many of these little mysteries all in one place.  I think it also solves the puzzles once and for all.  Let’s think some of this through.

Example:  The key of G, with its one sharp, could be considered to be a key with one flat.  Couldn’t it?  Let’s see.  The scale now is:  G A B C D E F# G.  But the five main notes that can be expressed as a sharp can also be expressed as a flat.  F# is the same note as G♭.  But that would make the scale be:  G A B C D E G♭ G.  That would be more confusing.  So that one makes sense.  The key of G should be considered a key — the only major key — with one sharp.

I think the same thing’s going to happen if we try to use two flats instead of two sharps for the key of D major.  Let’s try it.  The scale now is:  D E F# G A B C# D.  Two sharps.  Let’s try it with 2 flats.  Two ♭s.  D E G♭ G A B D♭ D.  Wow.  That’s more unnatural and potentially confusing than G.  I was expecting just one of the flatted notes to be a repeat base letter, but it’s both.

So probably, for A major, with 3 sharps will give three repeating base letters if we try to use flats instead.  Let’s try that.  The A major scale now (to write these scales, by the way, I’m stepping up from root note … music experts call the root note, the “tonic”, which is the tone-ic, the tone around which the scale, chords, and key are built, the tone they start and end with … anyway, stepping up from the root/tonic note with the 2-2-1-2-2-2-1 c-steps intervals) is: A B C# D E F# G# A.  3 sharps.  Re-write with 3 flats:  A B D♭ D E G♭ A♭ A.  Well, it gives only 2, not 3, repeating base letters, but it skips a letter.  the whole package is much less natural and more potentially confusing than using 3 sharps for A major.

Very nice.  Very clear.  I like it when it works out this way.  In this case, we can remember/memorize A is three sharps if we want to, but, if we forget and don’t have a reference — or it we just feel like doing it — we can figure out what the standard right way ought to be and is.  Sweet.

No doubt E major with its 4 sharps will have awkward repeating base and skipped letters too.   Let’s rock:   E F# G# A B C# D# E.  4 sharps.  With flats: E G♭ A♭ A B D♭ E♭ E.  Ugggggggggleeeeeeeee.  [likely prezView]  Double ugly. [likely tSrView]

Five sharps: B. We’ve been there for something.  Oh, that was the “5 sharps is same as  7 flats” idea.  This is a different analysis, different question.  B with sharps:  B C# D# E F# G# A# B.  5 sharps.  With flats:  we have done this before … that’s ok … with flats: B D♭ E♭ E G♭ A♭ B♭ B.  Skips C and F.  Doubles E and B.  Double ugly again.

I see no reason to ever use 7 sharps or flats.  The 5 sharps/flats works just fine.

Anyway, I’m sure the situation is the same on the left side of the Baseball Diamond, the side with the 6 keys with 1-5 flatted notes.

Applications to Heavy Metal

If Joe Satriani were here, he would tell us the traditional Circle of Fifths and the new and exciting Baseball Diamond of Chromatic Fifths were very helpful in using his Pitch Axis Theory for dealing with lots of scales of many kinds on the heavy metal guitar.

What Else for Olga to Inspire Us to Understand? Oh … Relative Keys

There’s still at least one issue left.  There’s the question that began really back in the diatonic modes discussions of how the same notes can give different sounds and be considered different keys.  It applies for all the diatonic modes, but let’s not go all the way there.  Let’s just look at two of those 7 modes, the Ionic and Aeolian, which, in non-modal parlance are just the “relative major key” and the “relative minor key.”

Let’s use an example to make the question more clear.  The key of C has scale notes as follows:  C D E F G A B C.  It’s relative minor key, the A minor key, has the same notes in a different order:  A B C D E F G A.

Back in the discussions of the seven diatonic modes, I got a little bit of understanding of how seven different sounds, experiences, moods, effects are created from the same scale notes, but I don’t think what I took away as understanding was enough.  What I got was that the different … let’s take the simplest case of the mode using a constant low “drone” note … so playing the same scale notes with 7 different low drone notes just gave a different mood.  One could also play certain chords and maybe chord progressions, but I didn’t really understand how that worked.

Keeping this discussion, at least for the moment, on a major key (one of the seven modes) and it’s relative minor key (another of the seven modes), … ok, there’s two questions:  (1) how do composers and performers get the different minor vs major “sound” from the same scale notes? and (2) how, seeing no sharps or flats on a time signature, does the performer know if it’s C major or A minor and what do they do differently and does it matter?

This issue came up early on this page in the section about examples of time and key signatures of Chopin Etudes.  There was one that I noted as having a certain number of sharps or flats, I started to call it the associated major key, and I noticed my notation that the work had a characteristically “minor” sound about it.

So that, I think, (as we say) “frames” a few parts of the question.

As to what produces the “minor sound”, the consistent low drone note can be the right answer for ancient modal music, for bagpipes with that big drone note or those big drone notes whatever they use, and for rock n roll jamming including some of the meditative psychedelic stuff and maybe some jazz that hold a tone and let’s jamming and improv happen for a long time.   But that relatively simple answer of the drone notes or maybe drone chords I think doesn’t account for the “minor vs major” sound in the much wider range of popular and classical music.  For example, that Etude … let me get which one that was … Cello … here’s the prior comment, ” ….’Cello’ (25-7) is 4/4, slow play, 5 min long,  and the key with 4 sharps (kind of sounds ‘minor key’ … i don’t get how that works really …”

So ‘Cello’ (25-7)” has sheet music that says 4 sharps.  We now know that would be E major if it didn’t sound so “minor”, right?  But it DOES sound “minor.”  There’s no drone note, no long-standing note or chord.  In fact, as usual for Chopin Etudes, there’s a lot of different things going on in both the left and right hands of this piece.  So, when the pianist sits down to play this, opens the sheet music to the page, sees the four sharps, is she thinking E major or c#minor (note on Circle of Fifths both of these are 4 sharps).  If she thinks E major, does she DO something different, other than play the notes as written, than if she were thinking c#minor?

Meanwhile, what’s Chopin done in the composition that creates that darker “minor” sound.

And, meanwhile, like the fact that C major (C D E F G A B C) and A minor (A B C D E F G A) had the same scale notes, E major and c# minor have the exact same scales notes in a different order.  E major ( E F# G# A B C# D# E) and C# minor (C# D# E , F# G# A, B, C#).

Note:  a minor scale has flatted/diminished third note which is why the E isn’t an F.  a natural minor scale also has a flatted/diminished sixth note which is why the A isn’t an A#.  i knew that before … but …

Hm … interesting … the intervals on those c# minor notes are a bit surprising, but maybe it shouldn’t be … the flatted/diminished third is standard for all minors … i do remember now there was a diminished later note in a “natural minor,” but both the 6th and the 7th? …

so a relative minor, which is also a natural minor, which is also the 6th diatonic “aeolian” mode, must also have a diminished 7th note which is why the B isn’t a C?  it looks like that’s true.  and the A minor made with the C major keys piano white notes is doing that too … a whole note (2 c-steps) between the 7th and the octave … hm …

wow.  i know that seems a bit complicated, and, to be honest, i’m a little surprised.  on the other hand, i remember from the “modes” discussions that the issue of “minor” gets into issues of natural, vs melodic, vs harmonic,  vs ascending, vs descending “minor” scales.

the main thing to work from all of this — that i’m finding helpful — is the C major and A minor example is impossible to confuse since they come with the nice physical and mental picture that both the C major and relative A minor notes are just the white keys (unsharped and unflatted keys, ie, not the black keys) on the piano.  I checked the c-step intervals on the c# minor scale that came from starting the E major scale’s notes and they match the c-step intervals on the relative A minor scale made up of re-ordered C major piano white key notes.  In other words, the c# minor scale we are using is right.  it is what it is, diminished third and sixth and seventh notes and all.  Wow.  Can that be true.?  It must be.  Leave it there for now.

Ok, so getting suddenly snared again by all the lovely complication that goes on with minor scales was interesting, and some additional facts and distinctions in that area just became a bit more clear than they were that last time we went there (but still not completely clear), but, now that we’ve extracted ourselves from all of that …

… it doesn’t change the question we were starting out with here.  The question here is centered on the fact that the relative major and minor keys — the twelve pairs of them that are placed in the outer circle (relative major keys) and in the inner circle (relative minor keys) around the Circle of Fifths and also around the exciting and glamorous Baseball Diamond of Chromatic Fifths — have, not only the same number of sharps or flats in their key signatures, but also the exact same scale notes (but from a different starting point) so (1) does the performer need to know whether it’s the minor or major, (2) if so, how do they know from seeing the same number of sharps and flats in the key signature on the sheet music, (3) if they know whether they’re playing the relative major or minor, what difference does it make, and (4) from the composer’s viewpoint, how do the same notes shared by a pair of related keys, relative major and minor keys, make those different moods, sounds, effects, tones, etc?

Ok, so there.  Now the question is definitely — and, at long last — well-framed.

Ce-la pour maintenant.  Amour.  Sans doute.

000000000000000000

Bonjour.  L’après-midi à  un bloggèrre musique.  Quoi?  Parle-je Francais?  Un peu.  Quoi?  Un très petit peu?  Pas gentille … jeez … : ) …

Where we left off was thinking again about how the sounds of musical songs and other works written and performed in “minor keys” differ from the sounds of those in “major keys.”  We can tell they are different.  We try to use words to describe each one and the difference, but, most aspects of experience — like what does chocolate ice cream taste like — the words only communicate the experience once both the sender and the receiver have had the same experience and agreed on words that point to it.  The sounds are what they are, and the effects in experience are what they are.  The words we use are, at best, approximations and pointers to and reminders of the experiences themselves.  So when we hear others and find ourselves saying things like, “oh, minor key songs are darker, more serious, sometimes maybe sadder, sometimes even doleful, etc” and “oh, major key works are brighter, happier, etc”, it’s interesting and useful and not completely wrong, but it’s also never really very close at all to being correct.

Quite a few interesting questions and answers have arisen during these 30 discussions of modes, music theory, and music about the issue of sounds and their effects in our experience.  What sounds are just sound vs. those that are “music.”  When movie music becomes “sound effects.”  Emancipation of “dissonance.”  The changing nature and role of what’s considered “dissonant.”  The line between “dissonance” and “just sound” or “just noise.”  Tritones.  Atonal music.  Sevenths.  Jazz.  How composers create different tonalities (the things we refer to as moods, emotions, those sounds, the effects music makes in us, etc.)

My first inclination is my usual one when things start to seem complicated — to create a starting point by, at least at first, walking away from all the complexity and finding some simple and clear “natural fact” aspects of the situation to start with, learn from, and then use to build back up to the actual complexity again. In this case, that’s walking away from all the complexities of “musical” sounds and their effects — of the many different combinations and sequences of sounds, the different experiences in us they can create (different even within the same person at different times? in different situations, moods, etc?), and the different words that might come to different people’s minds when hearing them — and just start over with simple individual sounds.

Simple like two-note chords.

Even simpler like which sound is a “musical note” and which is just a “sound” or a “noise.”

Goldmine! (Lypur)

I was looking for a source of sounds of two-note chords and found this excellent video.  This guy, “Lypur” (Andrew Furmanczyk), is brilliant.  His strategy for preparing oneself to practice recognizing “intervals” (two-note chords and two-note sequences both have pitch “intervals” between the notes) is very smart.  His seemingly-casual comment that “… but you need to have a way to practice them [ie, practice recognizing/humming/performing intervals], right?”, is right on target.  Perfect.  “Intervals” is another way of saying simple two-note chords or two-note sequences.  These are very close to being the most basic building blocks of all music.  Thinks about it.  Music is either one note played by itself, or one note played after another note (with pitch intervals), or two notes played at the same time (with pitch interval between them), or more than two notes played at the same time (chords), or some combination of these.  He’s also a remarkable singing talent, sort of.  Listen for the sounds, the names of the sounds, and sample songs he uses for mnemonics, but don’t pay much attention to when he calls some of the sounds “ugly”, “pretty”, “good”, or “bad” or other evaluations.  His opinions and reactions are not unreasonable, wrong, or not unusual, but his personal enculturated good/bad evaluations, though charming and interesting, aren’t the point of my bringing him and his video to our attention.  The primary value here is it’s an organized and clear opportunity — much better than I thought I would find (I thought i’d need to create one myself from little sound files) — to get the “facts”, the “natural facts,” i.e., (1) the direct experience  of the sounds of the two-note intervals sequences and chords and (2) the ability to refer to the now-shared direct experiences with words, and (3) the songs as mnemonic memory aids and inner voice and outer voice training aids are brilliant too.

From the notes in Lypur’s (Andrew’s) video.  Brilliant!  Oh, and I just noticed this list of songs is different than the ones he speaks of in the video.  So use both the examples in the video and this list PLUS, as he says, you can make up your own little songs that use the intervals.  Also, his approach to developing the ability called, “perfect pitch”, is right, very smart, interesting, and valuable, but it’s another thing that’s not why I’m bringing this video to our attention.  The valuable part of this is a different experience, knowledge, and skill set:  getting the direct experience and vocabulary for the 12 basic building block pitch intervals.  For example, the 12th of 12 intervals, the interval that has 12 c-steps or semitones of pitch difference, is, “Some-WHERE” (over the rainbow) for the interval called in music theory, the “octave.”  Another example, the 9th of 12 intervals, the interval with 9 c-steps or semitones of pitch difference, is “my BON”(nie lies over the ocean), called in music theory, the “major 6th interval”.  Get all 12 of those in experience/memory/innerVoice with names to refer to them and you’ve got something in “listening to, discussing, and making music” akin to having the alphabet nailed down for “reading and writing” books, magazines, and pretty good internet music blogs (like this one).

These songs and comments are from the notes in Andrew’s video:

“Minor 2nd- Jaws
Major 2nd- Happy Birthday
Minor 3rd- O Holy Night
Major 3rd- Oh When the Saints
Perfect 4th- Wedding March
Tri-tone- Maria (from West Side Story) or The Jetsons Theme Song
Perfect 5th- Star Wars
Minor 6th- Love Story or Close every Door to Me (from Joseph and the Amazing Technicolor Dreamcoat)
Major 6th- My Bonnie Lies over the Ocean
Minor 7th- Star Trek
Major 7th- Psycho Theme
Perfect Octave- Some where over the Rainbow

In this lesson, I explain how to find intervals by ear and by sight on the keyboard.

If you want to play by ear you’ll need to know how to recognize the intervals in your head.

Make sure to visit my website and join the music community forum at http://www.howtoplaypiano.ca”

Another Good Video for Ear Training

This video is good to use as a tool within Andrew’s overall strategy.  It’s a very efficient for getting the basic idea that the sounds of the 12 basic intervals are different, getting a direct experience of each of the 12, for learning the 12 official music theory names, and for the quick focused review, practice, and drill that’s useful in the beginning of having some useful basic building block be “second nature”.

http://www.youtube.com/watch?v=U-vD7Swr3DQ

I would use both videos.

Just noticed this video deals with 13, not 12, “intervals”.  When two of the same note are played at the same time (no pitch difference), that’s called a “unison” “interval” (although there’s no “inter-“, no distance, no real “interval” between the two notes).  The “unison” is sort of a zero interval.  When I first encountered the idea of unison, I thought, now that’s a waste of time, but I later heard unisons (two pianos or two guitars playing the same notes, or one piano and one violin, etc) and realized they are a useful part of the musical palette since they provide different textures of sound than simple single notes.  Anyway, “unison” and “unison interval” are useful ideas too.

Bits and Pieces Concerning Intervals

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Using the “Happy Birthday” Song for Learning Intervals

The “Happy Birthday” song is an excellent tool for learning and practicing intervals since we all know it so well and since it starts and keeps returning to a low base reference note.

There are four phrases in the song.  The first phrase gives clear examples of the Major Second and Perfect Fourth intervals.  The second phrase shows Major Second again and Perfect Fifth.  The third shows the octave very clearly like “SomeWHERE over the rainbow” and “Happy TRAILS to you.”

There’s also a Major Sixth like “My BONnie lies over the ocean” and the first two notes of Frank Sinatra’s “My Way” (And NOW …).   It’s between the last note of the third phrase (when you say the person’s name, like “johnny” and the first note of the fourth phrase (HAP) … so the interval is to johnny, HAPpy birth …

the first happy birthday intervals video I found had good points, but also some errors.  I found the errors because I’m starting to get the “feel” for the intervals … i became sure because it became clear the “somewhere over the rainbow”, “happy trails” and 3rd of 4 happy birthday examples were teh same interval, thought the video said the birthday video had the wrong name … also, i found this on the internet that confirmed the octave (vs major 6th interval):

“In C major, it becomes: G G A G C B | G G A G D C | G G + G E C C B A | F F E C D C. Please note that the + sign means octave, so when you see G+ I mean the next octave (Higher) G note.”]

When it made the point that the next to last “Happy BIRTH”(day to somebody’s name), the one that goes to the highest note, is a major 6th interval (9 semitones or c-steps), I noticed it was also the interval used in the song, “Happy TRAILS” (to You, Until We Meet Again) Roy Rogers theme song … [update: both of these are octaves, not, as the video says, major 6ths]

This focus on intervals is pretty cool, especially associating parts of familiar songs with the standard intervals.  Wikipedia has a nice chart here.  [Update: the column, “diatonic intervals”, in this chart makes sense to me.  In the Jan 3 version of this Wikipedia chart, the column labelled, “chromatic intervals,” completely baffles me, makes no sense to me, and might be wrong, though, of course, I might just not be understanding something.  But, even if it’s right, it’s too confusing, so I’ll leave the link to the chart for the diatonic names, but suggest ignoring the chromatic names.]

Lest We Make This Interval Names Thing Too Confusing …

The names of the intervals could be as simple as stating the number of c-steps (or semitones) of their pitch distance:  zero c-steps (unision), 1 c-step (minor second), 2 c-steps (major second), and so forth up to 12 (octave) for the standard intervals and even further for the more unusual intervals as 13, 14, 15, and 16 c-steps and so forth.  If you lower your head while singing the lowest note you can reach, and then raise your head while singing the highest note you can reach, the difference in the pitch between the notes is an “interval” which can be measured and described as being some number of c-steps.

The idea of c-steps is used only on this blog.  I invented during some of the earlier discussions because the terms “tone”, “note”, “step”, “degree”, and “key” could mean different things in different contexts of music pitch, melody, harmony, timing, and key.  C-step means the same thing all the time, like guitar “fret” or the piano “key” (IF you consider all the keys, both white and black).  C-step is always the pitch interval of moving one note on the chromatic scale … see, there’s the problem … moving one “note” or “step” on the chromatic scale is sometimes different than moving one “note” or “step” on the diatonic scale … anyway, no big deal … just re-explaining c-step.  In this context of intervals, using “semitones”, the usual official music theory term, is usually clear and unambiguous too.

So the intervals could have been named simply as:  zero semitones (unison), 2 semitones (minor second), 3, 4, 5, 6, and so forth.

Why did they not do that?  Why did they give them these other less simple and (at least initially) less clear names like “perfect fourth” (5 semitones or c-steps) or “octave” (12 semitones or c-steps)?  For “unison” and “octave”, I think the answer’s clear.  The whole system of both chromatic and diatonic scales is oriented around dividing the pitch interval called, “the octave” into useful steps and intervals.  But why “minor and major second, third, sixth, and seventh” and “perfect fourth and fifth” and “diminished fifth or augmented fourth or tritone”?  I don’t know for sure,  but I’m assuming those names, in various contexts of use, give various kinds of greater intuitiveness, clarity, or efficiency when composing, reading, hearing, or playing music.

Another Word About Andrew’s Video and Approach

It turns out that there are quite a few videos on YouTube that in some way address the learning of musical intervals.  Most are useful for one aspect or another of initial learning, hearing the intervals, associating them with familiar songs, or practice.  Andrew Furmanczyk’s video is still the best so far for overall approach to the project of getting the sounds and names of intervals in mind for fluent … that’s the issue … he may not be the most polished professional presenter, but the way he’s teaching and suggesting continued self-learning and practice is an approach that will lead to fluency in the use of the musical intervals and not just to knowing some information about intervals.  It’s like the difference in approaching learning a second language in a way to gives rise its fluent use vs. results in knowing some things about the language but not being even close to fluent in its use.

Unlike other videos, Andrew presents the intervals, not in the usual formal ascending or descending order, but in the order that he thinks people will recognize and have fun and satisfaction with intervals right away.  Instead of starting with unison and continuing with minor second, major second, minor third, etc., he opens with the well-known interval in “Twinkle TWINKLE Little Star.”  : )  That’s “well-known” in the sense of being familiar in all of our minds.  He then links the label, “Perfect Fifth,” to that common shared experience.  Later, he does the same for “Here COMES the bride” and the “perfect 5th” concept, and for “My BONnie lies over the ocean” and the “major sixth” identifier.

He doesn’t have songs for all the intervals.  And he forgets how to play some of the songs and forgets some of the words and bounces around in the order.  He uses one incomplete list of songs in the video in one order and puts a different list of example songs in the usual order of ascending order in the notes to the video.  That little bit of charming disarming chaos isn’t important compared to the correctness and quality of the strategy Andrew’s suggesting for moving quickly from knowing nothing about intervals to having pretty stunning fluency in use of the intervals.  We can get an orderly demonstration and list of the intervals almost anywhere.  So use Andrew’s video to get the self-awareness and self-training strategies for taking the process all the way to fluency in listening, remembering, singing, playing, and sheet music writing of intervals, and for getting into the fun of it all, and then go to other more typical places for more orderly lists with no typos, omissions, or other funny little screw-ups. ♥

Contents of Andrew’s video:  Introduces the objective, logic, and nature of his approach … introduces the 12 intervals in an oddball order that hits familiar, amusing, and high-satisfaction and high-confidence-building home runs in the first few song examples and then wanders around a little through the rest … : ) … at minute approx 13-14 discusses smart strategy for getting perfect pitch …

(why not?  training for perfect pitch is not necessary for intervals, but, if you’re into this at all, why not get little habit-anchors to correct, for example, Middle C too? … in other words, what “perfect pitch” means is, when you sing that note you always sing, you know it’s C, not D or B … and when you learn what D “feels like” “sounds like in your mind”, you can sing the right D when somebody says, “sing D” … it’s just calibrating your ear and inner voice and outer voice to “know” when they are hearing or performing at specific pitch levels … it’s simple and Andrew’s strategy for that is also very concise and very correct (by ‘very correct’, I means there are lots of other ways to think about perfect pitch and try to get it, but his is, again, concise and psychologically and cognitively and psych-dynamically correct … what?  do i think Andrew’s approach is pretty smart?  grrrr ….)

… anyway, Andrew’s program then proceeds to suggest quizzing with friends and conducts a well-designed but sort of charmingly flubbed up a little bit quiz at minutes approx 14-22 … and at end, repeats some ideas about the approach …

The order in which Andrew introduces the interval sounds, interval names, and some song examples (for 7 of the 12 standard intervals) is:

Perfect Fifth – Twinkle Twinkle Little Star – (Twink) “ul TWINK” (UL little star) – great song example

Perfect Fourth – Here Comes the Bride – “Here COMES” (the bride) 2:45 – great example

Minor Third – Canada’s National Anthem – “Oh CAN”(ada) 3:13 – good example for Canadians.  need another for the rest of us

Major Second – “major scale” – [“do RE” mi fa so – good example]

Minor Second – “like a chromatic scale” – [no song example – that’s ok.  gives the direct experience of the tone and the name.  we’ll find song examples elsewhere]

Major Third – “think of a triad” – [whatever a triad is … i don’t know] …. [no song example – that’s ok.  gives the direct experience of the tone and the name.  we’ll find song examples elsewhere]

Tritone – [no song example – that’s ok.  gives the direct experience of the tone and the name.  we’ll find song examples elsewhere … no good mnemonic here, but gives the experience of the tone … i suggest trying to ignore Andrew’s comment here of “ugly” and “wouldn’t want to use in a song” and “doesn’t sound like anything” … why?  because it does sound like something … it sounds like itself … it sounds like it sounds … its sound is a fact, a phenomenon, a “natural fact”, an unconceptualized datum of experience … it is what it is … it sounds like it sounds … what?  is it really what it is?  well, yes, it … oh, buzz off, will ya? … : )  … anyway, that’s first … every interval sounds like it sounds … after that, we might say “it also sounds like xyz” or “i don’t like that” or “i like that” or “it’s bad or ugly or good and lovely” … but the right starting point is getting our own direct experience of what it is, what the sound sounds like … to begin, we just want to get a un-judged unevaluated direct experience and any useful labels for referring to it and examples that are also useful for mnemonic/memory purposes and for referring to it, but not good/bad judgments … judgments can show up later within ranges of validity … tritone is, in some circumstances, or in some people’s perception, is good or bad or indifferent … i know that some view tritone as good in some places like scary movie music, movie music, organ music, maybe DeBussy’s use of dissonance later in his career, maybe Schoenberg in his atonal work later in his career, maybe in Bartok’s unusual chromaticism, definitely in heavy metal rock music, maybe [now definitely] jimi hendrix “purple haze” opening notes (have to verify that, but i think that’s a tritone in the opening riff [now verified]) … many think of the tritone as unattractive or unmusical, and, historically, some churches have banned it because of suspecting it as being evil … so, andrew’s reaction to the sound of the “dissonant” tritone is not unusual, illogical, unreasonable, or “wrong” … it’s just not the point of calibrating our ears and inner/outer voices to recognize and sing the various intervals … we’ve seen this issue of the tritone being controversial before in the earlier discussion of the evolution of the idea, definition, perception, response, and use of “dissonance” … the “emancipation of dissonance,” et al … but the point of all of this — as, to be sure, Andrew also says — is just be able to recognize and repeat in inner/outer voice tritone along with the other interval sounds … note: one commenter on Andrew’s YouTube video said Purple Haze uses the tritone … i know it’s used in a lot of tony iommi’s black sabbath heavy metal music  …  update:  i stumbled into a video that does several things:  (1) shows how certain religious people in current times still think of the tritone, as some churches in middle ages did, as the “devil’s tone”, (2) confirms that the opening to “purple haze” is repeated tritone intervals, (3) unbelievably, to me anyway, says eric clapton’s “sunshine of your love” opening riff contains the “devil tone”, and (4) mentions jethro tull’s ian anderson as a user of the devil’s tone … i guess that’s enough for this revisiting to the tritone part of the “emancipation of dissonance” story within the overall Story of Music … ]

Minor Sixth – Love Story – very good song example

Major Sixth – “My Bonnie Lies Over the Ocean” – 9:23 – very good song example

Major Seventh – [no song example – that’s ok.  gives the direct experience of the tone and the name.  we’ll find song examples elsewhere]

Perfect Octave – “SomeWHERE Over the Rainbow”

Minor Seventh – [no song example – that’s ok.  gives the direct experience of the tone and the name.  we’ll find song examples elsewhere]

On the video, Andrew suggests googling on “interval song chart” for a list of songs that use intervals.  I tried it.  Here’s one hit.

The order in which Andrew quizes on the intervals is:

–

–

So, the order Andrew uses in his video for initial introduction and quizzing is ok for what it is and does, but it’s also useful to know them in their official actual ascending order which is shown on the nice Wikipedia chart here.

Intervals:  One At a Time

Earmaster.com – Great site for example songs for intervals.

Unison (zero semitones)

–

Minor Second (1 semitone)

Ascending

A Hard Days Night (Beatles) – youtube

White Christmas (Irving Berlin) – youtube

Jaws – youtube

Chromatic scale – youtube

Pink Panther theme – youtube – first two notes

Major Second (2 semitones)

Ascending

“Happy BIRTH day” – Second-to-third notes of the first two of four lines of the Happy Birthday song.

Are you Sleeping – youtube

Silent Night (Christmas) – youtube

Rudolph The Red-Nosed Reindeer (Christmas) – youtube

Strangers in the Night (Frank Sinatra) –youtube

Minor Third (3 semitones)

Ascending

Greensleeves – youtube

Smoke On The Water (Deep Purple) –youtube

So Long, Farewell (Sound of Music) –youtube

O Canada (national song) – youtube (for Andrew)

Major Third (4 semitones)

Ascending

Oh, when the Saints – youtube

Morning has Broken – youtube

From the Halls of Montezuma (Marines’ Hymn) – youtube

Perfect Fourth (5 semitones)

From the Wikipedia page for Perfect Fourth:  “A helpful way to recognize a perfect fourth is to hum the starting of the “Bridal Chorus” from Wagner‘s Lohengrin (“Treulich geführt“, the colloquially-titled “Here Comes the Bride“). Other examples are the first two notes of the Christmas carol “Hark! The Herald Angels Sing“, and, for a descending perfect fourth, the second and third notes of “O Come All Ye Faithful“.”

Ascending

Here Comes The Bride

Love Me Tender (Elvis)

O Christmas Tree

Descending

Tritone (6 semitones)

Ascending

Maria (West side story) – youtube

Simpsons – youtube

Purple Haze (Jimi Hendrix) – introductory riff – alternating low and high bass notes

Descending

Blue Seven (Sonny Rollins) – youtube

Black Sabbath (Black Sabbath) – youtube

“The doomy guitar riff was written by Tony Iommi, he played a [middle second note] Db note against a G [low first note and octave higher second note], which is a flatted-fifth or augmented fourth interval. Right when he played it, everyone else looked at him and said ‘What the hell was that?’ The flatted-fifth interval is known as a tritone, and has been called “the devil’s interval” for centuries. Many metal people use it in harmonies when looking for anger. Black Sabbath was potentially the first rock band to really use it.  By the way, guitarist Tony Iommi is missing two fingertips from his fretboard hand.  – Eddie, Lachine, MI”, commenter on the song, Black Sabbath, on songfacts.com

That means the opening riff, the introduction, of the song, “Black Sabbath”, by the band, Black Sabbath, ascends an octave interval (12 semitones or c-steps) from a lower G to a higher G, and then descends one tritone interval (6 semitones) to Dflat, and then descends again by one tritone interval back to the low G.

It creates a pretty spooky sound.  The interesting question  is:  Is the sound spooky because it’s been used in spooky scenes in scary movies, or is it intrinsically spooky and scary?

“Far as the flat 5 interval…nearly EVERY rock band used the flat 5, as it (along with the dominant seventh, another tri-tone off the third) is the basis of blues, and therefore the earliest rock. – Steve, Louisville, KY”, commenter on the song, Black Sabbath, on songfacts.com

As we have seen a few times on these music blog pages, discussions on the subject of the tritone interval can get a little bit lively.

Perfect Fifth (7 semitones)

Twinkle TWINKle

Star Wars – first two notes

From the Wikipedia page for Perfect Fifth: “”

Minor Sixth (8 semitones)

Ascending

Somebody to Love (Jefferson Airplane) – song on youtube

Gracie Slick ♥ would tell us we should have a “Somebody to Love Story” mnemonic for the Minor Sixth interval … like the Jeopardy game before and after game where there’s two answers and the last part of the first answer is the same as the first part of the second answer, like “I Left My Heart in San Francisco” (Tony Bennett song) and “San Francisco Nights” (Eric Burden and the Animals song) … anyway, first, locating the interval in the Jefferson Airplane song:  “Don’t you want somebody to luh-uve? Doooooooon’t you need somebody to luh-uv.  Wouldn’t you love somebody to luh-uv?  You better find somebody to luuuuuuuuuuuuuuuh – uh – ove.”   Where’d that Minor 6th go?  Had it earlier today … ok, there it is … I put it in bold and italics.  If you know both songs — as Grace does — it’s kind of cute.  You can sing the “luh-uhv’ of the Jefferson Airplane and use the “Doo” as the first sound of singing the theme to the movie, Love Story … “Do you want somebody to luh [almost as low as low root] -uv [low root] – Dooooo [high minor 6th] doo [low root] doo [lo] doo [hi] dooooooo [hi]”

In My Life (Beatles) – youtube

Descending

Love story theme – youtube

Major Sixth (9 semitones)

Ascending

Frank Sinatra’s “My Way” – first two notes – “And NOW”

My Bonnie Lies Over The Ocean – “My BONnie”

It CAME upon a midnight clear

Minor Seventh (10 semitones)

Ascending

Star Trek theme (Original) – youtube

Somewhere (West side story) – “There’s AAAAA” place for us – youtube

Major Seventh (11 semitones)

Ascending

Take ON me – youtube

Bali Ha’I: major seventh interval is between the 1st and 3rd notes/pitches in “Ba(base) LI(octave) Hai(major seventh)” – (South Pacific) –youtube

Popular (Nada Surf) – youtube

Octave (12 semitones)

Ascending

“SomeWHERE over the rainbow”

“Happy TRAILS to you”

Third of four phrases of Happy Birthday … “Happy BIRTHday to Johnny” …

I’m SINGing in the rain

Learned Something About YouTube Just Now

Didn’t know we can create links to YouTube videos and start them anyplace within them.  This YouTube link puts #t=67s to have Celine Dion right at the point in the song from West Side Story, “Somewhere”, where she sings, “There’s AAAA place for us”, with the Minor 7th interval: http://www.youtube.com/watch?v=HtO2iC0KIQ8#t=67s.  Cool.

Don’t Use This Next Video …

… to learn about intervals.  It looks good at first, but has confusing mistakes.  So why keep it here?  Because it has, at the very beginning a convenient Middle C tone reference.  If you want one of those, go ahead and use it.  (The mistakes include assuming that the Happy Birthday song has only three lines.  It has four.  So, when it refers to the “last” … anyway, it has mistakes and is more trouble than it’s worth for intervals.  Good for a quick hit of Middle C, though. : )

http://www.youtube.com/watch?v=sS4blSM2aUQ&NR=1

An Exercise: 2001 (Strauss:  Thus Spake Zarasthustra)

This should be interesting.  Work out the intervals for those opening tones at the beginning of the Stanley Kubrick movie, 2001: A Space Odyssey. The music is from Richard Strauss’ Thus Spake Zarasthustra.

Many of the notes are chords, so we’ll have to figure out how to deal with that.

The solo horn.  FirstNote-SecondNote up-interval … humming it … the second note is higher than the “re” in “do-re”, the 2-semitone Major Second interval … i think it’s also even higher than the “here comes the bride” Perfect Fourth … it’s the Perfect Fifth since it matches “twinkle twinkle little star” … so that’s cool …  now, a decision … to try to get the next interval from the first base note or use the top note of that fifth as a new base note? …

neither … skip to the big first-phrase finish interval … Daaaaah (root) Daaaaah (perfect fifth) Daaaaaaaaaaaah (probably octave from root) Di DAAAAAAAAAAH.

didn’t finish that yet … moving on for now …

Odds and Ends About the Circle of Fifths …

Odds and ends about the Circle of Fifths … and the marvelous Baseball Diamond of Chromatic Fifths (which, by the way, are also Diatonic Fourths … you knew that?  ok.).

Major keys (base runners) on opposite sides of the circle (baseball diamond) are tritone pairs (6 semitones or c-steps, 1/2 an octave, apart).  Examples:  C (top, second base) and Gflat (bottom, home plate), F (left of second base) and B (right of home plate), Bflat (left of F) and E (right of B).

That’s true for minor keys on opposite sides too.

The inner circle of minor keys is the same as the outer circle of major keys except the minor key circle is shifted counter-clockwise three positions.  So A major is at first base in the outer ring and a minor is at second base on the inner ring.  And the two rings proceed in sequence clockwise from those two points (using intervals of 5 semitones/c-steps) as A, D, G, C, F, Bflat, Eflat, Aflat, Dflat, Gflat/Fsharp, B, E, A.

On both rings, the 7 unaccented (unsharped and unflatted) key names are clustered together and so are the 5 accented key names.  The unaccented names are more toward the upper or right parts of the diagrams.  The accented names are more toward the left and bottom parts of the diagrams.

Letter names of pairs of Major/minor key names — like C of C major and A of A minor at the top (second base) — create minor third (3 semitones) and major sixth (9 semitones) intervals, which together are an octave (12 semitones).

Just thought — if you’re the sort who enjoys reading telephone directories, dictionaries, and the fine print on credit card policies — you might also find these exciting facts to be interesting.  See the kind of exciting discoveries the lovely Ms Kern’s presence inspires?