Musical Scales

Do re mi fa so la ti do.

Why is our scale 7 notes? Are there any cultures that have a different scale? Is there some mathematical reason? Is there a difference between a C sharp and a D flat that I can’t hear? Are there tones between these two notes that my western musically trained ear cannot hear?

What is the difference between a musical note and plain old noise? The not-quite-tone-deaf want to know!

I can’t answer why our culture has those 7 steps. I guess they sounded good to whomever started writing music down.

Yes, other cultures have different scales - I believe Chinese music is largely based around a 5-note scale and Hindi music has many more tones than the western octave. Ancient Greek music followed a different scale logic, Gregorian chants had their own…it’s all a matter of cultural aesthetics.

There are tones that the Western ear isn’t trained to emulate - ever listened to Hindi music? The singers can skip around an amazing number of times almost within the same note. All a matter of culture and what they are trained to hear.

I’m sort of pulling this out of thin air, here, but the various parts of music theory - do, re, mi…C#, Db, doesn’t really “exist”. It’s a theory. It’s imposing an aesthetic logic on the universe of possible tones.

If I play a C# on a piano, and then play a Db, of course it is the same note - what would matter would be the key that the song it is in - the key, or “logic” of some songs call for that one note to be a Db, as described in relation to the other notes of the song, and others would call for it to be a C#. It’s not defining the sound itself, it’s defining how the musician thinks about the sound and ultimately how the song hangs together.

The difference between a musical note and plain old noise falls out of this as well. You live in New York, right? So right now, outside your window, we can assume there is at least one car alarm going off. The alarm could be making recognizable notes - you could try to match the main note on a piano and find out what notes it’s sounding on. But the car alarm isn’t making any noise that follows a set logic - it’s not playing a tune, it’s not following a do, re, me, fa, sol logic, or a rhythm - it’s not put together as a piece of music. Ditto for a doorbell or car horn. Any sound can resonate as a certain note, but unless it’s in some kind of aesthetic pattern, it’s not music.

Yes, other cultures certainly do have other tonality systems. Asain cultures, for instance, base much music on pentatonic (five-note) scales.

The major/minor tonality that your Western ear is used to evolved over many centuries. In fact, it is still evolving. Witness music by Schoenberg, Glass, and other contemporary art-music composers. Anyway, the common major/minor system came to its culmination during the Baroque period. It is during this time that the most commonly-used nomenclature was codified and the tonality was more firmly established. Often, one will find Johann Sebastian Bach credited with confirming modern major and minor keys (see his Well-Tempered Clavier).

There are other tonal systems besides major/minor that would sound familiar and pleasing to you. There are the modes, such as dorian, lydian, mixolydian, etc.

As for C#/Db, no there is no difference. They are two names for the same note. Of course, there are sounds that can appear around C#, but generally, we would call these sounds “out of tune”.

Gotta run. My eighth grade class is here. They’re definately experimenting with alternate tonalities!

Let’s see if I can answer the ones I’m sure about.

Well, the Chinese, IIRC, came up with the pentatonic scale (now widely used in jazz) and the Greeks came up with six or seven, although they were based on the eigh-note scale we use today (and which I think they came up with in the first place).

No, it’s the same note - it just depends on the key you’re in (meaning, which note you started from and if it’s a major or minor scale). The basic principle of a scale is that each note name should be used once, i.e. in C major the notes run CDEFGAB.

Say you’re using the key of D major. You start up and go D E F# G A B C# D. All well and good. But if you’re in a key that for some reason has already named the C (B-flat minor, for example) and you need to go up to what you see as C# on the piano, that note has to use the D note name and thus becomes D-flat, hence Bb C Db Eb F Gb Ab Bb . It’s all really a matter of perspective.

No, people’s ears are generally sensitive enough to pick up on that. 'S how piano tuners make their living.

Loosely defined, a musical note has one source of vibration (air through a flute or horn, a string on a violin, the vibrating head of a drum) whereas noise has several. Take an orchestra, for example. Each instrument can generate a note when played. But if you all have them play whatever note they feel like, then you get noise. Of course, some noise sounds more pleasant than others, which is how you get musical works.

Technically, nothing.

A pure tone has just one frequency. Looking at its frequency graph you’d just see a simple sine wave. But it also sounds boring.

A note played by an instrument produces a base tone that is mixed with several harmonic tones. For example, a particular horn might have a base tone, a harmonic tone that is a 4[sup]th[/sup] above it and only 1/2 the amplitude, and another narmonic tone that is an octave above it at 1/4 the amplitude. These unique patterns of harmonics give a particular instrument their “timbre”, or flavor.

What one might call noise (say, static from an TV tuned to an unused frequency) can be mathematically broken down to many harmonics (though not harmonious to our ears). Besides it’s base tone, the TV static would have mixtures of frequencies that probably don’t fall on any culture’s traditional musical steps. Since our ears wouldn’t judge there to be any musical equivalents in it, we call it noise. It may be also why music from cultures with different musical scales sounds “noisier” than our own.

Not to belabor the obvious, but for clarity’s sake, it should be pointed out that what Biggirl mentions in her OP is only the major scale. The minor scale is (using the some solfege syllables): la ti do re mi fa sol la. Both draw from our Western 12-tone system of music. Which is to say, Western music divides the octave up into 12 equal semitones. From those 12 we derive the major and minor scales as well as all of the modes, each of which divides the octave into 7 tones as noted.

Well, now there isn’t, thanks to equal tempering.

Are the cultures that use a 5 tone scale using the same tones as we do? I mean, if we heard a Chinese 5 tone scale could we just add the next two tones and have a western scale?

And the cultures that have more tones in their scale, is it just the same as the western scale with part of the next octave thrown in? Or are flats and sharps incorporated into the scale?

Anyplace on the 'net were I can listen to music based on other scales?

Yeah, the personality clashes between C# and Db before their tempers got equalized were horrible. I heard it almost ruined a concert Bach gave before Frederick the Greak it 1747. :wink:

That should say “Frederick the Great in 1747”.

Just to expand on the difference between C# and D-flat - someone mentioned that now they’re the same because of equal temperament.

Prior to the 18th century, there was a difference between C# and D-flat - and of course any other “enharmonic equivalent” (which basically means any notes with different names that are played by the same key on the piano.) See, when you work out tunings of scales based on acoustical ratios, working out D-flat and C-sharp would produce slightly mis-tuned notes. Think of it as the acoustical equirvalent of rounding error.

What this used to mean was that a keyboard (like the harpsichord, precursor to the piano) would sound really good in, say, C major, sound decent in F and G, and then gradually more and more out of tune as you moved to other keys.

The solution was to not tune based on acoustic ratios, but instead make each interval a little out of tune, so that every key sounded virtually right, but that no key sounded completely wrong. One of the reasons J.S. Bach wrote his Well Tempered Clarvier was to demonstrate the ability of a single keyboard to play in every key without needed re-tuning.


I think what I mean is there a difference in music besides the way it is written? Is our concept of what is music based on what culture we were born in? I have heard Chinese music and it does sound “musical” to me. Not what I’m used to, but musical nonetheless.

I also have a sound file of supposedly Chinese music. It is really just a few western classics played on what sounds like a lute. The tones also sound a little flat to me. But I think the flatness of the sound is what makes the producers of the music think they can classify it as “Chinese”.

So now you are wondering whether it is possible to answer a question when the askee only thinks she knows what she means. Thanks for trying guys.

Here’s what what I’ve learned over the years. If any of this seems wrong, I hope someone helps clear it up.

The Romans had 4 note scales called “tetra chords.” These were produced by making a lyre (a little, hand-held harp) with 4 strings. Whatever tones the strings sounded were called that lyre’s tetra chord.

The Chinese developed the pentatonic scale because the primitive flutes they were making could produce only those notes (those pitches are stronger in the harmonic series. See below. )

Some African cultures used (still use?) a “sesqui-heptatonic” scale. It’s a scale that is one octave long, and has 7 notes, but the interval between each note is the same. It has been postulated that this is where the modern “Blues 3rd” originated.

There’s no difference between a C sharp and a D flat. But there are slight differences in pitch for the same note depending on its function (not necessarily the key of the song). If a note is functioning as a “leading tone,” for example, it should always be played a bit sharp. There are really good psycho-acoustic reasons for this that concern tension and release. Let me know if anyone wants to talk about it. Anyway, fixed pitch instruments like pianos can’t produce those subtle differences, but most other instruments can. I do it when I’m playing saxophone, for instance.

Our 7 note scale (do, re, mi, etc.) is not just culturally based but also acoustically based. Every sound that is made produces several fainter tones called “harmonic overtones.” The pattern that these overtones produce is called the “harmonic series.” Our scale is derived from this natural phenomenon. I recall science fiction accounts that portray aliens with the same 7 note scale structure for their music, since if the alien world has the same physical laws as ours, they’d have the same harmonic series too. Isn’t that why scale tones were used in “Close Encounters?”

  • JAlan

Just a note - there’s some artist who built a “car horn” organ. She plays “I love New York” on it (clumsily). It’s kind of amusing to hear, once. There are always a few people performing music on wildly ridiculous non-instruments, usually for laughs, and with varying degrees of success. I recall a brass player whose shtick was playing things like car mufflers. Not to mention those people who splice animal sounds together - somebody always digs up those damn dogs barking “jingle bells” every Christmas. Personally, I always wanted to do cows performing “Swing low, Sweet Chariot”.

Nobody’s brought up Debussy’s 6 note whole tone scale yet.

There are seven notes in an octave … so why do they call it an “octave” instead of a “septave”? The only answer I’ve ever heard is that you count the first note of the scale twice, which begs the question of why on earth you would do so.

Well, here’s the way it works (as best I can write it). We’ve talked about octaves, right? And how in Western music, the octave consists of twelve tones? A scale as we know it is nothing more than a pattern of notes going from one note to its octave note. They’re just patterns. The pentatonic scale means the octave is divided up into five notes, say, in Western terms, E G A B D E. The scale starts at the first tone (called the root), the goes up 3 tones, then 3, then 3, then 2, then 2, arriving at the octave. In a major scale, the pattern is root, up 2, up 2, up 1, up 2, up 2, up 2, up 1. In a minor scale, it’s root, up 2, up 1, up 2, up 2, up 1, up 2, up 2.

In Western written music, we have twelve tones, with the seven letters distributed along the minor scale, from A to A. We name the five tones not on the scale with sharps and flats. So, to play an A mionor scale on the piano, you’d only play white keys. As it works out, to play a C major scale, you’d also play only white keys. This is all easier to see if you look at a guitar than a piano, since the notes are layed out evenly on a guitar’s fretboard.

So, adding two notes to the 5 tone scale would just put you at two notes above the octave. Does that make any sense, or am I rambling again? Please feel free to correct my ignorance (like you wouldn’t anyway).

Biggirl, if you want to listen to music not written for an eight-note scale, you might want to track down some of the works of Harry Partch. He was an American composer (died in 1972, or thereabouts) who wrote for his own 43-note scale. Interesting guy, IIRC he spent some of his life as a railroad hobo. And since he was writing for his own scale, he had to build his own instruments from scratch, too. But he does have fans, and you can find his music if you look hard enough for it. A CD store with a good classical section might have one or two of his recordings, may even be some samples on the web. And his piece “Barstow” will be instantly recognized by any Dr. Demento fan.

Like others have said, C# and Db are considered to be the same note under what I think of as the even-temperament “approximation” to actual tuning.

My understanding of this is far from complete, and I’ve seen enough to realize that musical scholars still fight over just what constitutes “perfect” intonation. However, I’ll toss this little example of the compromises of even temperament out there:

The interval of major third (M3), ideally, is a ratio of frequencies of 5:4. A M3 above A=440, for example, would be a C# at 550 Hz. This “sounds right” to the well-trained ear.

Even temperament spaces things a bit differently, making the ratios between half-steps 2[sup]1/12[/sup], so that twelve half steps of equal size make up an octave (doubling the frequency). Under equal temperament, then, a M3 (four half-steps) is a ratio of (2[sup]1/12[/sup])[sup]4[/sup] = 1.2599: this would put the C# I mentioned above at 554.4 Hz.

Musicians are told that when they’ve got the third of a major chord, they need to play it “a little flat” - that’s why. If they play an even-temperament C# as part of an A major chord, it will sound slightly sharp - because it is more than a M3 above the root.

This opens a whole new can o’ worms, I realize. This type of comparison of true intervals to their even-temperament versions is how one begins to address why C#/Db are different notes until even temperament averages them out.

My knowledge runs out about here…

If you produce the scale, you have to sing or play the root note twice to complete the definition of the final interval, and not leave it “dangling”, so you’ve sung or played 8 notes. Somebody just chose to count the fenceposts rather than the intervals of fence (the distinction between interval markers of some sort and the intervals themselves, is familiar to all programmers, and “fencepost error” is a common term for mistakenly counting one when you should be counting the other, or forgetting to count the fencepost at one end).

minty green:

Regarding seven notes in the octave - it’s because the system of naming intervals is based on ordinal numbers, not cardinal numbers:

c/do - first note
d/re - second note
e/mi - third note
f/fah - fourth note
g/sol - fifth note
a/la - sixth note
b/ti - seventh note

Which brings us back to . . .

c/do - eighth note.

I used to wonder about this too, but it’s the same reason why 2001 is the first year of the third millenium, not 2000!


So much to say and where to start.

First a caveat: not all scales have seven notes. There are many types of musical scales: what is called “music” depends on the culture, year, place, so many factors (semi-detailed later.

Let’s see what I can dredge up from college…

“Standard” Western European music is the 7 tone diatonic scale based on the Pythagorean system - five whole tones (T) and two semi-tones (S). It is the arrangement of these steps and half-steps that gives a piece of music its modality (major, minor, etc.) that we are used to.

Diatonic or Major - TTSTTTS
c – d – e – f – g – a – b – c[sup]1[/sup]

Harmonic Minor - TSTTSTT
c – d – e-flat – f – g – a-flat – b-flat – c[sup]1[/sup]

Melodic Minor - ascending! - TSTTTTS
c – d – e-flat – f – g – a – b – c[sup]1[/sup]

Melodic Minor - descending! - TTSTTST
c[sup]1[/sup] – b-flat – a-flat – g – f – e-flat – d – c

Other scales include:

Aeolian - ‘pure’ minor scale (can’t find my notes)

These were used by the ancient Greeks for different ‘humors’ of the body (inspiring the phlegmatic, etc) as well as different celebratory occasions

(Any doper, please feel free to add to/correct this - I know I am missing a couple of scales).

Not to further confuse the issue, there is also the Gypsy scale: a seven-tone scale that has three semitones between the 3rd and 4th degrees of the scale.
c – d – e-flat – f-sharp – g – a-flat – b – c[sup]1[/sup]

Western European music also uses:

Whole tone (a whole step between each scale degree)

c – d – e – f-sharp – g-sharp – a-sharp – c[sup]1[/sup]
Also found in Western Europena music is the
Pentatonic (has five tones to the octave)
c – d – f – g – a – c[sup]1[/sup]

also found in MANY cultures - African, Chinese, Celtic, etc., as well as several Gregorian chants. Anyone can play a pentatonic scale: use only the black keys on the keyboard.

Please note also that scales can start on any note. ‘C’ is used by default, since that is the way many of us were taught in school. It is the intervals that make the scale, not the names of the notes.

I’d end up taking up a lot of bandwidth discussing “just intonation” and “equal” temperments (ways of tuning an instrument so the intervals are constant between each note), and I haven’t even touched:

Javanese (which has 18 types of tunings and based on 3, 4, 5, 6, or 7 tones scales, depending on the century of development),

Indian (continental) music (I cannot for the life of me find the notebook, and but the professor went into the Vedic system, the classical period and the development of the ragas, the Medieval period and the fusion of Islamic and Hindu elements, and the modern period (all of which have their own scales!), and

Jewish (based on a four note tetrachord, IIRC and depending on which book is being chanted) [this notebook is irretrievably gone, and I really could use it right now]

all of which have their own scales.

Not to mention the fact that most people are talking about keyboard music (and to an effect valved and keyed instruments) - the human voice, stringed instruments and the trombone are capable of quarter tones and tinier intervals. To our modern ear, these sound “wrong”, but there are 20th Century pieces written necessitating these intervals.

Oh geez, and Schoenberg, Berg and Webern - 20th Century composers known for serial music (atonal - complete suspension of traditional harmonic function) and the dodecaphonic or twelve-tone systemn (using all twelve tones of the chromatic scale in any order chosen by the composer, but no tone may be repeated [either melodically or chordally] until the other eleven have appeared).

E-mail me, and I can see if I can scan in my notes - far too many to type here (if I can get the scanner to work).

Excuse me from this board for awhile. I have developed a tic and a flashback to to Freshman Theory I, Advanced Theory V and survey of Ethnic Music. I’m gonna play in MPSIMS for a bit to calm down. If I find more info, I’ll stop back.