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A more practical formulation of the question is "Why do we count by tones, instead of semitones?", but its meaning could be misinterpreted; the target of the question is actually on the concept of "1 tone" as a unit: "Why wasn't the smaller "interval leap", the actual semitone, taken as the unit and therefore called "tone" (or "one tone")?

We say there're 6 tones in an octave and then that the distance of the notes of major scale (for example) jump 1-1-1/2-1-1-1-1/2 tones.

Why wasn't what is known as "half tone" called a tone since the beginning, as a tone is not any unit whatsoever? Using the actual semitone as a unit, i.e. as a tone, we would have and octave with 12 tones and then simply show that the the "leaps" go 2-2-1-2-2-2-1 tones.

Is there a practical rationale for things not being this way and being the way they are? Are they this way merely for arbitrary or historical reasons?

  • How about the pentatonic scale? – Carl Witthoft Oct 3 '17 at 12:47
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I believe it has to do with how humans have played music over the years. Just as audible language was invented before written language, so too was music. Theory evolved in order to write down what people were already playing. Your question is similar to asking "why don't we use the half inch as a base standard instead of the inch?". (Someone invented the metric system for just such a thing.)

One of the earliest scales is of course the major pentatonic scale. Starting on C, this goes C, D, E, G, A, C or 0, 1, 1, 1.5, 1, 1.5. No semitones to be found next to each other. People back then knew about semitones but they felt the pentatonic sounded better, was easier to play/sing, etc. In common usage of the time, scale degrees a semitone apart were rarer. Once the Major scale started to become the standard it still only contains two semitone intervals among 5 whole tones, making it the minority. The 4 and 7 are also often used to lead back to the tonic because of this dissonance.

Then, concerning the interval of a semitone (or minor second) itself, it is considered dissonant. The ratio between pitches is more complex than in a major second. It wants to resolve to something more stable.

Nowadays, music an a whole has evolved along with everyones ears, such that counting in semitones is very common. Dissonance is more accepted and semitones are in vogue. But musicians are slow to change when it comes to conventions like these.

In short, it's because whole tones were more commonly used than half tones. Splitting a tone in half occasionally is also easier than constantly having to double up, especially for larger intervals. Notation is also written to take this into account.

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    "I believe" is a statement of speculation and opinion, not fact. – jjmusicnotes Oct 6 '17 at 11:40
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    Well it is speculation, but she deserves a higher score as it is the only one answering my question. Not only that, but it does make a lot of sense! If no semitones were involved in scale steps, then it makes sense to call "one tone" to the not only most common but the minimal distance between two notes of a scale... And there was barely no need to talk about semitones except for 1.5 tones... Thanks @Tama! – Martin Oct 6 '17 at 20:56
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Who says there are 6 tones to an octave? There are seven notes, and they are not evenly spaced. In equal temperament, considering them in units of semitones (which divide an octave into 12 equal intervals) makes some sense.

But equal temperament is a late comer to the game. And when you talk in terms of equal temperament, the unit for talking is semitones: a fourth is considered to be a distance of 5 semitones, not 2½ tones. A major second is two semitones, not "1 tone". At best, it is "a whole note apart".

Note intervals are named 1-based, semitone distances are counted 0-based.

This kind of distinction is done very rigidly, and yes, historical reasons play a large role. But once you leave the idea of equal temperament, semitones (or tones) as a unit stop making perfect sense.

And for better or worse, our precise notes may these days be equal-temperament, but the hearing of intervals in Western music isn't: you can walk in "thirds" through whole scales, and the resulting sound will be natural to our ears even though the result is having an irregular pattern of major and minor thirds (or 4 and 3 semitones of distance).

Playing such scales of thirds smoothly on an instrument organized by semitones (like a guitar or chromatic button accordion) rather than a note-based keyboard (like a piano) is actually taking a lot of practice.

So the "historical reasons" dividing an octave into non-equal notes rather than equal tones are actually still quite alive: dodecaphonic music has not taken the day.

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    Heh, how can two notes a major 2nd apart conclusively be called "a whole note apart"? Looks like a misspelling here, but an important one. – Dekkadeci Oct 3 '17 at 14:45
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    Thanks for trying to help user44521. Maybe the question is harder to answer or ask that I thought: "Who says there are 6 tones to an octave? " I studied solfege and harmony at the Conservatoire several years ago when I was a child, and the way we learnt, was that a major second was 1 tone, a major 3rd two tones, a fourth two tones and a half, a 5th 3 tones and a half, etc. It is more convenient to count half-tones/semitones, rather than tones, specially since applying it to guitar, although cognitively speaking, is quite understandable that many, or some, use tones as they are the "unit" . – Martin Oct 3 '17 at 23:36
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    I do count by semitones, since later on while studying modern harmony in the guitar. But anyway, if a tone is two semitones, and an octave is 12 semitones, then you can say it is 6 tones. No need to study logic for that. – Martin Oct 3 '17 at 23:38
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    But, that's not the question. I feared that misinterpretation and tried to warn about it. The question doesn't have anything to to with temperament (although yes, tones and semitones make sense in the equal temperament most played instruments use), or notes. Maybe my using of the word "interval" might have lead you to explain that "note intervals are named 1-based, semitone distances are counted 0-based." but I never referred to note or scale intervals, except for the distance in tones. I've been very reiterative about it. – Martin Oct 3 '17 at 23:38
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    The other things you say might have more or less sense, and I appreciate your contribution, but to clarify things I must say that they don't relate to my question (or at least it is not derived from your explanations). My question is just about the concept of choosing the name "1 tone" for that thing that results from dividing and octave into 6 intervals (yes, in equal temperament). And if someone is going to say that the octave is divided into 12 intervals, which doesn't matter for what is at stake, then the question is why choosing "1 tone" for 2 subdivisions? Why not 1 tone = 1 subdivision? – Martin Oct 3 '17 at 23:39
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As with most foundational questions in music, the answer is rarely "it's just an arbitrary convention." Usually, there is some sort of impetus for why these conventions arose historically, as is the case here.

The summary answer is that the whole tone emerged very early as a rather common interval in scales (generally tuned to a 9:8 ratio) and was standardized in size over 2000 years before a standard semitone size was settled on. From a practical standpoint historically, the semitone was treated as an afterthought in scale construction, effectively the "error" leftover after the other notes had been tuned.


More details:

The answers that discuss the pentatonic scale (which is found in many cultures) give perhaps a start at why semitones are not a necessary component of music, but they really don't explain why the whole tone became the standard measurement in Western music.

The simplest explanation is that the ancient Greeks realized superior consonances were to be found in ratios of small numbers. Specifically, they recognized consonances like the 2:1 octave, the 3:2 perfect fifth, and the 4:3 perfect fourth. (Note that at that time, they couldn't measure frequency, but these were the ratios of strings with the same size and tension but different lengths, which also create these intervals.)

The Pythagoreans in particular experimented with ways of combining these perfect consonances, and one of the most common arrangements was to divide an octave both with a perfect fifth and a perfect fourth. If you build a 4th and 5th up from the bottom note, as well as a 4th and 5th down from the top note, you end up with four notes in a 6:8:9:12 ratio.

All the intervals in that ratio are octaves, fifths, and fourths except for the one in the middle, which had a 9:8 ratio. As this interval was so easy to create from the other consonances, it became a standard fourth interval to use for tuning purposes. It was called a tonos, which comes from a root related to "stretching" or "tension," as the stretched string was the model for tuning scales.

The Greeks experimented with many other intervals, but the tonos became one standard measure, used to tune what we now call the diatonic (tuned "through the tones") scale.

Originally, what we now call "semitones" were not half of this tonos. The tonos was impossible to divide precisely in half, according to the Pythagoreans, who didn't believe irrational numbers were practical. Instead, a typical Pythagorean would start filling in tones of the scale by starting with the 6:8:9:12 framework I mentioned above, which could be thought of perhaps as spanning E to E on a modern scale.

The Greeks would tune downward, starting at the top to fill in the topmost perfect fourth (4:3). They would place two whole tones with 9:8 ratios (such as notes E-D-C), and then there would be the leftover bit (C-B). A 4:3 perfect fourth minus two 9:8 whole tones leaves an interval with a ratio of 256:243. That last interval is not a nice ratio, and the Greeks often treated this bit as almost a kind of "error" left over when all the other notes had been properly tuned.

At some point, some Greek musicians noticed that the 256:243 ratio (~90 cents, in modern interval measurement) was roughly half the size of the 9:8 whole tone (~204 cents). There were some vague murmurings in ancient Greece about a potential 12-fold division of the octave using these smaller intervals, but it never went very far. No practical tunings of this nature (to my knowledge) were ever recorded at that time.

Fast forward a thousand-plus years, and the Greek scale was borrowed as the foundation for medieval music. The 256:243 interval was still treated as a kind of dissonant "leftover bit" in the tuning of scales, but it acquired the name semitonium, denoting the fact that it was roughly the size of half of a 9:8 tonus.

As more tuning experimentation went on over the centuries, the semitone was almost always an afterthought. In addition to the perfect octave, fifth, and fourth from ancient Greece, eventually musicians started experimenting with 5:4 major thirds, 6:5 minor thirds, etc. For example, if you divide up a 4:3 fourth with a 5:4 major third, you end up with a 16:15 interval left over, which was 112 cents. Again, this was roughly half the size of the 9:8 whole tone, so it too was referred to as a semitone. But note the wide variance of these "semitones" -- even with the examples of 256:243 and 16:15 we already see a range of 90 to 112 cents. Actually, the term semitone was sometimes used to refer an even greater range of intervals, as again, this semitone was generally just the "leftover bit" (of whatever size was convenient) after all the other intervals had been tuned.

With that context, it becomes clear that the semitone could never be used as a standard unit of measure. It varied wildly over time and from tuning system to tuning system, whereas the 9:8 whole tone had been standardized for thousands of years. (I should note that with these tuning experiments, the "whole tone" also could refer to intervals of other sizes too, especially 10:9 or some other compromise. Yet, despite different size "tones" sometimes being used in scales, there was always THE tone, the 9:8 one the ancient Pythagoreans originally settled on when deploying the octave, fifths, and fourths together.)

It was only around the years 1700 to 1900 that Western scale tuning systems gradually moved toward equal temperament, where there are exactly 12 semitones in an octave (each exactly the same) and a semitone is always exactly equal to half of a whole tone. From the perspective of the past couple centuries, the semitone can seem like an obvious standard measure for the scale. But historically, it was very ill-defined and varying in size, the "leftover bit" after all the important notes of the scale had been tuned.

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Taking a look at any diatonic instrument (and for better or worse, Western music is built on diatonic scales), the most common scale step (a major second) is two semitones. A major third is a distance of two major seconds, and four semitones. There is no two-semitone third (twice-diminuished is not really cutting it). So there is some point in calling the most common scale step a "tone" rather than "two tones", even thought the underlying grid is that of semitones.

It's not that uncommon: angles are often viewed/analysed in terms of "quadrants", with a quadrant being a quarter of a full revolution/circle. "In the third quadrant" will ring a louder bell with mathematicians than "in the second half-plane". Indeed, the latter can even trigger the question "which quadrants do you define your half-planes to be on?".

Now while the most common step in a scale covers a distance of two seminotes, you never place 6 such steps in a row in diatonic scales: a subdivision of an octave into 6 equal intervals is highly unnatural while a subdivision into 12 equal intervals is the basis of current scale construction.

So the principal unit is semitone (which, as a word, means "half tone"). If that offends your sense of mathematics: the principal standard international unit of mass is defined as the kilogram, 1kg, namely 1000 grams. According to etymology, the basic unit should be the gram.

If something as dignified as an international unit standard can use a multiple as a base unit, why shouldn't musicians be allowed to use a "semitone" as their base unit? It turns out that "1 cent" is actually 100th of a semitone, so the semitone as an anchor of musical reckoning is pretty firmly established, its name notwithstanding.

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  • Talking about quadrants does make sense, but a circle is a very identifieable unit in itself. Again, I'm not talking about using the semitone as a unit per-se, but to the previous step of using "one tone" to the distance between C and D. Commonality is a criteria but not useful in itself, as it is proven but the fact that, as you said, most people now is counting by semitones. Being also the minimal distance, as Tama suggests clarifies things a lot. I've already answered to other things you say in the comments to the previous answer (I guess you are the same user). Thanks anyway though. – Martin Oct 6 '17 at 21:06

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