Etymology of word “Octave”

How come the etymology of the word octave is related to the number eight, when the numbers that you would associate with the meaning of the word are either two – doubling of the frequency – , or alternatively five, seven, or twelve, if we think about the number of notes within commonly used scales, starting from any note and stopping one octave higher?

Etymology dictionaries don't help as they simply point out the Latin root of the word - Related to the number eight – and also the Wikipedia article doesn't seem to mention anything about this.

My question is thus about why the number eight is anything special in dividing up one cycle of unique pitches , since it ("8") is only relevant for the diatonic scale , which is itself salient only in western cultures, and even there with strong competition from other scale types such as the chromatic or pentatonic. Why, then, is the interval that doubles the pitch not called a pent for instance?

• The frequencies have very little to do with it. – Neil Meyer Oct 23 '18 at 17:52
• "as they simply point out the Latin root" you mean "ocatvus" meaning the 8th as in it is the 8th note? – eques Oct 23 '18 at 19:22
• Choose a scale, start on it's root, or 1st, note. Move one step up the scale 7 times. Those are the second, third, fourth, fifth, sixth and seventh notes. The next one is called the eighth, or octave. – AJFaraday Oct 24 '18 at 8:39
• @EricLippert you're counting intervals rather than pitches. There are twelve semitone intervals in an octave. But if you play a chromatic octave scale, you'll play thirteen pitches. Similarly, there are seven (variously sized) diatonic steps in an octave, but if you play a diatonic octave scale, you'll play 8 pitches. – phoog Oct 24 '18 at 20:48
• @phoog: Indeed. My comment was intended to address mathreadler's statement above that there are eight whole tones in an octave, which plainly there are not. – Eric Lippert Oct 24 '18 at 21:21

It's because in music, when you're talking about intervals, you count the first note, all notes in between, as well as the final note. For example, if you play two notes that are right next to each other, the interval is a second - even though the second note is just "one note" away from the first. In fact, if you play the same note at the same time, it's called a prime, even though there's no distance between those two notes. A third is only two whole notes apart, a fourth only three, and so on. And the same way, an octave is only seven whole notes apart.

• +1, this point was somehow missed in the other answers. The only thing that's new with the octave is that the English interval names suddenly drop from counting in English to counting in Latin: "... fifth, sixth, seventh, octave, ninth ..." But some other European language uses Latin names throughout for these intervals, eg. German: "... Quite, Sexte, Septime, Octave, None ..." – Henning Makholm Oct 23 '18 at 23:57
• Just a guess, but doesn’t “octava” predate the introduction of zero as a concept? – Jim Garrison Oct 24 '18 at 16:25
• @HenningMakholm some of the German names are wrong, it is "Quinte" and "Oktave". – rexkogitans Oct 24 '18 at 17:47
• This is the answer. It should be noted that this method of counting appears in other contexts as well, such as the French expression quinze jours for "two weeks," and indeed the use of octave in the Christian calendar. See also en.wikipedia.org/wiki/Counting#Inclusive_counting. – phoog Oct 24 '18 at 20:13
• @EricLippert correct. An octave has seven diatonic scale degrees, however; some of those are semitones. – phoog Oct 24 '18 at 20:42

The term "octave" originated in the west, so it should be no surprise that it's based on features of western music. And the diatonic scale really is central in western music, as evidenced by the fact that a piano has eight white keys in an octave, and the notes are named by seven different letters, modified by sharps and flats (with the eighth note in the octave repeating the letter of the first). Other answers have made similar points with more sophistication, but I thought it would be good to have those two points up at the front of an answer.

• Exactly this. OP seems surprised that the word would be based on Western musical conventions, but it's a Western word so why not! – Lightness Races in Orbit Oct 24 '18 at 11:08
• "The notes are named by eight letters", erm, A,B,C,D,E,F,G - I count 7 – Rodney Oct 25 '18 at 14:04
• @Rodney, well, Germans have H, but it's only to complicate the matter :) – Zeus Oct 26 '18 at 5:16

The octave would be the eighth note. There are seven scale degrees and if you take an additional step, you will land on the octave.

An octave is the space, pitch wise, which can be divided into eight. With seven intervals between. Take the octave C-C. C D E F G A B C eight notes later we're back on C.

You certainly wouldn't say 'octave of C is B', surely? The first C is not no. 0, like the start of a ruler, or a stopwatch. It's 1.

• Of course - but that still assumes that the diatonic scale, with its 7 - 8 if you count the same note reached again - is the only way to divide the doubling-of-frequency space, or at least the most salient, whereas I would suspect it wasn't at the time when the meaning of the word came into use, not even in the Western world! – z8080 Oct 23 '18 at 17:57
• It's my understanding that at the time of developing the scales, which were derived from simple ratios, there were 7 notes per octave, so the eighth was named based on the word for 8. There are plenty of ways to divide the octave but at the time the term was invented, there was really only the one approach. – Basstickler Oct 23 '18 at 18:00
• Well in that case this would be a very obvious explanation as to the link between the number 8 and the physical concept of octave. I didn't know this was the case – many thanks for your contribution – z8080 Oct 23 '18 at 18:58
• "An octave is the space, pitch wise, which can be divided into eight". I don't understand this explanation. As you said, there are seven intervals inbetween. – Eric Duminil Oct 24 '18 at 9:29
• In fact this answer is worded badly. The octave is divided into seven diatonic interval, that stand between eight diatonic notes. – Simone Oct 24 '18 at 15:28

Your argument is, then, why is is not a "hexave" instead of an octave in the case of, say, a pentatonic scale and not a diatonic scale?

That is because in the standard western system, a pentatonic scale is represented with note names that correspond with the idea of the diatonic scale. It is more correct to say that, calling it an octave and using diatonic names is an approximation applied unto other scale types, for the sake of keeping talk about music the same.

It would otherwise be chaotic if, say, you have a pentatonic scale written C-D-E-A-B-C and a diatonic scale C-D-E-F-G-A-B-C, and the only notes on which people can agree on the sound on are then C, because they are at similar frequency intervals, but none of the degrees are agreeable.

It makes more sense to keep to a standard, if you will, so that music discussion is always on the same page. Given that the western standard of music revolves around the diatonic, when talking about music from a western perspective, it would make more sense to describe the pentatonic in terms of the diatonic, that is, assuming the Major Pentatonic scale, what would have been C-D-E-A-B-C in its own pentatonic format would be represented as C-D-E-G-A-C in the western standard, aligning the pitches of the diatonic and the pentatonic. Therefore, the "hexave" is the same as the octave, so for simplicity's sake, we refer to it as just the octave instead.

A lot of the musical terminology is in Italian. Partly because of the modes that come from Gregorian music (~9th century from the Roman Catholic church), the precursors to the modern day scales, and Renaissance (starting around 14th century) where Italy was prominent. A lot of musical dynamics are in Italian (Allegro, Piano, Tremolo, Calando ...), pitch registers (Soprano, Alto, Basso, ...) and music classifications (Concerto, A Cappella, Aria, Opera, Serenata, Sonata ...)

In this case it is just the index of the notes of the conventional scale, 1st, 2nd, 3rd ... 8th, in Italian.

Primo (C)

Secondo (D)

Terzo (E)

Quarto (F)

Quinto (G)

Sesto (A)

Settimo (B)

Ottavo (C) <--- Octave

Since scales came from Gregorian Modes much earlier than Renaissance, it is probably the case that the monks at that time used Latin for formalising music structures (especially since the chants themselves are in Latin). So the modes themselves were probably in Latin, while more recent scales in Italian (not sure about the historical accuracy here). But in either case the etimology is the same. (Octavus instead of Ottavo).

• This is a nice answer, but can you expand on it a little bit? What language is this for example? – Shevliaskovic Oct 25 '18 at 8:31
• @Shevliaskovic Added some more detail. I had wrote it partly with tongue in cheek because I thought it was too obvious (since other classical music terms are all in Italian) but it was a wrong assumption. – jbx Oct 25 '18 at 12:33

There are two ways of counting a range of things: inclusive counting, and exclusive counting. "Exclusive counting" is where the first element of the range isn't included: "Monday + 3 days = Thursday". "Inclusive counting" is where the first element is included: "Monday + 3 days = Wednesday".

The English language uses exclusive counting for almost everything, where the Romance languages use inclusive counting. English music terminology comes from the Romance languages (mostly via French), and thus the range terminology reflects inclusive counting: "C + 8 notes = C", hence "octave".

• Actually, it's not a question of inclusive/exclusive counting at all. It's that the first is the first rather than the zeroth. C + 7 notes takes us from the 1st to the 8th. The name comes from the 8th, not from the number of steps between 1 and 8. – Monty Harder Oct 25 '18 at 19:20

If you know some computer programming languages, note that in some of them the arrays begin with the index 0 and in others with 1. I'd say the way we count intervals is one-based, that's all :P If you count in one direction until you find the same note, you get the number 8.

• You might want to read the other comments on here. My question was precisely why the number eight is anything special in dividing up one cycle of unique pitches , since it ("8") is only relevant for the diatonic scale , which isitself salient only in western cultures, and even there with strong competition from other scale types such as pentatonic. Why then is the interval that doubles the pitch not called a pent? – z8080 Oct 23 '18 at 20:58
• Oh, ok! It's a music history question then, if I understood it correctly. "Why diatonic scales became so important throughout history?" Because you could make the same question with all intervals: Why the interval of 5th is equal to such distance, why the word "3rd" is allowed to such and such distances, etc. – Allan Felipe Oct 24 '18 at 0:38

I don't have a source for this, but it seems self-evident to me that the context in which this term was developed was not an environment in which "pent" was a contending alternative - nor "sept", twelve, or any other number of scale degrees.

You seem to want to deny the saliency of the Western system, and the relevancy of the diatonic scale. You do make the valid point that today chromatic and pentatonic scales could arguably be "strong competitors" against the diatonic, but for one thing that wasn't true in the time and place when the expression "octave" came about, and for another the competition developed within the Western system in a context in which the term "octave" had already long since been defined. With the possible exception of very early Greek musical analysis, I (again unsourced) just cannot imagine a time when anyone talking about a chromatic scale or a pentatonic scale would have seriously considered trying to ignore the traditional diatonic modes in describing those scales.

The answer to your question seems to be, the reason we use the term "octave" even when "it's not all about the notes of the diatonic" is, at the time the term was developed, it was - and it has not stopped being useful within more-recent developments which use scales of some number of degrees different from the diatonic. People know what it means, people know why it means what it means, it would be asking more of them to throw it away and make up a different term than it is to just ask them to keep talking about "octaves" in the context of non-diatonic scales.

I've no idea if this is just an accident, but there is a very real physical connection between octave and eight. It is via the natural harmonics of a pipe, which of course are what a brass player selectively excites (and slightly "bends" into tune, if possible given the physical constraints of his instrument and his skill). The harmonic series can be expressed, approximately,

C C' G' C'' E'' G'' Bb'' C''' D''' E''' F''' G''' A''' Bb''' B''' C'''' (and then sixteen further harmonics up to C''''' and onwards to infinity with double the number of further harmonics in each octave, largely theoretically)

The bottom octaves of the harmonic series are actually rather hard for a brass player to produce in a musical sense. They tend to sound like flatulence. So on an un-valved brass instrument one can play C'' E'' G'' Bb'' and then (perhaps) all notes of the scale in the next octave up. Above C''', C'''' is the 8th subsequent natural harmonic. Hence, octave?

NB the mathematical frequencies of all these harmonics except for Cs and Gs are somewhat out of tune compared to the even-tempered musical notes. This is where a brass player's skill comes in, to bend the notes into tune. Some need more bending than others. On an instrument with valves, there are of course multiple harmonic series to choose between, so fingering can replace the need to bend hard-to-bend notes.

You can research the history of early music, where the concept of keys and modulation was fighting with the natural harmonics which give perfect fifths and fourths.

• This is indeed pure speculation. The octave formally comes from the division of the scale, into 8 notes. Most modern musicians (and probably ancient) would consider C''' three octaves above C. The doubling of pitch appears more accidental. – theREALyumdub Oct 24 '18 at 20:57
• The D harmonic is pretty close to an equal-tempered D, being only about 4 cents sharp -- or rather the equal tempered 9th is about 4 cents flat, acoustically. – phoog Oct 24 '18 at 20:57
• @theREALLyumdub but the division of the scale into eight notes is strongly related to the harmonic series, and the term octave goes back to early music before the advent of even tempering. There are other musical traditions, f.ex Indian, which do not use Western 7- (not 8) or 12-chromatic note scales. – nigel222 Oct 25 '18 at 8:00
• I have to agree with @theREALyumdub. If the 7-note diatonic scale were truly derived from the harmonic series, the notes wouldn't be so badly out of tune with it. For example, if you apply Pythagorean tuning principles to the medieval hexachord system, b-flat:c comes out at 16:9 rather than 7:4. It looks to me more like the tuning of the scale was altered for acoustical reasons (therefore becoming a closer fit to the harmonic series) as harmony became more important in the middle ages. – phoog Oct 25 '18 at 19:45
• I think the only certain thing is that it goes back to the 12th century, and probably before. I was going to add that in German, B-flat is known as B, and B as H. But apparently on ancient manuscripts, flat and sharp were indicated by writing the note slanted backwards or forwards, and hence modern flat and sharp symbols. But a forward-slanted B in the script of the times looked like an H and it stuck. So says wiki. Another mere coincidence with the harmonic series? And then there's the modern melodic minor key which uses both seventh notes...? – nigel222 Oct 30 '18 at 9:11

protected by Dom♦Oct 25 '18 at 0:13

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