![]() Guido's system had eight pitch classes, the seven letters of the "white key" scale, A through G, plus B-flat. There's no theoretical reason not to call it an eighth it's just custom, perhaps influenced by the special status given to that interval by octave equivalence. Keep in mind that the day one week after some other day was also called the octave, which is simply Latin for "eighth," and, as has been noted elsewhere, the periods of a week and two weeks are to this day called eight and fifteen days in at least some modern Romance languages.Īs an aside, I note that the only difference between numbering the intervals of the second, third, fourth, fifth, sixth, and seventh, on one hand, and the octave on the other, is that we use our native (Germanic) ordinals for the first set of intervals and a word derived from the Latin ordinal for the last. In his treatise Micrologus, published around 1026, he mostly refers to the interval that we now call the octave as the diapason, but it's also clear from chapter V that the term "octave" had come to its musical meaning. I'm a little hazy on the state of music theory before Guido d'Arezzo, who worked in the early 11th century, but it's pretty clear that the letter names A through G were in use before he published his system of solmization with the six syllables ut, re, mi, fa, sol, and la. What system was in use in medieval Europe when the term octave arose, and what did the term octave refer to? As shown below, it was already in use by the 11th century to denote the musical interval (although the principal name for the interval at that time seems still to have been diapason). Was the term “octave” coined after the development of early music theory? If the term octave refers to the 8 notes in a major scale, then in is placed in retrospect, and after the development of enough music theory to define diatonic scales. However in this case we require a 12 semi-tone tuning system. As the modern major scale arises from the division of an octave into 12 intervals (12 notes + an octave), and selecting a sub-set of 8 out of it. This division will give me 7 pitches + an octave, but this will sound nothing like the major eight-note scale we know today. If I want to build an 8-note system, I can divide an octave into 7 intervals using a harmonic series. My question is about the chronology of a 12 semi-tone tuning system, the use of an 8-note scale (major scale), and the introduction of the word 'octave' to refer to those 8 notes (7 notes + root). To clarify: I am not asking why an octave is called an octave (meaning eight) if we have 7 notes. When did people start using the word octave, and what does it really refer to? It seems to me that the term "octave" refers to these 8 notes within the 12 note system, and was used in retrospect after some music theory was already in the making (during definition and use of the ionian major scale -I know modes weren't defined up until much much later-).Īll answers to questions related to the name "octave" just explain the history of modern tuning systems, but I haven't yet seen an explanation of why we use the word "octave" for a 12-tone system, which was never an 8-tone system. Later on, within the roman civilization and gregorian chants, this system was still applied and a notation system invented which contained 7 note names (today A to G), probably to refer to the common (ionian) major scale. This already produced a division of an octave into 12 pitches. The (western) tuning system comes from the Pythagorean division of the octave, based on consonant frequencies, found by simple ratios. They are meant for my personal review but I have open-source my repository of personal notes as a lot of people found it useful.I have some confusion as to the use and history of the word octave in the context of music and tuning systems. I would like to give full credits to the respective authors as these are my personal python notebooks taken from deep learning courses from Andrew Ng, Data School and Udemy :) This is a simple python notebook hosted generously through Github Pages that is on my main personal notes repository on. Elements of Theta Vector (Theta0, Theta1, Theta2).Vectorized implementation of gradient descent.Compress for loop to one line of vectorized code.Transposing theta would have a more simpler and efficient code.Determine concentration of numbers on a grid. ![]() Three commands using comma to chain commands.Divides plot a 1 x 2 grid, access second element.Divides plot a 1 x 2 grid, access first element.This ‘hold on’ allows you to print two graphs together.Put all elements of A into a single vector.This would replace second column (all rows).This gives everything from Row 1, 3 and all Columns.Get longest dimension (normally applied to vectors).1 x 3 Gaussian Distribution, mean = 0, SD = 1. ![]()
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