What is the rationale behind the tone tone semitone ton tone tone semitone format of the standard octave?

what is the rationale behind the tone tone semitone ton tone tone semitone format of the standard octave?

This is actually an interesting question that I'd like to get to the bottom of. The standard answer in part is that it's derived from harmonic overtone series and traditional tuning practices that lead a specific set of apparently pitch class equivalent notes being placed in the octave, but that doesn't explain:

a) Why it is specifically that the brain has adapted to hear the particular scales it does, including the minor and other alternate modes, as being coherent in the particular way it does and how this differs between individuals and cultures.
b) How this pattern will result in some people perceiving the first scale degree as a tonal center when appropriate musical material is played, which seemingly doesn't work with other patterns and scales.

I'm doing some work related to how perception of music relates to the perception of voice and how our listening habits and abilities are possibly impacted by this. I suspect that overtones relate to feelings of consonance because, if they didn't, then single bare tones would naturally feel dissonant, which forces a constraint on our hearing on order to allow it to make sense of sound.

I suppose what I'm getting at, is why isn't it a constant step between tones?

do you think it is learned? I know the Chinese have a different set of scales that seem offkey to Western ears, even if their music still sounds kind of nice

it's fairly specific. 2^(4/12) is about 1.25 and 2^(7/12) is about 1.5, which gives nice resonances in the usual fifth C-E-G. it's all about the frequencies and their resonances

there is a constant step between semitones, you can think of them as 12 evenly spaced notes, with the usual naming (C-D-E...) corresponding to the major scale, which is just traditionally used

Octaves were known a long time ago. The Greeks knew you could cut a string in half to get an octave higher. They knew subsequent cuts would give different notes in between. The problem was trying to find a way to divide the strings evenly to form the full scale. This wasn't easy, so concessions were made. What we end up with is the standard major scale.

>corresponding to the major scale, which is just traditionally used

That's the core of what he's asking about though. Why is it that, out of all the possible ways of selecting the notes, the major scale is the most vibrantly tonal, as opposed to any other. There doesn't seem to be any clear and obvious answer to this, as just looking at "the frequencies and their resonances" themselves doesn't lead to this specific selection without it coming about from a specific musical practice based around humans using tonality in specific ways. i.e. it is heavily dependent on the specific ways humans happen to perceive and want to structure music as opposed to some purely mathematical derivation of harmonics.

The selection is somewhat arbitrary, but at the same time you couldn't substitute a different scale and achieve all the same things musically. You can totally write music chromatically, but the major scale allows you to avoid certain effects of doing so by default. Why it 'ought' to work that way we have no idea.

I heard it's just because Mozart thought it sounded better. That's probably wrong though.

>Major is most vibrantly tonal
No, it's not. The most vibrantly tonal scales would involve microtonal pitches. As to why it's been arranged this way, it's because it has been noticed that there are 12 distinct repeating sounds across the very wide range of listenable frequences.

The Chinese figured this out many many years ago, as have others. They even noted that there are 12 notes as there are 12 zodiac signs, but that may not be significant.

there's basically only one real scale of twelve notes in Western music, the chromatic scale. Each note is called a 'half-step' for no particular good reason. Different cultures pick some of their favorite notes out and call these scales, too, but they're all just subsets of the chromatic scale.
for instance, some retard liked 8 particular notes and called this the major scale, and decided all the other equally good notes would be called sharps and flats. then his retarded followers made up an insane music notation based on this incredibly stupid idea, and we got stuck with idiotic, unnecessary, overcomplicated things like key signatures, sharps, and flats.
note that if music notation was based on the chromatic scale, like any sane person would have done it, notation would be much simpler, clearer, and easier. A staff of 6 lines could show all twelve notes in their own space with no need for any of that moronic garbage.

>The most vibrantly tonal scales would involve microtonal pitches.

You're really going to have to justify this. If you mean tones that aren't in even temperament, then I don't disagree, but if you're talking about scales with tones between the chromatic notes, then please name the specif ones you're talking about.

>it's because it has been noticed that there are 12 distinct repeating sounds across the very wide range of listenable frequences

You can start from the consonant tones of the pentatonic scale and 'revolve' them, resulting in twelve 'logical' tones if you place them in a given temperment through enharmonics, but there's still nothing preventing you from adding more discreet pitches to the scale within an octave in principal. We only figured this out through hearing, but there aren't a piori principles that lead to this just working out.

>for instance, some retard liked 8 particular notes and called this the major scale

The problem is that this isn't arbitray, the major scale is the only one, aside from the minor, that seems to result in the perception of a tonal center, which is what allows songs to be written "in a key". Why this specifically works, but other scales don't result in this, is really a mystery that isn't at all trivial.

At the very least I must ask you if you perceive music as actually being "in a key" in the first place?

this is pure bullshit. a key is based on a root note. pick any root note and you have the key. move away from the root note and you build tension. return to the root note and you resolve tension. That's all there is to a key. this doesn't require any horseshit about major or any other subscales of the chromatic scale.

>pick any root note and you have the key
How? Lets say I "choose a note", how do I then make a piece "in that key"? Do you just play the note and then play any other note after? If so, what causes the tonal center to be perceived as such?

What about modal music that can progress without resolving tension?

The over tone series. The sequence of the major scale can be found from the harmonics.

>>pick any root note and you have the key
>How? Lets say I "choose a note", how do I then make a piece "in that key"?
the same way you do it in any scale, i.e. exactly the way you do it with a major scale, with sequences and combinations of intervals in timings and ryhthms that sound good. this is so fundamental to music composition that i can't conceive why you even pose it. note that the major scale and all music based on it is contained within the chromatic scale.
Do you just play the note and then play any other note after? If so, what causes the tonal center to be perceived as such?
you can choose any note. the human brain has a way of making a particular note the 'fundamental' note of a piece. thus the key. you choose other notes and combinations of notes and timings in a way that sounds good. chopin in particular could make incredibly beautiful melodies from dissonant notes.
>What about modal music that can progress without resolving tension?
whatever is pleasing to the ear is good enough. it doesn't require strict adherence to arbitrary rules.

>with sequences and combinations of intervals in timings and ryhthms that sound good

>you can choose any note. the human brain has a way of making a particular note the 'fundamental' note of a piece


That's exactly my point, you do this "by ear" (or in your head), but there's no other way of determining this aside from the general guidelines traditionally offered by the scales. You're essentially acknowledging the mysteriousness of this.

>whatever is pleasing to the ear is good enough. it doesn't require strict adherence to arbitrary rules.

And I'm not saying it does. But in this case I'd argue that modal music, is actually not properly tonal, and in fact I'm defining tonality in this specific way, excluding music that doens't invoke candential tension. In this regard, tonality does seem to function with respect to the major and minor scales specifically, even if you can still use chromatic notes and modulations.

>That's exactly my point, you do this "by ear" (or in your head), but there's no other way of determining this aside from the general guidelines traditionally offered by the scales. You're essentially acknowledging the mysteriousness of this.
most people with any musical sense can intuitively base a key on a single note.
you play the note. it's 'home'. it's headquarters. it's center. it's zero. it's origin. it's orientation for all of the other notes. it's relief. it's base camp. it's the foundation of the musical house you're building. you create around it but always return to it. if you like, you can even change it midtune, if it produces a pleasing effect. but a single note is all that's necessary to define a key. anything else is just adding training wheels.

You can put as many notes in an octave as you want.
You can create a mode by choosing any sequence of numbers in that octave.
You can follow this scheme using any note in the octave to get your key.

There's tons of modes besides the major scale, which is what you're asking about. It sounds pleasing because it's popular in the western world. Other places use pentatonic scales like in asia, or chromatic scales like in india. They have scales with like 72 tones in an octave.

Theres nothing about the harmonics that's fundamentally better. It's just the result of social acceptance. Popular modes were different in the west a long time ago.

>most people with any musical sense can intuitively base a key on a single note.

Either this is bullshit or you're only describing modal 'tonality' where you just frequently play a given note at the start of what you perceive as the strongest beat and aren't specifically aiming to develop themes that possesses classical tonality with the intend of ultimately bringing them to candential resolution. In which case, you're not actually talking about the same specific thing I am and are using tonality in a completely different sense than I am, either because you've been taught differently or because you don't actually understand what I'm speaking of (as I suspect many people don't actually experience tonality at all).

In these terms, anything that doesn't feel wrong if it isn't closed with a cadence towards the specific tonic isn't 'tonal' in the sense of properly having a tonal center. That doesn't mean that other forms of music aren't valid, but I'm specifically talking about the kind of music Heinrich Schenker developed his methods of analysis for and considering that to be properly tonal, to the exclusion of most other music.

alas, if you can't intuitively base a key on a single note then you're the equivalent of tone-deaf regarding keys. key-deaf. there's no other way to explain an inability to understand this. you just don't get it.

From my perspective it's clearly you who don't get it. You can't "intuitively base a key on a single note" on an arbitrary degree of an arbitrary scale. It's naturally possible with the full chromatic scale, but you won't be able to pick a major scale with C as the root and just decide to make B the tonic within that.

Might it be that what you are speaking of is due to the habit of hearing music in tonalities because of the (Western) culture you are a part of?

This is actually what I'm arguing in favor of. I didn't always hear music 'tonally', but only did so after many years of listening. It is intimately tied up with the experience of musical themes progressing towards a goal. Prior to a certain point I had no experience of what I now know is 'tonality' proper, so I'm fairly certain that this is actually a learned ability, but one that once learned is highly dependent on the specific way scales are used which doesn't seem to be arbitrary.

I suspect that if you don't hear music according to classical tonality, then you won't perceive an actual tonal center (which is something you will clearly be aware of if you do experience it), and that many people mistake he ability to push a melody into an arbitrary 'home' as what tonality really is because they have not had the specific experience of "perceiving the tonal center as an unconditional absolute goal", which involves very deliberate use of temporary modulation and cadence in order to maintain and complete it.

Wrong.
Everyone can tell instantly if a song is happy or sad. That's tonality.
Certain progressions have been done to death in pop music. An average person might not be aware of it, but they at least subconsciously expect songs to resolve at their tonal center.

>Everyone can tell instantly if a song is happy or sad. That's tonality.

No, that really isn't. This can certainly be affected by the choice of the major or minor scale, but you can't strictly classify music into just major or minor tonality, nor is it impossible to write 'happy' music with minor scales.

>An average person might not be aware of it, but they at least subconsciously expect songs to resolve at their tonal center.

No, this is absolutely 'learned'. Not in the sense that simply hearing things that progress in a certain way a lot leads you to expect that again, but that the expectation of resolution to a tonal center is something that must initially develop within a given person's mind. If it is there, you will know.

If you have tonal expectations, you will absolutely be conscious of it, it's isn't a vague subconscious thing. You will know you have it because possessing it will center the whole piece of music (if the music is fully tonal) within a tension that absolutely must be resolved, and you will be irritated if this resolution doesn't happen in the same way that you would be irritated by a movie cutting off just before you see what happens in the end. That is what I mean when I talk about proper tonality, which is unfortunately confused with the construction of melodies/harmonies using the scales that tonality happens to be based on.