Music theory is not logical

Chords, scales, harmony, melody, etc.
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slipstick wrote: Coming to it fresh it doesn't seem very logical that the same note on piano or guitar or DAW piano roll might be called C or B# or Dbb. And an interval consisting of A plus that note might be called a minor third or an augmented second (but what is it called if it's A + Dbb ?) and so on. Same two keys/frets/squares, same sound, different names. The logic is not easy for people to spot.
I remember, when I was starting to study music, having seen a movie with a friend of mine (also a music student, and also a beginner), and at a scene, one movie character mentioned that the singer (in the movie) didn't sing the Cb in tune.

He commented that the authors didn't know music, because they mentioned Cb, which didn't exist. I laughed, but when I got home I went searching for that because I found it weird. And, much to my surprise, Cb existed.

It was a revelation. So, I agree with you. For beginners, things like B# or Cb don't make sense. You need to go deeper in music knowledge to understand that they do make sense, and why. But that's the problem with knowledge.

Common people understand time in our dimension, and "know" that the shorter distance between two points is a straight line. But in Cosmos, time has other dimensions, and the shorter distance between two points is NOT a straight line (I think I am not saying stupid things, but if someone knows this better, please correct me). Anyway, you need to go deeper into that knowledge to understand that.
Last edited by fmr on Sat Jun 30, 2018 2:17 pm, edited 2 times in total.
Fernando (FMR)

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slipstick wrote: Coming to it fresh it doesn't seem very logical that the same note on piano or guitar or DAW piano roll might be called C or B# or Dbb.
They are not the same notes!

They just happen to be close enough that 12-note equal tempered tuning cannot differentiate between them. The whole 12-note equal tempered scale is a huge pile of compromises and this is one of them.

edit:

ok.. a slightly more serious answer is that when you're playing on an instrument that isn't constrained to a fixed set of notes, you typically don't (well, really never do) follow equal tempered tuning exactly, but rather you tend to adjust notes slight more towards the "true" harmonic ratios to make consonances stronger.. and since all the above notes are part of different scales and form different chords you actually end up playing them slightly differently. In practice the exact pitch you go for usually then further depends on what other stuff is around the music context, but unless you're trying to play with a 12-TET instrument and match that, you're probably not going for 12-TET exactly.

This is always a little bit of a compromise thing as the "true" harmonic ratios don't really form a closed system the same way 12-TET does so you might have to adjust as you go from one chord to another, the differences are pretty small in the first place and them sometimes you're playing with an instrument like a piano that's stuck in 12-TET and you have to try to sound in tune with that, but the point is that this whole rigid 12-tone system only really applies to instruments with a fixed set of notes you can choose from and for the rest of them the universe of different pitches is a lot more fluid thing and the difference between C, B# and Dbb can be quite meaningful in terms of which direction you should compromise. :)

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mystran wrote:
slipstick wrote: Coming to it fresh it doesn't seem very logical that the same note on piano or guitar or DAW piano roll might be called C or B# or Dbb.
They are not the same notes!

They just happen to be close enough that 12-note equal tempered tuning cannot differentiate between them. The whole 12-note equal tempered scale is a huge pile of compromises and this is one of them.
In the pedagogy and then practice of the violin, and this is a verifiable fact, it is taught that there are more inflections available for tonal music. Let's say the tonic is C: the G# and Ab are not dealt with the same. One school of thought is that Ab down to G is closer to G than on the piano. G# to A, a leading tone to vi is closer to A than it is on the piano.

This is before we get into ensembles of [non-fretted] strings and wind instruments seeking more concord than 12-tone strictly speaking even provides.

Here's an example in virtual instrument software: the Vienna Instrument [Pro] provides scala implementation so that, eg., Just Intonation may be transposed to the tonic of a new key, a hybrid of transposable-to-12-places and the more acoustically 'correct' concords (EG: major 3rds in the 12th root of 2 derivation known as '12tET' are 13.69¢ sharper than 5:4), in a new 'matrix' in that interface. For this exact reason (albeit there are other more 'exotic' reasons, a frequent enough Feature Request from Turkish musicians for one instance).

So really the whole tack there is an aggressive argument from ignorance. It has been said here than I'm barking up the wrong tree even hoping to persuade someone like you, "slipstick" but this is the subforum known as Music Theory and I think the wider readership such as may happen on to this thread should be provided better information and that shit needs to be set right. 'There is no such note.' is demonstrably not a fact, you aren't doing "logic" in any way, shape or form there, and this "coming to it fresh" is a cutesy way of you trying to normalize being willfully ignorant, doubling down on an indefensible assertion that has no use for anyone except to keep them on your level. You have no idea what you're doing. You're just very low information and now you want to argue? Get lost.

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(this is obviously exceeding beginner 'Intro to Theory' by a bit, but I'd like to demonstrate my point technically)

Before anybody figured out 12th root of 2 for a system, *temperament* evolved to this end.

There is a little thing in our history called the Well-Tempered Clavier. It seems a kind of pun to me. But, JS Bach did not have 'equal temperament', which again is irrational, 12th root of 2 as the seemingly necessary math achieving that.

It was Well-Temperament, that's its name. Or "wohltemperiert". Werckmeister is believed to have come up with that one.

<The "Orgelprobe" 1681, and other Werckmeister publications were the source of inspiration for Prof. H. Kelletat, for the elaboration of the "Wholtemperiert" definition given below, and published in "Zur Musikalischen Temperatur", page 9 (ISBN 3-87537-156-9):

Wohltemperierung heißt mathematisch-akustische und praktisch-musikalischen Einrichtung von Tonmaterial innerhalb der zwölfstufigen Oktavskala zum einwandfreien Gebrauch in allen Tonarten auf der Grundlage des natürlich-harmonischen Systems mit Bestreben möglichster Reinerhaltung der diatonische Intervalle. Sie tritt auf als proportionsgebundene, sparsam temperierende Lockerung und Dehnung des mitteltönigen Systems, als ungleichschwebende Semitonik und als gleichschwebende Temperatur.

Well temperament means a mathematical-acoustic and musical-practical organisation of the tone system within the twelve steps of an octave, with the goal of impeccable performance in all tonalities, based on the natural-harmonic tone system [i.e., extended just intonation], while striving to keep the diatonic intervals as pure as possible. This temperament acts, while tied to given pitch ratios, as a thriftily tempered smoothing and extension of the meantone, as unequally beating half tones and as equally beating [i.e., equal] temperament.>

origins of well-temperament

Meantone Temperament
The reasoning for quarter-comma meantone can be boiled down to these premises:
Four ascending fifths (as C–G–D–A–E) tempered by 1/4 comma produce a perfect major third (C–E), one syntonic comma narrower than the Pythagorean third that would result from four perfect fifths.
IE: 5:4 is smaller than 81:64 via the application of the syntonic comma, 81:80.

The more prevalent Just Intonation produces two sizes of 'tone' (ie., whole tone): a major and a minor tone. 9:8 and 10:9 in its doings. The difference here is again the syntonic comma.
Another look at this: before long we run into the 'wolf' interval, eg., 40:27, inverted 27:20. EG: in the C major diatonic scale, an impure perfect fifth arises between D and A, and its inversion arises between A and D.

So, for one application of this concept, Danielou's conception of '22 Śrutis' in Indian Classical Music, 3:2 concord is provided for 10 of the remaining 11 tones (besides 1:1/2:1) via the syntonic comma. (This is non-transposable music, ie., this is all for a single 'tonic' and this stems from the desire for that interval in purely melodic terms; hence there is but one 3:2 from the 1:1.). Here is my chart in the Wiki <Just Intonation> article showing the results, from Danielou:
JI: Indian

So here is a 22-to-the-octave system just for melodic purposes. The name of the note is not as important there, but if we were to name notes out of meantone applied to transposable, it appears there will be easily more than 12. 12 is a compromise. A sort of kludge in terms of concords, in order to make keys equal. But with flexible instruments in terms of intonation, other things are done. Also NB: singers in choirs.

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mystran wrote:
slipstick wrote: Coming to it fresh it doesn't seem very logical that the same note on piano or guitar or DAW piano roll might be called C or B# or Dbb.
They are not the same notes!

They just happen to be close enough that 12-note equal tempered tuning cannot differentiate between them. The whole 12-note equal tempered scale is a huge pile of compromises and this is one of them.
Except they are the same note on a piano and many other instruments. Equal temperament has been in use for a long time. And yes, I do know that it's a compromise and I do know and even occasionally use other tunings. But equal temperament is what people coming new to music will generally start with. And it's definitely where the OP of this thread was starting from.

I'm not trying to claim that the last several thousand years of Western music theory from Pythagorean tuning on don't exist. I simply say that people find some of it difficult to understand (or even to believe when it's explained to them). Over the years I've tried to help quite a few people get their heads round conventional music theory so I know this for a fact. That some people refuse to recognise this reality is where the "wilful ignorance" and "shit" comes in.

Steve

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I've answered all your questions in the first reply. The reason you don't count the first note is counting the interval between C and C as a semitone makes absolutely no sense. How can 2 notes that are the same also be different? Doesn't that raise a red flag for you that you are trying to do that?

As posted above, it's a lot more logical than you think. If you are this confused by the very basics, dump your teacher/online course. It's obviously rubbish. Also, read the information already posted. The fact that you are asking questions that have already been answered in this thread suggests you are not reading the posts, you are just looking at the words. That's not how you understand new concepts.

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Fernando (FMR)

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I didn't read any of this before. I think this could produce confusion:
fmr wrote:
lobanov wrote:
fmr wrote:
lobanov wrote: We have intervals. We can define them in 1) semitones or 2) semitones AND whole tones. We get minor second (C - C#), major second (C - D), minor third (C - D#), major third (C - E) etc. E.g., minor third = three semitones = whole tone + semitone.
One semitone is a distance between two notes, as I've said. (C - C#) - (C# - D) - (D - D#) - we have three semitones.
WRONG again. There aren't C-C# or D-D# in a tonality. You either have C or C# and D or D#. You can't have BOTH. Intervals sare defined inside the tonality. Actually, if you want to be completely correct, you'd have to differentiate between diatonic semitones (E and F, for example, or D and Eb) and chromatic semitones (C and C#, for example, or D and D#). Apparently, they are all the same, but in what concerns tonal system theory, they are not.
It's not about a tonality. It's about a chromatic scale. Change the order of the first two part of my post and you'll see what I mean. They're interchangeable.
Are intervals in a chromatic scale impossible? Why? If they're possible (they are) how we could name them?

But you're right, it's important to distinguish between a tonality and a chromatic scale. May be I've not distinguished them explicitly. And in modern European music (not historically) there is nothing wrong in regarding tonal scales as constructed from a chromatic scale. I see no reason why it could be wrong.
In Music Theory, intervals and their classification is about the Tonal System, of which the chromatic scale isn't part of. All intervals, chords, etc. are born out of the Tonal System.[...]
And how would you define them, anyway? Why would you consider a C# instead of a Db, for example? And a G# insteads of Ab?
First lobanov produces intervals in the abstract; then it's objected to strongly as wrong, because tonality rules ok.

I'll then just give, eg., C and C# both within tonality. You're in C major and you modulate to D minor. Dominant of ii is A C# E. C and C# happily coexist; this is not outside of "tonality" at all. Additionally it changes nothing about C to C# being a semitone. Here's the thing, though, C to Db in 'C major' is also chromatic usage.

Yes, you could well say diatonic versus chromatic semitone. The history of Music Theory ("all about tonality") could well get rid of modulation if you want it to, though. So I don't see the use of saying 'classification of intervals' except making a (contextual) distinction such as E to F is a diatonic _usage of_ a semitone while C to C# is a chromatic usage.

A diminished seventh chord, historically is rather old. In minor, it exists as soon as you create a dominant V or a 'harmonic' version of minor. In C minor: B D F Ab. So if you construct a diminished scale now, from the same idea of symmetry found there: B C D Eb F G Ab A# or Bb you have two Bs, or two As, ie., an 8-note scale. We're not being atonal just through that. If you objectively consider the useful notes within the definition of minor (in the 18th century) for "C minor" we get C D Eb F G Ab A Bb B, nine notes. This is not even chromaticism. Contextually, yes, running the last five here is called a chromatic passage regardless. But what I'm saying is that regarding, eg., Ab and A as impossible to coexist within tonality is erroneous.

So while this is not illogical, there exists two meanings of chromatic: chromatic semitone vs chromaticism. And the chromatic scale in tonal music happens. Seems confusing, needs sorting.

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jancivil wrote: Thu Nov 01, 2018 4:49 pm there exists two meanings of chromatic: chromatic semitone vs chromaticism. And the chromatic scale in tonal music happens. Seems confusing, needs sorting.
And thanks for that. Yes, alterings by chromatic movements as such is compatible with tonality as part of modulations like above or tonal twistings to a mode or just melodic coloration generally but atonal usage of the chromatic scale falls out by default.

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"Tonality" also includes the chromaticism in harmony. I was looking for examples just for general reception and of course I landed on Schoenberg's Verklärte Nacht, for string sextet.

There was an illogical music theory objection to it: a group refused to perform it because a 4th inversion chord happens; which doesn't exist therefore a performance of it can't exist.
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Nice normal i6/4, V7 in D and but wait!

He's sliding into like ii of A but the 7th in the bass clef for the iiø7 comes sliding in parallel by contrary motion, creating this thing. Ab9 in 4th inversion.
As far as I can figure, this breaks figured bass. Broke my brain anyway.

But at a certain point, and this is a known example, the thought here begins to break tonality, and we tend to think of Arnold S as an 'atonal' composer. IE: there are so many 'deceptive cadences' leading to new keys which are a bit distant.

But here we find a number of things which show linear thinking rather than chord names, moves made in order to create effect (mystical). It's a striking, bold work and for me a fascinating look at the transition a composer was kind of inflicting on the world through that boldness.

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jancivil wrote: Sat Nov 03, 2018 7:24 pm
But at a certain point, and this is a known example, the thought here begins to break tonality, and we tend to think of Arnold S as an 'atonal' composer. IE: there are so many 'deceptive cadences' leading to new keys which are a bit distant.
Guess that is something to sort out too. To me atonal music would be any music without a tonic, key and root note as a resting point but that does not necessarily mean that the music would appear “dissonant” in all phases, but rather “restless” or constantly “unresolved” in terms of tonality, which is how I percieve Shoenberg. However, it is definitely not my ballpark and I do not know how many degrees between harmony and complete atonality there are or even how I would identity something completely atonal.

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Well, 'deceptive cadence' speaks basically of a dominant to tonic relationship, and all analyses of the composition, formal and harmonic talk of the keys. 'Keys' is tonal. F# major to Eb minor (supposed to be 'the lightest' to 'the darkest' area pertaining to the poem) is quite a move, but it's easily enough identified as such. And the harmonies are all tertial. Compare R. Strauss Salome, which also is a tonal work.

I used to have the Lewin analysis ... wait, I found it as donationware.

Figure 5b shows our eleven-nine-minor-six chord tonicizing the pivot b flat. A Iocal function for the tonicization is thus manifest: it is always appropriate to tonicize a pivot for its modulation, and it is especially appropriate to do so when the pivot itself is a deceptive substitute for the tonic of the opening key.


He's really trying to make sense of the harmony in ways I wouldn't even imagine. He's arguing that formally this chord foreshadows key relationships (In doing he's setting aside the Ab of this so-called Ab9 in favor of this odd 11 m6th chord.).
There is a lot of disagreement in academia as to what de fuq gwyne on heah...
But this paper is kind of mind-expanding. This is why I loved "Chromatic Harmony" and put up with it for a second go-round.

But again, that's so totally talking about tonal function.


Compare 'the harmonies are all tertial' to what is later known as the atonal triad (aka 'the Rite chord'): quartal, aug 4 plus a P 4. Ab D G.
I bring this in to indicate - on topic - that in so-called 'atonal' music, the spellings tend to be meaningful as well.

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