Which D minor? "D minor" is not as simple as the name may suggest. There are three types. Minor scale is a fabrication made later than a period where <the minor mode> has another name. Theorists made that up as they went, there were numerous opinions as to what to do. Is Dorian as sad as Aeolian? Are either or both those sadder than harmonic minor? Why was harmonic minor's augmented second avoided strenuously (until it wasn't)?
So back to the original context, intervals in music are about affect, and a lot of that is conditioned. "The augmented second shall be avoided" is a matter of taste, and that taste was more or less enforced on the church musician of the time, in the localities where that church prevailed. In other cultures it was the shizzle!
interval quality question
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- KVRist
- 275 posts since 26 Mar, 2017
Thanks for your replies jancivil!
I will respond to them in this single post. Apologies for some obvious things in parentheses, I'm trying to keep it understandable also to readers not familiar with the subject.
* * *
You are correct in that my cognitive abilities are better suited to decoding visual correlations - moreso than symbolic associations, anyway.
Thus, some of differences in our approaches and opinions are probably related to us having different brains. Perhaps you're simply better at associating heard experiences with symbolic representations.
Not sure how large segment of population has wetware like mine.
But I believe I'm not the only one who experiments with novel approaches to music theories
* * *
Regarding scientific basis of what I've posted:
The grid illustration is indeed a curiosity, a fun numbers-play more than a practical measurement. I believe I stated as much when posting it: viewtopic.php?p=8260511#p8260511
It is an easy target to deconstruct - personally, I would have started with questioning why are the grids scaled to same width
Spectrum analysis, however, is as much of hard science in music as it is in other fields. Spectrum analyzer with logarithmic visual representation of frequencies is, as far as I understand, grounded in physics and acoustics.
It also corresponds to human perception of pitch, which is logarithmic-like.
For example [in 12-TET, Middle C=C3 and A=440Hz]:
- C3 to E3 is the difference of 261.63 Hz to 329.63 Hz (68 Hz)
- C5 to E5 is 1046.50 Hz to 1318.51 Hz (272.01 Hz).
In terms of pitch, both steps will very likely be perceived to be of same distance by most humans.
So I dare to say that high-resolution log scale spectrum analysis corresponds to human hearing well enough to be practical - albeit, taking into account the compromise between time and frequency resolution of Fast Fourier Transform, on which spectrum analyzers are usually based.
It also corresponds to the equally spaced 12-pitch piano roll in 12-TET. That is easy to test perceptually by playing for example the C Major scale (CDEFGAB) and C chromatic scale (all 12 pitches from C to next C), and considering in which case one perceives the pitch steps to be of equal distance.
I believe that for most of us, the chromatic scale sounds like each step has the same pitch distance to the previous one. Whereas the C Major will sound like it has larger pitch jumps in some places - such as C to D - and smaller in others, such as E to F.
Spectrum analysis of sine waves playing C major and C chromatic scales will look like this:
So it is not so much a case of "image instead of the thing" - more like "image which corresponds to the thing". Obviously, seeing is not the same as hearing - but neither it is in case of the staff, which corresponds even less to what's heard, due to lack of visual proportionality. I'll get to that in later paragraphs.
For anyone interested, attached is the REAPER project used there: The analyzer JS plugin used in the project is linked here: https://forum.cockos.com/showthread.php?t=258602
***
Now, to the matter of proportional vs. non-proportional visual representation of pitches in notation. That is: arguable illogic of the "7 naturals + alterations" staff, as requested
Intervals of C Major scale are marked on the staff as having visually equal distances, despite the fact that we hear some of those distances as not equal. In comparison, piano roll shows the steps much like a log scale spectrum analyzer, corresponding more closely to how they are actually heard.
Here's an illustration, again with spectrum for comparison:
I hope it helps to clear up what I mean by potential source of confusion and Spock-like exclamations of illogic
I will respond to them in this single post. Apologies for some obvious things in parentheses, I'm trying to keep it understandable also to readers not familiar with the subject.
* * *
You are correct in that my cognitive abilities are better suited to decoding visual correlations - moreso than symbolic associations, anyway.
Thus, some of differences in our approaches and opinions are probably related to us having different brains. Perhaps you're simply better at associating heard experiences with symbolic representations.
Not sure how large segment of population has wetware like mine.
But I believe I'm not the only one who experiments with novel approaches to music theories
* * *
Regarding scientific basis of what I've posted:
The grid illustration is indeed a curiosity, a fun numbers-play more than a practical measurement. I believe I stated as much when posting it: viewtopic.php?p=8260511#p8260511
It is an easy target to deconstruct - personally, I would have started with questioning why are the grids scaled to same width
Spectrum analysis, however, is as much of hard science in music as it is in other fields. Spectrum analyzer with logarithmic visual representation of frequencies is, as far as I understand, grounded in physics and acoustics.
It also corresponds to human perception of pitch, which is logarithmic-like.
For example [in 12-TET, Middle C=C3 and A=440Hz]:
- C3 to E3 is the difference of 261.63 Hz to 329.63 Hz (68 Hz)
- C5 to E5 is 1046.50 Hz to 1318.51 Hz (272.01 Hz).
In terms of pitch, both steps will very likely be perceived to be of same distance by most humans.
So I dare to say that high-resolution log scale spectrum analysis corresponds to human hearing well enough to be practical - albeit, taking into account the compromise between time and frequency resolution of Fast Fourier Transform, on which spectrum analyzers are usually based.
It also corresponds to the equally spaced 12-pitch piano roll in 12-TET. That is easy to test perceptually by playing for example the C Major scale (CDEFGAB) and C chromatic scale (all 12 pitches from C to next C), and considering in which case one perceives the pitch steps to be of equal distance.
I believe that for most of us, the chromatic scale sounds like each step has the same pitch distance to the previous one. Whereas the C Major will sound like it has larger pitch jumps in some places - such as C to D - and smaller in others, such as E to F.
Spectrum analysis of sine waves playing C major and C chromatic scales will look like this:
So it is not so much a case of "image instead of the thing" - more like "image which corresponds to the thing". Obviously, seeing is not the same as hearing - but neither it is in case of the staff, which corresponds even less to what's heard, due to lack of visual proportionality. I'll get to that in later paragraphs.
For anyone interested, attached is the REAPER project used there: The analyzer JS plugin used in the project is linked here: https://forum.cockos.com/showthread.php?t=258602
***
Now, to the matter of proportional vs. non-proportional visual representation of pitches in notation. That is: arguable illogic of the "7 naturals + alterations" staff, as requested
Intervals of C Major scale are marked on the staff as having visually equal distances, despite the fact that we hear some of those distances as not equal. In comparison, piano roll shows the steps much like a log scale spectrum analyzer, corresponding more closely to how they are actually heard.
Here's an illustration, again with spectrum for comparison:
I hope it helps to clear up what I mean by potential source of confusion and Spock-like exclamations of illogic
You do not have the required permissions to view the files attached to this post.
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
back to use value of intervals and their identities in language.
An augmented second and a minor third are plainly said to be three semitones wide. On a piano, there can be no difference that is not a use case that defines one or the other.
But in the use case presented where it demonstrably is aug 2nd, it may be intoned differently where possible (on a non-fretted string instrument, or wind instrument, something that can bend the note, the voice...). It may turn out to be true that in the case where it leads to a major 3rd, it's intoned more sharply then the seemingly identical m3; but it may also be true of a m3 into M3 in our blues thirds conception, C - C# on an A chord as opposed to say 'C - A' where there is no desire for that expression, ie., the thing absolutely is *minor*.
It may be that stylistically a Bb descending to A is a smaller interval, hence a different real pitch than that Bb in relation to another next tone. Leading-tone semitones may be intoned higher; B - C is a diff. B than if it moves to G.
An augmented second and a minor third are plainly said to be three semitones wide. On a piano, there can be no difference that is not a use case that defines one or the other.
But in the use case presented where it demonstrably is aug 2nd, it may be intoned differently where possible (on a non-fretted string instrument, or wind instrument, something that can bend the note, the voice...). It may turn out to be true that in the case where it leads to a major 3rd, it's intoned more sharply then the seemingly identical m3; but it may also be true of a m3 into M3 in our blues thirds conception, C - C# on an A chord as opposed to say 'C - A' where there is no desire for that expression, ie., the thing absolutely is *minor*.
It may be that stylistically a Bb descending to A is a smaller interval, hence a different real pitch than that Bb in relation to another next tone. Leading-tone semitones may be intoned higher; B - C is a diff. B than if it moves to G.
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
this was not written well, in haste and before caffeine 
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it appears I'm a crap writer
the smaller interval in comparison to its neighbor (at the same time) - or the closer it is to being the same note while not being that - the "rougher" it appears to the ear. There is an older term, 'a bad unison' which applies here.
This is true per se. Now, the lower our pitches are (on musical instruments, or anything that's disturbing air molecules as opposed to sine waves/no upper partials at all), the more roughness we'll perceive, so we're careful with even the seemingly no problem concord of a major third way down in the bass of say a piano, where a fundamental off the big strings is quite pronounced hence more harmonics are perceptible, it just doesn't sound so concordant as we tend to expect.*
AND: the closer to "a bad unison" the more "dissonant". A major seventh (typoed 'second' here) is not in this regard really different than a minor second. Take either and squeeze them together more and more (to the close neighbor) and the rougher and rougher things get for the ear.
However a major seventh is in another regard noticably different than a minor second. A major seventh is the third partial - a perfect fifth - of/from the major third; in a sense there is a coherence to this the smaller interval doesn't enjoy. By itself, naked (as opposed to hitting up against its neighbor, the octave simultaneously) it's just not as rough as, so the distance gives some relief if only up to a point where we rub up against the bad unison.
*: Note well, though, that a cluster of issues arises when we consider upper partials and vibratile materials, such as difference tones and all kinds of interest beyond our scope here.
-it appears I'm a crap writer
Why, one should ask. It's down to what is called sensory roughness, a psychoacoustical phenomenon when
the smaller interval in comparison to its neighbor (at the same time) - or the closer it is to being the same note while not being that - the "rougher" it appears to the ear. There is an older term, 'a bad unison' which applies here.
This is true per se. Now, the lower our pitches are (on musical instruments, or anything that's disturbing air molecules as opposed to sine waves/no upper partials at all), the more roughness we'll perceive, so we're careful with even the seemingly no problem concord of a major third way down in the bass of say a piano, where a fundamental off the big strings is quite pronounced hence more harmonics are perceptible, it just doesn't sound so concordant as we tend to expect.*
AND: the closer to "a bad unison" the more "dissonant". A major seventh (typoed 'second' here) is not in this regard really different than a minor second. Take either and squeeze them together more and more (to the close neighbor) and the rougher and rougher things get for the ear.
However a major seventh is in another regard noticably different than a minor second. A major seventh is the third partial - a perfect fifth - of/from the major third; in a sense there is a coherence to this the smaller interval doesn't enjoy. By itself, naked (as opposed to hitting up against its neighbor, the octave simultaneously) it's just not as rough as, so the distance gives some relief if only up to a point where we rub up against the bad unison.
*: Note well, though, that a cluster of issues arises when we consider upper partials and vibratile materials, such as difference tones and all kinds of interest beyond our scope here.
Last edited by jancivil on Wed Nov 10, 2021 5:15 pm, edited 2 times in total.
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- KVRist
- Topic Starter
- 70 posts since 24 May, 2021
ok....let me take a brief tangent that doesn't really relate to the topic I started, but maybe someone has an answer.
The backing track I am playing to has 4 chords - C then A minor, then E minor, then G I was playing notes in the scale of C major (sometimes pentatonic, sometimes the whole scale), but I notice that when the chord shifts to Em, I like the sound F sharp is making vs F, which got me thinking.
even though the entire chord progression is in C, when it comes to individual notes, should I be thinking of the scale of the chord that is playing at the moment ? Eg, instead of playing notes in C major throughout, should I shift the notes I play when the E minor and G major take their turn ?
(and yes, I know there are no rules and I should play what sounds good to me....)
The backing track I am playing to has 4 chords - C then A minor, then E minor, then G I was playing notes in the scale of C major (sometimes pentatonic, sometimes the whole scale), but I notice that when the chord shifts to Em, I like the sound F sharp is making vs F, which got me thinking.
even though the entire chord progression is in C, when it comes to individual notes, should I be thinking of the scale of the chord that is playing at the moment ? Eg, instead of playing notes in C major throughout, should I shift the notes I play when the E minor and G major take their turn ?
(and yes, I know there are no rules and I should play what sounds good to me....)
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
You like that F# for a couple of reasons. As I showed, the 'primary' as it were seven note scale constructed stacking the Perfect Fifth gives Lydian.
(Forgive a bit of pontification here: there have been many arguments to nature for tonal music from persons with a vested interest in that culture's supremacy. Lydian is closer to 'natural' very simply like that.)
Then, if you like a 9th on iii, E minor with a -9 is kinda not pretty. F# is a P5 from the 5th in the E minor harmony.
I have no opinion on that without hearing what you did if you were considering iii and V separately. You lose V7 to I and the key with that choice.
So you want the F natural when, you like the ii chord Dm? For the ii-V7-I convention (tonal function, the "dominant-tonic paradigm") you simply stay with F.
You may well have a taste for Lydian. But absent the musical example, I can say nothing except that kind of thing, indicate sort of facts and convention. Another of which is that in definitely tonal C major functional harmony-oriented music, F# suggests the dominant of G, D major (secondary dominant, marked "V/V", V of V). It's a chromaticism at any rate.
It seems that at this stage you just are considering sonority before function. Which is not wrong, it's just another way than tonal function. TBH I was the same. I actually don't gravitate to dominant/tonic kinda music much, I had my fill of V7 - I long ago. I wanted the 9ths and all that jazz lush stuff, what I grew up in.
(Forgive a bit of pontification here: there have been many arguments to nature for tonal music from persons with a vested interest in that culture's supremacy. Lydian is closer to 'natural' very simply like that.)
Then, if you like a 9th on iii, E minor with a -9 is kinda not pretty. F# is a P5 from the 5th in the E minor harmony.
I have no opinion on that without hearing what you did if you were considering iii and V separately. You lose V7 to I and the key with that choice.
So you want the F natural when, you like the ii chord Dm? For the ii-V7-I convention (tonal function, the "dominant-tonic paradigm") you simply stay with F.
You may well have a taste for Lydian. But absent the musical example, I can say nothing except that kind of thing, indicate sort of facts and convention. Another of which is that in definitely tonal C major functional harmony-oriented music, F# suggests the dominant of G, D major (secondary dominant, marked "V/V", V of V). It's a chromaticism at any rate.
It seems that at this stage you just are considering sonority before function. Which is not wrong, it's just another way than tonal function. TBH I was the same. I actually don't gravitate to dominant/tonic kinda music much, I had my fill of V7 - I long ago. I wanted the 9ths and all that jazz lush stuff, what I grew up in.
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
So, a harmony like E G B D F# may be considered by stick-in-the-mud conservatives to contain "dissonances" like we should worry.
As a technical matter, ok, we've that major 7 but that's really all. So what? It's not like G B F, V7 in a context demanding resolution of that one, the B-F into C-E, it can just sit there and remain cool. It enjoys two perfect fifths, it's sonorous af!
For me, ^7 is so P5 from M3 (cf the M9 a P5 from P5) it's rather "consonant", but I'm not into the old bewigged composer style(s) much. Occasionally I make a classic move
.
It does occur in JS Bach a number of times unresolved, note well, it's a strikingly pleasing thing that happens.
As a technical matter, ok, we've that major 7 but that's really all. So what? It's not like G B F, V7 in a context demanding resolution of that one, the B-F into C-E, it can just sit there and remain cool. It enjoys two perfect fifths, it's sonorous af!
For me, ^7 is so P5 from M3 (cf the M9 a P5 from P5) it's rather "consonant", but I'm not into the old bewigged composer style(s) much. Occasionally I make a classic move
.It does occur in JS Bach a number of times unresolved, note well, it's a strikingly pleasing thing that happens.
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
another point on the interval major 7th particularly for functional music: (in tonal function) if a leading tone to tonic may be intoned with choice (as opposed to on a piano or like that) it's more pronounced a leading tone if it's sharper, more insistent on its target, owing to that roughness. And this kind of thing is taught eg., in violin pedagogy for 'classical music'.
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- KVRAF
- 11162 posts since 16 Mar, 2003 from Porto - Portugal
I think the problem in your vision is that you are looking at music notation as something "scientific". IT ISN't. It is a language, a way to translate sounds into a visual code that could be recorded (at a time where there was no other means to record it) and that way preserve the sounds being sung/played for the future. It was a code that developed VERY SLOWLY and with a high degree of abstraction, as it happens with other codes (like written language, for example).N__K wrote: Wed Nov 10, 2021 12:37 am Intervals of C Major scale are marked on the staff as having visually equal distances, despite the fact that we hear some of those distances as not equal. In comparison, piano roll shows the steps much like a log scale spectrum analyzer, corresponding more closely to how they are actually heard.
So, intervals in music notation relate with the way that code is built. They don't necessarily translate into frequencies and whatever. Actually, the pitches changed very much since humans first start to notate music, and it is possible that things we now sing in a certain way would not be sung that way back then.
Intervals are related with scales, which are related with the way pitches are organized tonally (and modally before that). There was even a time where what was sung was not even what was written (the music ficta period), and times where musicians were supposed to play things that were not written at all (ornamentation during the baroque, or the continuo, which was just approximately suggested by the figured bass).
Trying to translate notation, which is just an approximation to what should be played, into an absolute and scientific reality is nonsense. That's why in terms of sound an augmented second being different from a major third doesn't make sense, while in terms of notation it makes all the sense. Because we are talking of different realities.
Fernando (FMR)
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
there's no good reason for B# to occur with any proximity to Cb really. 'double augmented seventh' is not so useful.
the key areas are 7 sharps to 6 flats for that derivation; we've gone around the entire circle and started around a second time. So key-wise it's a nonsense; & if it was 'post-tonal' in any way you'd prob'ly just say C to B, C to Cb. Key-wise an Ax to B# is not in itself untoward.
Cb to B# I suppose technically amounts to doubly augmented 7 or the other one in the inverse, but at that point we're naming just to name shit.
the key areas are 7 sharps to 6 flats for that derivation; we've gone around the entire circle and started around a second time. So key-wise it's a nonsense; & if it was 'post-tonal' in any way you'd prob'ly just say C to B, C to Cb. Key-wise an Ax to B# is not in itself untoward.
Cb to B# I suppose technically amounts to doubly augmented 7 or the other one in the inverse, but at that point we're naming just to name shit.
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- KVRist
- Topic Starter
- 70 posts since 24 May, 2021
yes, I realize it is a ridiculous question, but just curious to see what the answer is when the higher lettered note ( c flat) is a lower tone than the lower lettered note ( b sharp). ( Being a theoretical mathematician by background I like consistency in definitions)).
Thanks
Thanks
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- KVRAF
- 11162 posts since 16 Mar, 2003 from Porto - Portugal
As I wrote earlier, notation is a code language. It has its rules. The example you gave is simply absurd. You could also very well assemble a bunch of random words, put them side by side, and ask anyone majored in literature to classify the sentences and explain the meaning. They would probably have a mental shock, and would simply come to you telling that simply made no sense grammatically, syntactically or anything. That's what I would tell you as an answer, regarding your question.shugs wrote: Thu Nov 18, 2021 12:23 am yes, I realize it is a ridiculous question, but just curious to see what the answer is when the higher lettered note ( c flat) is a lower tone than the lower lettered note ( b sharp). ( Being a theoretical mathematician by background I like consistency in definitions)).
Again: Notation is a language code. It has no absolute meanings. And it is just an approximation to what music realization woul dbe. If you listen to the same piece of written music you will notice differences in the interpretations (sometimes NOTORIOUSLY BIG differences). Yet, they all followed the same score.
Answering directly - my answer would be a minor second, obviously. Remember that intervals are classified in absolute terms - it doesn't matter which note is higher and which not is lower.
Fernando (FMR)
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- KVRist
- Topic Starter
- 70 posts since 24 May, 2021
thanks for humoring me. I am in a music theory I class, going through 100+ exercises of being given two notes and defining the interval and quality. I am actually (and finally) getting pretty quick at them whereupon this pairing came to my mind.
SO yeah, it's a stupid pairing. I decided that it is probably a double diminished second which in the real world may never actually exist in any composition.
A minor second above B sharp would be a C sharp; a diminished second would be a C; and hence, C flat being the double diminished is my thinking
SO yeah, it's a stupid pairing. I decided that it is probably a double diminished second which in the real world may never actually exist in any composition.
A minor second above B sharp would be a C sharp; a diminished second would be a C; and hence, C flat being the double diminished is my thinking
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- KVRAF
- 26033 posts since 20 Oct, 2007 from gonesville
People do occasionally say 'diminished second' but it tends to indicate something at say a syntonic comma sharp to the actual unison.
Carnatic scales are built from the very flattest next letter name (or there, a sanskrit name) and progressively systematically raise each interval. So there are 72*.
But a diminished second is not part of it, because for them *the 1 and 5 (diatonic 1 and 5, Sadja and Panchama) are sacrosanct, it would just be 'a bad unison' considered useless. But in chromatic common practice period material, for say a violinist taught to intone things contextually it can be an actual thing, in theory.
Carnatic scales are built from the very flattest next letter name (or there, a sanskrit name) and progressively systematically raise each interval. So there are 72*.
But a diminished second is not part of it, because for them *the 1 and 5 (diatonic 1 and 5, Sadja and Panchama) are sacrosanct, it would just be 'a bad unison' considered useless. But in chromatic common practice period material, for say a violinist taught to intone things contextually it can be an actual thing, in theory.