# Intervals

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### Deaf Boots

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Mar 27, 2019, 8:49:54 AM3/27/19
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The pitch-distance 3rd is that between "I" and "iii" ultimately
expressed as "a" frequency ratio (i think!). But "the" 3rd as two
combined notes is "I" AND "iii" sounded together. In C Major E is "a"
3rd from C while C+E is "the" 3rd in that scale. Please correct me if
I'm wrong.

Would it be correct to say that G-B is also a 3rd as pitch-distance? How
about G+B, that interval surely can not be "the" 3d as a combination of
2 notes in the same scale, or can it?

### steve...@gmail.com

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Mar 27, 2019, 5:00:13 PM3/27/19
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Is this question inspired by the idea that there's ambiguity around the use of the word "third" (or "3rd")? If not, then please disregard this answer. :) But, if so, then here's my take on that ambiguity.

To me, there's only one concept to which we apply the term "third", and that concept is, "an ascending or descending interval (or pitch distance if you prefer that term) that involves three note letters, in alphabetical order, inclusive". So, a "third" (if that's all you know about it) is a general interval. You know its quantity (a third; three note letters), but not its quality (whether it's major, minor, diminished, etc.). So, A natural up to C natural is a third. But, by the way, we also know that it's a minor third. D# down to Bb is a third. But, by the way, we also know that it's an augmented third.

Intervals also crop up in scale degree names. A major heptatonic scale can be formulated with the string of numbers "1 2 3 4 5 6 7". The implication is that that's a cycle, rather than a ladder. In other words, the 1 loops (descending) around to the 7; and the 7 loops (ascending) around to the 1. Each number is a code telling us what interval that scale degree is from the root. So, "1" is a unison from the root. It *is* the root. 2 is a major second above. 3 is a major third above. If we wanted the third scale degree to be a minor third above the root then we'd use the scale formula "1 2 b3 [...]". In scale degrees, "3" does not mean "the third degree of the scale". It means "the degree of the scale that's a major third above the root. And, as I say, "b3" means "the degree of the scale that's a minor third above the root". Similarly, the convention is that 4, 5, 6, and 7 encode, respectively, perfect fourth, perfect fifth, major sixth, and major seventh. You can alter those numerals (with sharps and flats) to encode something different. So, you don't pronounce "1 2 3 [...]" as "first, second, third, [...]", but rather as "one, two, three, [...]". And you pronounce "1 2 b3 [...]" as "one, two, flat-three, [...]". Again, "three" means "a major third above the root", "flat-three" means "a minor third above the root", and so on. That way you're using numerals to encode an interval just like you can use terms such as "major third" to do the same thing in a different context. That's my understanding, anyhoo.

My understanding of the upper- and lower-case Roman numerals is that they're used to encode triads. So, "I" is a major triad whose root is scale degree 1. "i" is a minor triad whose root is scale degree 1. And "iii" is a minor triad whose root is scale degree is 3. "bIII" is a major triad whose root is scale degree b3. For triads, we say, "the root, third, and fifth". But there's not enough info in that, out of context, to actually for the triad. That's because, here, the word "third" is a general interval. We know its quantity but not its quality. If, however, we know from context that we're talking about a C major triad, for example, or "bIII", then from that context we know everything we need to know about the "root, third, and fifth" to play the chord. You could also think of the word "third", when used in the sense of a general interval, as just a regular ordinal number (ordinal numbers are "first, second, third"; existing to place things in order. Cardinal numbers are "one, two, three"). In other words, you're talking about whatever note is the third of some heptatonic scale formed on the root note. But, again, the scale degree "3" (a cardinal number), is NOT ambiguous like the word "third" is. "3" is unambiguous simply because of the convention that we take it to mean "the scale degree a major third above the root". We don't (or, IMHO, shouldn't) assume any such thing about the word "third" when used like that, unqualified. If someone says "a third" (which can only mean an interval), then don't assume anything more about it than its quantity; if you know its quality from context, then you're not assuming anything.

### e7m

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Mar 27, 2019, 6:01:22 PM3/27/19
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You may just have a problem of notation context. I iii notation, upper/lower case Roman numeral indicate a tonic triad and a chord built on the 3rd step of a major scale. In Cmaj that is CEG and EGB chords. The tonic has a major 3rd from C and a m3rd from that (or P5th from C.
The iii is a m3rd over the E (note G) and then a Maj3rd B over that(EGB). Byond that I am not sure what exactly is your confusion. Unfortunately on my phone, I can't switch back to the post (I will try later on my computer to see if that is explained better later in the post.

Does that help?

### e7m

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Mar 27, 2019, 6:04:39 PM3/27/19
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Other than that. There are melodic 3rds and harmonic thirds and that might just be what is causing you a glitch in your understanding.

### steve...@gmail.com

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Mar 27, 2019, 8:22:37 PM3/27/19
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On Wednesday, March 27, 2019 at 3:04:39 PM UTC-7, e7m wrote:
> Other than that. There are melodic 3rds and harmonic thirds and that might just be what is causing you a glitch in your understanding.

Ah, that's a great point, I just noticed the OP's mention of "sounded together", and so now the hyphen and plus notation make sense. :) Right, so if I play a C natural note followed by an E natural note, then it's true to say that I just played a major third, but I happened also to play a melodic interval (a melodic major third), because I played the notes one after the other, and not simultaneously. Conversely, if I play both those same two notes simultaneously, then it's still true to say that I played a major third, but that time I played a harmonic interval (a harmonic major third). ~Steve

### Deaf Boots

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Mar 27, 2019, 8:47:05 PM3/27/19
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I'll reply to my own OP as a single answer to e7m and steve, thanks a
meg for your responses BTW! And I thought that this NG was dead...

At 75 I'm kicking music around to forestall brain rot, and liking it,
although definitely as a beginner.

Let me start by staying at C-Major level, there's no point in discussing
flying to the moon before earth-orbit is practiced blindfolded. I know
there are minor 3rds as well, but placing small details on a big ship
first requires knowlege of the overall ship :-)

As far as I've been able to determine "3rd" is used in at least 3 ways

1 - the 3rd NOTE of a scale

2 - the pitch-distance from the 1st to the 3rd note
i.e. from C to E, like so many inches on a tape.
One cannot hear this it being just a (non-musical)
measure (possibly a ratio)

3 - The sound of a 2-note chord, namely of the 1st
note C and of the 3rd note E; this one can be
heard because all it is is precisely a (unique?)
sound

Having studied and taught in many fields I think that getting the basic
terms down bulletproof is the place to start. I don't wanna get past
this for the moment.

I'm working on a graphic cheatsheet being convinced from experience that
trying to explain/teach is the very best way to learn anything. It will
cover Modes-Scales-Keys-Intervals-DiatonicProgs on a single page and
hopefully by the time it's done I will have purged all (related) fog
from my skull.

### Deaf Boots

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Mar 27, 2019, 10:17:09 PM3/27/19
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On 3/27/19 8:22 PM, steve...@gmail.com wrote:
> On Wednesday, March 27, 2019 at 3:04:39 PM UTC-7, e7m wrote:
>> Other than that. There are melodic 3rds and harmonic thirds and
>> that might just be what is causing you a glitch in your
>> understanding.
>
> Ah, that's a great point, I just noticed the OP's mention of "sounded
> together", and so now the hyphen and plus notation make sense. :)
> Right, so if I play a C natural note followed by an E natural note,
> then it's true to say that I just played a major third, but I
> happened also to play a melodic interval (a melodic major third),
> because I played the notes one after the other

Bingo, there's a 4th, 3rd that is

Looks like my question is getting wider but maybe I have fingered out
the initial one. There may be a distinction between "the" 3rd in a scale
and "a" 3rd either as 2 note chord or as you say a melodic interval :-)

In the major scale of C "the" third 2-note chord or melodic iterval or
pitch-distance would have to be C & E or C-to-E etc. G & B are also a
3rd marker-pair but in that same scale could oly be "a" 3rd
pitch-distance, 2-note chord or melodic interval. They would swap the
"a" for the "the" in the key of G however.

> , and not
> simultaneously. Conversely, if I play both those same two notes
> simultaneously, then it's still true to say that I played a major
> third, but that time I played a harmonic interval (a harmonic major
> third). ~Steve

There's a simiarly ambiguous thingie in Linux that gurus love throwing
at unsuspecting noobs: 'just mount /dev/mount under mountpoint /mnt'.

"THE" major 3rd
=============

- THE 3rd note in a major scale, not much used
as an expression

- THE Hz delta between the 1st note of a major
scale and the 3rd note

- THE sound of the above simultanously or arpeggiated

"A" major 3rd
=============

- the Hz delta between 2 notes 3 full steps apart
such as C-D and D-B

- the sound of the above notes at once or in rising
sequence (reverse sequence=reverse 3rd?)

Just trying to dot the i's and such...

### Deaf Boots

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Mar 28, 2019, 1:04:27 PM3/28/19
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On 3/27/19 8:46 PM, Deaf Boots wrote:

> I'm working on a graphic cheatsheet being convinced from experience that
> trying to explain/teach is the very best way to learn anything. It will
> cover Modes-Scales-Keys-Intervals-DiatonicProgs on a single page and
> hopefully by the time it's done I will have purged all (related) fog
> from my skull.

http://tinyurl.com/y6b2bxtm

may not be there for long & NB. it's just a draft

### steve...@gmail.com

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Mar 28, 2019, 6:48:46 PM3/28/19
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In honor of the Moon/Earth-orbit analogy, and "I don't wanna get past this for the moment", I'll try and keep this reply focused. :) By the way, if you want to learn foundation-first (Moon/Earth-orbit-style), I'd recommend this: http://voices.azurewebsites.net/elements/notes.htm. I worked long and hard getting the concepts in optimal order for that.

> As far as I've been able to determine "3rd" is used in at least 3 ways.

Lots of words in natural languages are overloaded, leading to ambiguity. But that's generally because folks are lazy with qualifiers. If I say "an interval of a third" then there's only one thing I can mean. If I say "the third note of a scale" then there's only one thing I can mean.

> 1 - the 3rd NOTE of a scale.

Yes, but that's just using the word as an ordinal number. There's nothing specifically musical about using the word in that context. So, I wouldn't count this is "a way that the word 'third' is used in music". I'd just say that's "a way that ordinal numbers are used by people". Is the word "second" in "second fiddle" meant musically? Or is it just an everyday word used in a musical context? I think it's the latter, and I think this is another example of that. It's true that the interval from the tonic to the "third" degree of a heptatonic scale is a third (and it's a major third if the scale is major), but when you get to pentatonic scales, the "third" degree of the scale is certainly NOT a third above the root. So, I wouldn't read anything more into this use of the word as just a plain ol' ordinal number, any more than I'd rely on the house number of the "third" house on the street being an offset of 2 lots away from the first. It might be; it might not (if there are vacant lots). Personally, I don't find the word to be useful in this context. The "third note of the scale" isn't as useful IMHO, as giving me its interval encoded as a cardinal number. For example, the degrees of the major heptatonic can be encoded as "1 2 3 4 5 6 7". The major pentatonic as "1 2 3 5 6". In both cases, the third degree is a third above the tonic, but the fourth degree, for example, is a fifth above the tonic for the pentatonic.

> 2 - the pitch-distance from the 1st to the 3rd note...

Yes, an interval is an offset. Being computer savvy, you know about bases and offsets. An interval is an offset from a base. Confusingly, the terms used are 1-based, when IMHO it'd be clearer if they were 0-based. So "first" is "no offset at all; stay on the note letter you're on". IMHO, that should be a "zeroth". Intervals use ordinal numbers to indicate the quantity only. That ordinal number is a sequencing of the note letters involved. So, for C to E, you fill in the blanks to get C-D-E, then you assign successive 1-based ordinal numbers to the note letters to get first-second-third, and then the largest ordinal number is the quantity of the interval you have. You still don't know its quality yet, though.

3 - The sound of a 2-note chord, namely of the 1st

I wouldn't say that the sound is itself a "third". The sound of a cow is not "a cow". It's "the sound of a cow". The sound of a third is not a third. It's "the sound of a third". So, again, I wouldn't count this as "a way that the word 'third' is used in music". I'd say it's an example of #2 being used in a sentence. As in, "Hey, please play C natural and E natural together for me. Yep, that sounds like a third to me."

> "THE" major 3rd

To me, this can only mean "the major third as a concept". The major third as a concept is: a musical offset exactly four semitones in size that spans three note letters, inclusive. "A" major third would be some application of that concept. For example, in a major heptatonic scale, there's "a" major third between 1 and 3. Another between 4 and 6, and another between 5 and 7. They're different instances of the same class.

> THE Hz delta between the 1st note of a major ...

It's not the frequency delta, since that'd be an absolute value. It's a ratio. Remember that the frequency curve is logarithmic.

> THE sound of the above simultanously or arpeggiated

That's a sound. Not an interval. I'm getting philosophical here, but only because I'm expressing what my own understanding is. Not trying to influence. If folks want to denote "the sound of a third" as "a third", then that's fine. :) I can't do that.

~Steve

PS, looking at your diagram, note that major and minor don't apply to fourths and fifths. They're perfect, or they're diminished/augmented 1 or more times.

### Deaf Boots

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Mar 29, 2019, 10:42:44 AM3/29/19
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On 3/28/19 6:48 PM, steve...@gmail.com wrote:
> On Thursday, March 28, 2019 at 10:04:27 AM UTC-7, Deaf Boots wrote:
> I'd recommend this:
> http://voices.azurewebsites.net/elements/notes.htm. I worked long and
> hard getting the concepts in optimal order for that.

looks good, I'll look there some more in time :-)

...
>> "THE" major 3rd
>
> To me, this can only mean "the major third as a concept". The major
> third as a concept is: a musical offset exactly four semitones in
> size that spans three note letters, inclusive. "A" major third would
> be some application of that concept. For example, in a major
> heptatonic scale, there's "a" major third between 1 and 3. Another
> between 4 and 6, and another between 5 and 7. They're different
> instances of the same class.
>> THE sound of the above simultanously or arpeggiated
>
> That's a sound. Not an interval. I'm getting philosophical here, but
> only because I'm expressing what my own understanding is. Not trying
> to influence. If folks want to denote "the sound of a third" as "a
> third", then that's fine. :) I can't do that.

I'm only a greenhorn but I suspect that some people want to talk of the
sound of a 3rd because like chords they have a common streak or a tone,
much like all dim chords resemble one-another somehow. My guitar prof,
bless his patient soul, wanted me to listen to my 3rd and 5th 2-note
chords to 'wrap my ear around them'.

As far as the "THE" I only stumbled on this twig on the forest floor
because I've heard people talk of 'THE 3rd' be that about a spread
between or the combined sound of 2 notes. I would not have halted if the
only version I'd have heard had been 'A third' of which there may be
several. Even restricted to within a scale there can only be one 3rd
that gets to be called THE 3rd and that's the spread 1-3 or the sound
1+3. That other one G-B or G+B has to do with being called 'A' third or
the 'also ran guy'. This is the distinction I'm trying to clear up in
this respect.

> PS, looking at your diagram, note that major and minor don't apply to
> fourths and fifths. They're perfect, or they're diminished/augmented
> 1 or more times.

So in creating a cheatsheet that must be as simple as possible how would
you label the 5th in the major and minor bars on the image? I thought of
M & m as interim handles for P or dim/aug, I suppose that P5 could do
that too.

### steve...@gmail.com

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Mar 29, 2019, 6:53:52 PM3/29/19
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So, I write documentation for a living (for Windows developer customers) and I always ask myself, of a document: what task does it help the reader do? There's always some goal or task that a user wants to do, either they're completely blocked, or they need some info to make it easier. So for the cheatsheet, what is that task? I looked at it, and I found a bunch of things I'd want to correct, but mainly I wasn't sure what its purpose is.

But specifically around written notation for intervals, "P5" would seem like a reasonable way to notate a perfect fifth. Personally I use "per5", but I don't know where I got that from; it's likely not standard. Alternatively, although this is really deviating from standards, if you want a single idea and symbol to represent what the major-ness of a major interval, and the perfect-ness of a perfect interval have in common, you might go with the idea of them being "natural", as in naturally occurring in the major heptatonic scale. "Natural" or "default", those would both work as ideas. I say that because the major heptatonic scale, from what I've seen, embodies the default semitone distribution of scale degrees. All the intervals are either perfect (1,4,5) or major (2,3,6,7). Those, then, to me are the "natural" or "default" qualities of those intervals. To get the other qualities, you're "altering" one of the natural ones. That's also true of the natural note names, in fact it's another way of saying the same thing, since those natural note names are so-named *because* of the natural intervals. In other words, C, D, E, F, G, A, B. Those are the natural note names; and if you want anything else then you alter them. Possibly too much and/or too-off-topic, info. :)

### Deaf Boots

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Mar 29, 2019, 11:17:18 PM3/29/19
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On 3/29/19 6:53 PM, steve...@gmail.com wrote:
> So, I write documentation for a living (for Windows developer
> customers) and I always ask myself, of a document: what task does it
> help the reader do? There's always some goal or task that a user
> wants to do, either they're completely blocked, or they need some
> info to make it easier. So for the cheatsheet, what is that task? I
> looked at it, and I found a bunch of things I'd want to correct, but
> mainly I wasn't sure what its purpose is.

It is to let me see AND understand at a glance the overall system so
that when I learm details of it I know where to pigeonhole every
'tidbit'. There's one thing for which there is absolutely no place at
this level and that is fine-print or exceptions! There are two kinds of
people: bottom-up analytical thinkers who can memorize a thousand
pigeonholes without havig a clue as to the structure and the top-down
ones who cannot learn anything unless they first understand the
structure. I belong in the latter group :-)

My cheatsheet shows me how we stumbled through modes until we hit the
right one and then built a music system on it. Then it moves on the the
DoReMi placeholder scale I learned in grade school as well as the roman
numerals for major-minors and intervals before the function names Tonic
to Octave. It will close with a singing-and-dancing progressions
diagram, its ultimate end and purpose I suppose. I have many other
cheartsheets already, each to an end.

> But specifically around written notation for intervals, "P5" would
> seem like a reasonable way to notate a perfect fifth.

P5 is ok with me, like I said I'm only poking around for things to lean
against. One I 'git'er done' I won't need my cheatsheet no more :-)

> Personally I use "per5", but I don't know where I got that from; it's
> likely not standard. Alternatively, although this is really deviating
> from standards, if you want a single idea and symbol to represent
> what the major-ness of a major interval, and the perfect-ness of a
> perfect interval have in common, you might go with the idea of them
> being "natural", as in naturally occurring in the major heptatonic
> scale. "Natural" or "default", those would both work as ideas. I say
> that because the major heptatonic scale, from what I've seen,
> embodies the default semitone distribution of scale degrees. All the
> intervals are either perfect (1,4,5) or major (2,3,6,7). Those, then,
> to me are the "natural" or "default" qualities of those intervals. To
> get the other qualities, you're "altering" one of the natural ones.
> That's also true of the natural note names, in fact it's another way
> of saying the same thing, since those natural note names are so-named
> *because* of the natural intervals. In other words, C, D, E, F, G, A,
> B. Those are the natural note names; and if you want anything else
> then you alter them. Possibly too much and/or too-off-topic, info.
> :)

hey, judging from the state of this group off-topic is almost as big a
word as IF :-)

### J.B. Wood

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Apr 1, 2019, 12:49:49 PM4/1/19
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On 3/27/19 8:49 AM, Deaf Boots wrote:
>
Hello, and it's good to see some folks are still lurking on r.m.t!
Getting back to associating a particular frequency ratio with a major
3rd, for example - that depends on the tuning system used. For a "just"
major third, that historically has been 5/4. A "just" perfect 5th would
have a 3/2 ratio. These intervals have somewhat different values in the
system of equal temperament (ET) used in Western music today.

The point here is that while historically the identification of major,
minor, perfect, diminished or augmented as an interval quality related
to pitch ratios can be argued, one can readily decouple tuning from
interval naming and rely on notation alone. For example, in ET the
augmented 4th (tritone) C-F# is enharmonically equivalent (sounds the
same) as a C-Gb diminished 5th. But a diminished 5th should not be
called a tritone (3 contiguous major 2nds). The A4 and D5 are different
intervals notation-wise (but would each sound differently in a non-ET
musical instrument tuning). Sincerely,

--
J. B. Wood e-mail: arl_1...@hotmail.com

### Deaf Boots

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Apr 1, 2019, 10:44:34 PM4/1/19
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Just waaaaaaay over my head at this time ...but SOLD!

https://www.youtube.com/watch?v=6fkw_xtPU-0

### e7m

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Apr 2, 2019, 6:16:05 PM4/2/19
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Don't worry. That kind of stuff is mostly physics. Important yes but more from the apects physics and this is very important to theory as it answers a lot of "why?" Questions with scientific evidence to explain why some conventions of the CPP. Most of the things one learns the common practice applications that melodic and harmonic movements that were used by the composers. I.e. it supports the movements that the composers heard as the "natural" way that music should move.

LJS

### e7m

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Apr 2, 2019, 6:18:34 PM4/2/19
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Good to see you too J.B.! And good to see that people are still interested in music theory.

LJSE7M

### Deaf Boots

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Apr 2, 2019, 8:54:04 PM4/2/19
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On 4/2/19 6:16 PM, e7m wrote:

> Don't worry. That kind of stuff is mostly physics.

Some gurus say that our music is the way we like it because that's what
we have gotten used to hearing. I figure that there are physical laws
governing and that when the ratios are there then it sounds good. Three
days ago I didn't know if 'temperament' was a new dance or something to
eat :-)

I am learning my 4th song and have improvised a solo into it that
technically fits the rules but I find myself bending strings to get to
where I think it should go. If I were not a beginner I would know why
but as it is I can only suspect some natural hunger for what is not in
the ET scale.

### J.B. Wood

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Apr 3, 2019, 6:57:23 AM4/3/19
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On 4/2/19 8:53 PM, Deaf Boots wrote:

> Some gurus say that our music is the way we like it because that's what
> we have gotten used to hearing. I figure that there are physical laws
> governing and that when the ratios are there then it sounds good. Three
> days ago I didn't know if 'temperament' was a new dance or something to
> eat :-)
>

Hello, and your first sentence can apply to myriad items. Certainly in
the performing arts (music, dance, film, etc) I believe it to be
axiomatic. Getting back to music, certainly for traditional,
fixed-tuned mechanical instruments (e.g., piano) ET is invaluable if you
want the "same" sound quality when playing in any one of 12 keys. Very
useful in accommodating a singer's voice range. To achieve the same
thing using "just" pitch ratios would require a lot more than 12 pitches
per octave. So if we take, for example, a major 3rd interval having an
ideal ("just", most consonant) pitch ratio of 5/4 we can vary this up or
down by a small amount and it will still sound pleasing to most folks'
ears. The human ear/brain allows for this, just like the colors
comprising visible light (ROYGBIV) have a bandwidth associated with each
color. The color orange is centered on an appropriate wavelength but we
can vary that up or down by small amount and people will still call it
orange not red or yellow. In the sound realm, ET allows us to
accomplish the equivalent and results in only needing 12 pitches per
octave and the ability to perform in any one of 12 keys with no sonic
restrictions/modifications other pitch shifting. Sincerely,

### Deaf Boots

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Apr 3, 2019, 8:37:51 AM4/3/19
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I am not even close to being able to argue intonation or music theory,
which is probably a good thing given my preference for zero-tolerance or
accomodation in just about everything. The just-intonation that I have
heard pleases me, and in an audio environment where maybe 95% of what I
hear is just noise to my ears I am drawn to it.

### J.B. Wood

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Apr 3, 2019, 9:39:56 AM4/3/19
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On 4/3/19 8:37 AM, Deaf Boots wrote:

> I am not even close to being able to argue intonation or music theory,
> which is probably a good thing given my preference for zero-tolerance or
> accomodation in just about everything. The just-intonation that I have
> heard pleases me, and in an audio environment where maybe 95% of what I
> hear is just noise to my ears I am drawn to it.
>

Hello, and fair enough, but I think one has to separate out musical
tastes based on a particular tuning system and the genre/style of music.
Would you be able to identify as pleasing music performed in just
intonation if you weren't made aware of that at the outset? Sure we can
argue the "sweet" sound of a 3/2 perfect fifth, a 5/4 major third, or a
4/3 perfect fourth when sounded outside of a musical context. When
embedded into musical performance one can obtain different outcomes.
For example, there was a period in Western music practice where a 4/3
perfect fourth occurring in certain settings was deemed contextually
dissonant. And then there's that no-no of employing parallel 5ths.

I've been fascinated by mathematics as applied to music for a number of
years but have to admit music performance is a combination of many
things and we experience them in the aggregate. To state that some
other system of tuning/temperament is better than ET absent
consideration of tempo, types of musical instruments and/or human voices
comprising an ensemble, skills of the performers and how this all comes
together in the mind of the composer/song writer ignores the big picture
IMO. One final comment is that the use of 12-tone ET provided a
flexibility to 18th c. and beyond Western music composers that other
previously-used tuning systems couldn't. Sincerely,

### Deaf Boots

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Apr 4, 2019, 1:28:51 PM4/4/19
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On 4/3/19 9:39 AM, J.B. Wood wrote:

> Would you be able to identify as pleasing music performed in just
> intonation if you weren't made aware of that at the outset?

I think so but definitely in a multiple-choice situation

> I've been fascinated by mathematics as applied to music for a number of
> years but have to admit music performance is a combination of many
> things and we experience them in the aggregate.  To state that some
> other system of tuning/temperament is better than ET absent
> consideration of tempo, types of musical instruments and/or human voices
> comprising an ensemble, skills of the performers and how this all comes
> together in the mind of the composer/song writer ignores the big picture
> IMO.  One final comment is that the use of 12-tone ET provided a
> flexibility to 18th c. and beyond Western music composers that other
> previously-used tuning systems couldn't.  Sincerely,

All I can say is that I'm very pleased to have 'discovered' just
intonation :-) What we like or do not like is very personal and far be
it from me to attempt any kind of generalization. Still I know that from
my perspective what I call music has to be evocative art else it is just
noise or at best some 'look-ma-no-hands' for audiophiles, distinction
being made along the lines of gymnastics vs. ballet. The role of
frequecy ratios in terms of any potential effect on our nervous system
is a mystery to me but I am optimistic. As to what 'evocative art' might
be, well, if it will stop me in my tracks to find out more, that's a
passing grade. Once I stopped on an autoroute in the middle of a
snowstorm at three in the morning to jot down the radio station
frequency and the exact time because I wasn't going to let slip away
what I had just heard. It was Enya's 'Watermark', no flash in the pan
one might say, but either you have it or you don't. Where does that
difference show in the theory of music? I can only ask :-)

### e7m

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May 19, 2020, 3:12:29 PM5/19/20
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### J.B. Wood

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May 20, 2020, 11:22:23 AM5/20/20
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I assume this is being forwarded for comment but I'm not sure what the
OP is asking. Sounds like he/she might need a short course on scales
and interval naming. We can talk about musical intervals exclusive of
how they are tuned, be it equal temperament (ET) or something else. For
example. in just intonation the higher pitch note of a perfect 5th is
3/2 times the pitch of the lower pitch note. The perfect fifth is still
"perfect" in ET. Certain intervals (fifths, fourths, octaves, and
unisons) are either perfect, diminished or augmented. These intervals
are never major or minor.

The other thing is naming and notation. C-B flat is always a minor 7th
while C-A# is an augmented 6th. These intervals happen to sound the
same when tuned in ET, but notation-wise they are different. Sincerely,
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