Perfect 5th question

[Dehaan]

If i have 3 copies of the same voice.
#1 is kept same.
#2 is pitched up an octave
#3 is pitched up a perfect 5th.

Then
* #1 and #2 are in harmony
* #1 and #3 are in harmony

But what about #2 & #3? Would they be in harmony with each other?
Also does perfect 5th only work if you pitch up 7 semitones? What if i pitch down 7 semitones? Is that a perfect 5th?

[askoan]

Just a comment on your first question :
I wouldn't use the expression "1 is in harmony with 2" which seems a bit metaphysical ; i'd rather use the expression used in the following wiki : "The perfect fifth is more consonant, or stable, than any other interval except the unison and the octave", and this is physically explained :
https://en.m.wikipedia.org/wiki/Perfect_fifth
(and sublinks like https://en.m.wikipedia.org/wiki/Harmonic_series_(music) )
The interval between #2 and #3 in your case is also a "perfect", the perfect 4th.
The perfect 4th and 5th are related in an other way too : add a perfect 4th to a perfect 5th, and you get an octave. see https://en.m.wikipedia.org/wiki/Complement_(music)

An interval is relative, like in maths ; so any 2 notes that have 7 semitones between them do form a perfect 5th.
But the expression "perfect 5th of C" leads to one and only one note : the G.

[DJ Warmonger]

@Dehaan correct. You're basically getting fundamental, x2 and x3 frequencies stacked together and these are coherently in phase.

All this harmony comes from simple Fourier Series.

I need to make a video about it!

[Domenico KVR]

If i have 3 copies of the same voice.
#1 is kept same.
#2 is pitched up an octave
#3 is pitched up a perfect 5th.

Then
* #1 and #2 are in harmony
* #1 and #3 are in harmony

But what about #2 & #3? Would they be in harmony with each other?
Also does perfect 5th only work if you pitch up 7 semitones? What if i pitch down 7 semitones? Is that a perfect 5th?

Greetings, Dehaan.
If you have three copies of the same voice, that means that they will always have the same interval relationship, of what I can understand. So, yes. That would be correct harmonisation, that is, if we are speaking of medieval harmony.
Because, really, the answer to your question regarding whether your voices will remain in harmony is relative to what "harmony" you're speaking of.
In the medieval era, especially in vocal music, composers would have two or three voices separated by constant, unchanging intervals, generally a fourth (which, when inverted, is a fifth as in your case).
Now these consecutive (or "parallel") fourths are not allowed in classical harmony, that is, starting from the baroque era. In fact, all consecutive perfect unisons, perfect octaves, fourths and fifths are not allowed in classical harmony. One of the only exceptions to this rule is when you move either from a perfect fifth to a diminished fifth (or the other way around), or when you move from a perfect fourth to an augmented fourth (or the other way around, once again).
Using baroque harmony in classical or modern-day music would be like going back in time, and re-adhering to a primitive idea, in some way. The human ear has developed over these periods of time, and such "harmonisation" is no longer acceptable in music that is said to be classical.
But it could give another dimension to modern music, as there are no such limits when it comes to this. :)

I hope this helps.
All the best.

[Domenico KVR]

Now these consecutive (or "parallel") fourths are not allowed in classical harmony, that is, starting from the baroque era. In fact, all consecutive perfect unisons, perfect octaves, fourths and fifths are not allowed in classical harmony. One of the only exceptions to this rule is when you move either from a perfect fifth to a diminished fifth (or the other way around), or when you move from a perfect fourth to an augmented fourth (or the other way around, once again).

Just to make sure I didn't lack specification, here, consecutive intervals that are not aloud are no more valid when doubled. For example, we know that consecutive fourth are not allowed, which means that consecutive elevenths are not allowed either (4+7). As can be seen in the previous phrases' parentheses set, you can always subtract seven to a doubled interval (an interval above an octave) to see what the simple interval is. For example, is you have a ninth and you want to know what the simple interval for it is, you go nine minus seven and the answer is a second.

[jancivil]

"In fact, all consecutive perfect unisons, perfect octaves, fourths and fifths are not allowed in classical harmony."
In four-part writing parallel fifths and octaves are generally not desirable in the Common Practice Period.
Also note well, the restriction is strictly within the 4-part writing paradigm. Classical music in the wider sense, for example piano music has parallel octaves all the time. The broad statement 'in classical harmony' is doing too much.

Perfect fourths are not the same problem. Occurs in JS Bach chorales with some frequency. Parallel perfect fifths quite more rarely but not non-existent.

But these rules serve a style. That style is academic at this point. But the P4 bit is not a fact; if JS Bach, pretty much the standard for and the codification of these principles did it it's legal . (Reminds me of my final at CCM where I had a guy who apparently couldn't stand giving anyone 100 so he took 4 pts off for a covered fifths on a German sixth to V move. Known as Mozart fifths rather widely, I learned later, as well as in Bach. It's clearly *the* move there, so it was a trick problem.)

[Domenico KVR]

In four-part writing parallel fifths and octaves are generally not desirable in the Common Practice Period.
Also note well, the restriction is strictly within the 4-part writing paradigm. Classical music in the wider sense, for example piano music has parallel octaves all the time. The broad statement 'in classical harmony' is doing too much.

Indeed. Thank you for specifying that.

If JS Bach, pretty much the standard for and the codification of these principles did it it's legal.

I don't believe I agree with this, though. When it comes to modern-day SATB, parallel fourths are considered to be just as obsolete as parallel fifths. Using parallel fourths in SATB (or even keyboard style) these days would be like going back to a sort of primitive idea. Now that the human ear has developed throughout the centuries, music is not the same as it used to be. And this is a big part of what reveals the beauty behind baroque music; its antiquity.
But like jancivil said, these restrictions only really apply to four-part writing.

Cheers. :)

[fmr]

Just to clarify, the rules you have been referring too are much older than J S Bach, and they predate the Baroque. Actually, you already have these more or less established in Josquin Desprez, and completely established in Palestrina.

But even in the Baroque, parallel fifths may occur in orchestral music. As jancivil stated, these rules only apply to polyphonic vocal music (which was pretty much abandoned in the baroque, in favor of the Opera, and instrumental music). Parallel 5ths and Octaves were not accepted because they were seen as a temporary omission of one voice (as if that voice was temporarily shut down) which wasn't acceptable in polyphonic style, where each voice has to always maintain independence and presence.

Anyway, empty fifths and parallel octaves are NO HARMONY whatsoever, even now, no matter how you look at them. In practice, they work as a boosting of the fundamental voice, nothing else. That's what octaves in piano pieces are there for, for example.

[jancivil]

Well, what I meant was really that inside of the basic 4-parts there's a reason for a restriction like that, ie., in earlier practice as you mention, and independence linearly hence a graceful or elegant clarity per se. But past that (or say 6-parts when the harmony contains 4 & 5-note harmonies) the use of the same word 'consecutive' this or that or 'parallel' as in voice-leading is not useful.

[fmr]

... the use of the same word 'consecutive' this or that or 'parallel' as in voice-leading is not useful.

Yes, we agree on that. In modern music, that terminology makes no sense. Neither the restrictions. The logic behind it is a completely different one.

[amulitz]

I worried about your creating perfect intervals by counting half steps. Perfect intervals are overtone phenomena. You can either hear them or you can't, but you can't get there counting half steps except for octaves on a tempered instrument. You can tune a scale in perfect intervals and even modulate to related keys (dominant, subdominant), but other keys start to sound terrible. Of course, most instruments can play perfect intervals almost all of the time if their "inner ear" works and they know the general key signature. It may be easiest to hear it in string quartets. Anyway, my opinion; I could be wrong.