58

Yes, there are ways to measure it, though there are many different algorithms claiming to be more correct than the others. This formula by Vassilakis is recent (2007). These measure "roughness", which is similar to dissonance. (Dissonance is basically roughness, but weighted towards certain intervals due to cultural conditioning, which is obviously hard ...


36

I don't know that there is any evidence that the tritone was ever formally banned by the Catholic Church, although that story does get passed around a lot. An actual Church document that discusses this and puts the claim in context is needed. I see no mention of tritones or intervals of any type in Musicam Sacram of 1967. The Sacrosanctum Concilium of 1963, ...


22

Is it an important thing to consider in Orchestration? You have in fact stumbled onto the very foundation (and art) of orchestration. Orchestration is about not only knowing how each instrument sounds, but how to blend those sounds together to get the effects / textures you're looking for. Composers generally don't think about blend in terms of harmonic ...


18

There are at least two explanations for why this leap is acceptable: First is the idea of "gap fill," also sometimes called "registral return" or the "post-skip reversal." In short, when there is a large leap, we can soften it by subsequently moving by step in the opposite direction. This is a Gestalt principle of good melodic design that can often explain ...


17

One pure sine wave does not have an overtone or harmonic. The sine wave is a single unit of information in some version of signal processing theory. It is a mathematical function. The overtones or harmonics that contribute to musical instrument tone or timbre come from solutions to the wave equation, which coincidentally is also, in many cases, a sine ...


16

In general, smaller intervals do not sound as pleasing in a bass register as they do in a treble register. This is a general effect that occurs regardless of whether you play a consonance or a dissonance, although it is more noticeable with dissonances. What happens is that the overtones of the bass notes end up having more noticeable clashes between them, ...


15

It's actually a suspension, which is to say that the actual chord is F Minor (F, A-flat, C, in first inversion) but the G and B-flat are held over from the previous chord before moving to F and A-flat. Dissonant suspensions resolving to consonant chords are very common in Baroque music. In jazz, 9th chords are treated as normal chords, so a G#maj9 might ...


15

Other answers so far make good points -- matching timbres (and sound spectra) is actually essential to orchestration, and composers have been noticing these patterns (and using them in orchestration) even before analysis of harmonic spectra was possible. I would add one other related issue to answering the title question about "differences in harmonic ...


13

There is a trick that organists do, which is to play parallel fifths on low notes in the pedals. The notes match the 2nd and 3rd harmonic of a lower note. The fundamental of that lower note is only present as "beats" produced by the two notes, but you "hear" it nevertheless. The low note is called a "resultant" and the pitches you hear are an octave lower ...


13

Tritones have been used since Gregorian Chant days. There are several common patterns that outline a tritone and a few instances where a direct tritone is used. The term "Devil's Interval" seems to refer to the difficulty of resolving the interval rather than in forbidding its use. One amusing (if true) use was the direct F to B (I think downward) interval ...


11

This may be due to the interferences that the tone combination generates. When you tune in a string to another, you can hear a vibration getting slower as you approach unison. This effect is known as kick and the resulting interference is the difference between the two frequencies. According to wikipedia, differences above 15 Hz are not perceived as ...


11

If you mean this curve: probably because it was only calculated using the first 6 harmonics. Plomp & Levelt 1965: In this way, the curves ... were computed for complex tones consisting of 6 harmonics. ... shows how the consonance of some intervals, given by simple frequency ratios, depends on frequency. And this one: was also only calculated with ...


11

As a beginner, or as an extremely experienced player/writer, you're allowed to do just what the heck you like. There are 'rules' - more like guidelines, or things that are known to work/not work well. It's called theory. But - the bottom line must always be: does it sound good, to you or others? You cannot make each and every note in a tune match the ...


11

I have to disagree with Todd Wilcox on this. The fourth as an interval is present in the overtone series, lower than the major third. It is the interval that exists between the 3rd and 4th harmonics. We don't have a major 3rd in the harmonic series until we allow the 5th harmonic to be considered. So, purely on the basis of the overtone series, the fourth ...


11

The only really 'stable' thing in triadic tonal music is the tonic triad, which consists of the tonic, mediant, and dominant notes. The subdominant isn't one of these, therefore according to the common expectations around this kind of music, it's seen as 'wanting' to move somewhere at some point. In terms of common notions of measured/calculated dissonance, ...


11

Let me first quote from James Tenney's book, A History of Consonance and Dissonance: There is surely nothing in the language of discourse about music that is more burdened with purely semantic problems than are the terms consonance and dissonance. A comparison of some of the definitions of these words to be found in current dictionaries, harmony textbooks,...


11

Does the difference in harmonic series between instruments have a significant effect on the consonance of the sound? Absolutely - and not only between instruments. Different ranges of the same instrument have different harmonic structures - a commonly-given example is the 'muddy' sound at the bottom end of the piano, caused partly by relatively weak lower ...


10

It certainly isn't banned now! And the whole historical mythology of banning the 'Devil's interval' though a nice idea, is rather dubious. As well as being the engine of a dominant 7th chord, resolving to a major 3rd (or its inversion, a major 6th) it's almost achieved consonance status when used as a b5 by jazz players.


9

It can be tough to define exactly what "dissonance" is (it changes throughout history, and it changes between genres), but Paul Hindemith created his own theory regarding ranked dissonances. He had two "series": Series 1 was a list of melodic intervals from most consonant to least consonant. Series 2, meanwhile, was a list of harmonic intervals from ...


9

The octave, the fifth, and the major third are all low-order members of a harmonic series. We can generate a harmonic series by multiplying a frequency by successive positive integers (1, 2, 3, 4, 5...). After multiplying a frequency, we can divide by a power of two to lower the octave of the new frequency. All multipliers that are powers of two (2, 4, 8, ...


9

I'd like to re-use the opening from WillRoss1's answer (First off, I completely agree that "that sounds good/bad" has NOTHING to do with consonance or dissonance! I, for one, LOVE a good dissonance! But I digress...) Consonance and dissonance are (mostly) objective, however they are not context-free. The same chord can work as consonant in one piece of ...


8

Yes, you are correct! At least there is a physiological explanation. The construction of the human hearing apparatus causes a quality that is called critical bands. A critical band represents a bandwidth in which a sounding frequency has to be alone for us to hear or perceive it clearly. This bandwidth is, relatively speaking, increasingly wider for lower ...


8

Harmony is a noun that means "simultaneous sounds." Consonant and dissonant are adjectives that describe harmony; think of dissonance as "tension" and consonance as "stability/release." In terms of composing a song, you'll often want your harmonies to match what's happening in the lyrics. If a song ends "happily ever after," it doesn't make much sense for ...


8

The minor seventh chord is indeed a pretty consonant chord, and this can be explained with objective maths. Recall that Western harmony is based on just intonation frequency-ratio. Most well-known, a major chord in JI consists of frequencies in ratio 4:5:6. Generally, a major third is 4:5 and a minor third 5:6. Now see what happens if you compose these ...


7

As some of the other answers have eluded to, there are two basic problems with your question: The first is the question of how you generalize a "tritone" in a non-12-TET based system. One possibility is to interpret it literally as three whole tones (which then begs the question as to how you define a whole tone in a non 12-tone system). Another ...


7

The answer is due to two factors: (a) harmonic series and (b) the formation of beats. If you pluck a string or vibrate the air in a wind instrument, you predominantly hear one note or frequency. But in reality, there are additional notes/frequencies being produced. The note we predominantly hear is called the "fundamental frequency," and the additional ...


7

You can certainly use non-chord notes. 'Theory' delights in labelling the various ways of doing this - 'passing notes', 'accented passing notes', 'suspensions', 'unprepared suspensions', 'chromatic passing notes'. Yes, whatever you choose to do, theory has a name for it! Are you writing melodies over a given chord structure for a music examination? In ...


7

The Argentine composer he referenced was Alberto Ginastera. Regarding the thirds and classical guitar, he's talking about playing the chords with tenths instead of thirds. A tenth is the same as a third, one octave higher. When he demonstrates the chords at 7:13, he's doing it as a very fast arpeggio. I suppose that, between the arpeggio and the fact that ...


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