45

It's because in music, when you're talking about intervals, you count the first note, all notes in between, as well as the final note. For example, if you play two notes that are right next to each other, the interval is a second - even though the second note is just "one note" away from the first. In fact, if you play the same note at the same time, it's ...


44

The reason there are multiple names for notes is that the same note may function differently in different contexts. If you just play a single note with no context, then it could have a multitude of different names. For example if you played the note in between F and G you could call it F# or Gb or more obscurely E## or Abbb. They are all valid names and are ...


39

You're correct; it should be called a fourth! But since "augmented fourth" won't be big enough for this, we kind of had to make up a term, and the world of music theory collectively decided upon calling this interval a doubly augmented fourth. This just means that it's one half step larger than an augmented fourth. (As such, the augmented fourth is not ...


38

The intervals between notes are "equal" not in the sense that the difference in Hz between them is the same, but the ratio a between them is the same. Let's say g is one semitone higher than f, then g = a f. Note Hz Ratio a to previous note, rounded to 3 decimal places A4 440.00 A#4 466.16 1.059 (466.16 / 440.0 = 1.059, and so on down the column)...


38

First, let's be clear that the standard (major) musical scale divides the octave into seven parts, not eight. The word "octave" comes from eight, because a unison (two notes sounding at the same frequency) is considered to be a "prime" or kind of a "one" in the system, rather than zero. Thus, the first interval created between a note and the next note ...


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, ...


30

Why does standard notation not preserve intervals (visually) It does, but I think you are probably not accustomed to reading it, or how it was developed. Let's first make an analogy with something familiar: reading English. What is the meaning of "right" versus "right?" I can read the words, but only reading the single word isn't going to tell me the ...


28

The division of notes has to do with human perception and psychoacoustics. One description of human perception is the Weber-Fechner law, where a human will perceive equal changes in some sensory input, such as sound level or sound pitch, not by absolute level or value difference, but by the ratio of the change. e.g. larger values need a proportionately ...


27

Yes, it'll change how you listen to music. Anything you learn about will affect your appreciation. Watch a magic trick, and it's magic. Find out how it's done, and it's not magic any more - to you. Several of my students have said that now, they don't listen to music like they used to. ' I know exactly what's happening in that part', 'I know what trick's ...


25

D-D is unison (or "prime") Db-D or D-D# is augmented prime and Db-D# is a double augmented unison or prime. P.S. This is really something different than the enharmonic variants Db-Eb, but that was not the question.


25

C sharp major has seven sharps, D flat major has five flats. Out of the box, the latter is preferable. The former may be more appropriate when there is more material requiring "flattening" the key signature than otherwise. Now major is a rather sharp mode, so it's not quite unlikely. For example, a "proper" fully diminuished chord in C sharp features C-...


24

Modes are what we call rotations of the major scale. This means that we can start off with the major-scale interval pattern and just rotate it to begin at different places to create the other modes. WWHWWWH Ionian (equivalent to the major scale) WHWWWHW Dorian HWWWHWW Phrygian WWWHWWH Lydian WWHWWHW ...


22

The confusion arises from the accidentals. Your answer of a whole step would absolutely be correct if those were sharps (♯), but in fact those accidentals are naturals, not sharps (♮). A note with a natural in front of it cancels any previous accidentals, meaning play the note on the white key. So, E♮ to E♭ is a half step (go down one key from E) and B♭ to B♮...


22

How about "double-diminished fifth". As you noted, some-B to some-F is a fifth, but in this case it's two semitones lower than a perfect fifth. If it were one semitone lower (e.g. B-F) it would be a diminished fifth. And if it's two semitones lower, I'd call it a double-diminished fifth.


22

I think the answer boils down to what you mean by "knowing" the intervals. To do this [sing a tune back] you surely need to be able to know the intervals in the tune you have just heard and then replay it back with your voice. I don't think "knowing" these intervals in order to sing something back means you know if an interval is, e.g., a major or a ...


21

I've always understood that the lower pitch of the harmonic second occurs on the left side: This is also true when additional pitches are added in. On beat four, the E is now on the right because the first second encountered is D–E (and no longer E–F). When you're writing separate voices, however, you write the higher pitch first, with the lower voice ...


20

My answer builds on the answer contributed by DR6. Based on your reaction to other very good answers posted here already, your question seems to boil down to: "Why do humans innately feel that certain intervals are consonant". And so much so that they are willing to call them "perfect". Before getting to that question, let's look at why Western culture ...


20

The interval from any G (flat / sharp / neutral) to any A (flat / sharp / neutral) (in the same octave) is always a second. In your case, since the G is flat and the A is sharp, you have a doubly augmented second. Of course, this interval is sonically equivalent to a major third.


20

It DOES preserve intervals (visually). What it does NOT tell you is whether those intervals are major or minor (or augmented or diminished). The distance of a space to its adjacent line will always be a second of some sort. This is because in part of history (which requires a discussion of Church modes and the history of notation), and partly because the ...


20

What happens if you go down by the same steps: 440Hz 1 step down : 403.33Hz 2 steps down : 366.67Hz 3 steps down : 330.Hz ... 11 steps down : 36.67Hz 12 steps down : 0Hz 13 steps down : -36.67Hz So, using your "equally divided" logic, we are at zero Hz after 12 steps, and the next step beyond that is minus 37 Hz! What does that even mean? But ok, let's ...


19

I really think the answer to this question has most to do with how music is composed. Tonal composers are not really thinking at all about the math behind the intervals; they're thinking about the sounds. Another way of looking at this is that all tonal music is scale-based, and when playing a scale from bottom to top you number the notes starting from 1. ...


19

Not all music theory is based around 7-note scales, but the 7-note diatonic scale basically 'caught on' and became popular due to a number of subjectively useful properties it has. Most of its modes facilitate many opportunities for consonant harmony, chord building around triads, have notes that are close enough for easy melodic construction, and so on, ...


18

A chord does not have to be made up of thirds. A chord is by definition two or more notes heard as if sounded simultaneously. Not all chords have three notes either. There are dyads (two notes), triads (three), tetrachords (four), pentachords (five), and hexachords (six). There's no limit on the number of notes, and also, by definition, there's no limits on ...


18

The technical term for the scale seems to be the Minor "Gypsy" Scale and it is also known as the Flamenco Mode. The basic idea is it is a combination of two Phrygian Dominant tetrachords, or a Phrygian Dominant with a Major 7th scale degree. Here are the links that show both scales match the pattern above and includes the root scale of it the Phrygian ...


18

There are four types of perfect interval: perfect unison, perfect fourth, perfect fifth, and perfect octave. These can be thought of as belonging to two groups. In the first group, all intervals of a unison or an octave are called perfect because the note is not changed. An octave is twice (or half) the frequency of the first note. The second group ...


17

The confusion lies here: I also have heard that an inversion is simply in the opposite direction of the original interval. So a descending 3rd from F to D is the inversion of ascending third F to A. This should instead read "a descending third from F to D is the inversion of an ascending sixth from F to D." The problem really lies in the wording of that ...


17

There is a kind of historic flow back and forth. A very long time ago during the Middle Ages - when parallel organum was way to harmonize - the perfect fourth was consonant. Later when triadic harmony developed along with counterpoint the perfect fourth was treated as a dissonance that resolved to a third. Later yet again, in modern time, the fourth is ...


17

In just intonation, you'd be correct. However, in order for the interval between the top and bottom strings to be exactly two octaves, some compromise needs to be made. (That is, given that the intervals between the open strings are as you say, one major third and all the rest fourths.) As you say, in just intonation, a perfect fourth is 4:3 and a major ...


17

The question has an underlying issue in naming the things it is converting. The formulas given in the question do NOT convert "Hertz to cents" but rather convert interval ratios to cents (and the reverse). The problem can be seen in a couple different ways: The "Hertz numbers" used in the question are not simply numbers, but ratios, like 3/2 = 1.5 being a ...


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