# Tag Info

12

You are exactly correct that it is the logarithmic nature of pitch that causes this effect. In cases like this, I find that a picture is helpful. Here I've labeled equally spaced octaves (1200 cents) along the x-axis (representing pitch). I've then labeled the corresponding frequencies on the y-axis as multiples of some arbitrary base frequency f. Note that ...

11

A trivial answer : yes. When I was quite young I wrote a computer program to spit out a succession of 'beeps' at random frequencies not related to any musical scale; I suspect many people who have a computer and a bit of an interest in music have done the same. In practice how close you could get to infinity (!) would be limited by the resolution at which ...

6

"Harmonies" by Gyorgy Ligeti is an interesting example of microtonal music. It's written for organ, but it's intended to be played with reduced air and manipulation of the stops, so the pipes don't play at their designed frequency. With (mainly) slow chord changes and wide voicings the overall effect is a slowly evolving harmony and dissonance through the ...

5

While 1.5 lies perfectly in the arithmetic middle of 1 and 2, the arithmetic middle is not relevant for music. The intervallistic middle of two frequencies is their geometric mean. Go two octaves up, and your frequency goes from 1 to 4 times its value. But one octave up is not 2.5 times the frequency, but rather 2 times. So if you have two notes with ...

5

Well, how about the starting clarinet solo in Gershwin's "Rhapsody in Blue"? It's been almost a century ago. Granted, doing the glissando continuously on its last part was not written into the score originally but was rather an impromptu trick by the clarinetist that the composer then insisted on incorporating into the premiere, but it has been very much ...

5

It depends on how you define the 12-tone octave. Up until at least the 19th century, several theories did not use equal temperament to conceptual musical space. Imagine that you ascend from C by perfect fifth; if you do this twelve times in equal temperament, you will end on a C that is perfectly in tune with the original starting C. If, however, you do ...

5

I would just add the (possibly obvious) answer that a capella choirs can also drift off because of singing out of tune. Typically, they tend to get flatter if the music has lots of jumps to high notes, which they don't quite get up to, and they sometimes get sharper if they are nervous about getting flat. I've experienced both in concerts.

4

Yes, many old organs were built with only some of the 12 chromatic keys in some octaves (particularly the lowest one, since the biggest pipes are the most expensive ones). The reason is that the more remote chromatic tones were rarely used in compositions of the time, and so this saved a lot of money for only a little inconvenience. The same was also done ...

4

The octave can be split into more intervals than 12. There is 19 equal temperament, and other temperaments based on octave division into 31, 41 or 53 equal intervals. Some 30 years ago I had to work on a mathematical problem where it was proved that some divisions were "better" than others. Better in the sense that they better approximated simple fractions. ...

4

theory that works on a continuous (or non-quantized octave). In musique concrète, the theoretical framework is audio waveforms, not octaves or tunings or scales. You’re not limited to a system of writing down musical notes so that the next person can play them on a standard instrument with a standard octave and standard tuning, because you write down ...

4

I would like to add the point that the comma pump may happen in either direction, resulting ascending or descending drift. However, tonal music is such that the intervals between the roots (the fundamentals of the chords) usually appear in one direction and not in the other: descending fifths or ascending fourths and ascending seconds, mainly. As a result, ...

4

First of all, putting a capo on does not change the temperament of your guitar. Your guitar temperament is equal temperament so and that's not changing so forget about the temperament aspect of this.. The only thing it does is change what strings are "Open". So without a capo, your open strings are the typical E-A-D-G-B-E. For every fret you move it, all ...

3

For practical musical performance purposes, a capo simply transposes up by a semitone per fret. All notes are "theoretically" simply higher by the number of semitones times the number of frets you move the capo. In a perfect world, what the capo attempts to do is the same effect as re-tuning your guitar one half step sharp for each capo position. In the ...

3

In terms of frequency ratios "flattening" is not "subtracting" at least not mathematical subtraction. In the way that you are expressing it the mean tone fifth would be (3/2)/[ (81/80)**(1/4)]=1.495... The reduction is achieved by division. Often you want to think about things in terms of cents: a logarithmic measure of pitch. By working with these the ...

2

John Luther Adams created a sonification for weather, astronomical and geological data in real time, called The Place Where You Go to Listen The sound parameters (mostly pitch, by I think others too) change "continuosly" (between comas, as of course we are talking about discrete digital events incrementally changing in time) according to the actual external ...

2

Mathematically, everything about pitch is logarithmic. "Adding a perfect fifth" really means "multiply the pitch by 3/2. So "subtracting a syntonic comma" means multiplying by the reciprocal of the comma; and "a quarter of" means the fourth root of. So try working out: 3/2 x 4th-root(81/80) ...and see if this is more like the correct answer. (I haven't ...

2

Well, before the keyboard instruments were well tempered [think of the Well-Tempered Klavier], it was impossible to play in tune (i.e. with good intonation) in certain keys. And by the old system it would be impossible to do the annual (or semi-annual) tuning in such a way as to be able to play all keys in tune. Modern string players still have this ...

2

Why do you require abbreviation? If there's a perfectly good term for this that doesn't use an abbreviation, will it be acceptable? "Notes per octave" or "pitches per octave" seem pretty widely used, universally understood, and tuning-agnostic. As an extension of this, scales themselves can be described as n-tonic, where n is a Greek number (as in, "...

2

A capo is a transposition device: everything gets moved to a higher pitch while retaining the same voicing that you have in the lower position. The resulting chord voicing may differ from playing the chord with the same "name" without capo. As an example, playing G major without capo will usually be voiced as G B d g b g', so 1-3-5-8-10-15 in scale steps. ...

1

That ratio applies to the frequency which is an absolute measurement, not cents which more of a relative distance measurement between notes. They are different in nature. Just a simple example, the perfect fifth above A4 (440 Hz) is E5 (660 Hz Just intonation/ 659.26 Equal temperament). This is where it makes sense to describe the interval in a ratio. A4 ...

1

A perfect fifth is just that. It's a fifth from the root, but that's not exactly the halfway point. That's saved for the TRITONE, which actually sounds an odd interval to some - used to be called 'the Devil's interval'. The tritone is equidistant from the root either way, so must be halfway. You're right that the P5 is not in the middle.

1

•Was I lucky in my example chord choice or does it always work like that? It will always work like that. (Capo-ing 1 fret higher will result in the same chord quality (minor, major etc) with a name (in this case E) that is a half step up in the case of 1 fret since 1 fret = one half step.) •If there IS a difference, is it all due to temperament? What ...

1

Temperament refers to consistent establishment of the relationship among the notes of an instrument, to adhere to a particular theory of pitch. Why the word "temper" is used is because the idea is that any means of choosing pitches for an instrument (particularly an instrument which supports modulation) is a compromise away from the pure intervals: the pure ...

1

Researchers in psychoacoustics and music psychology have been studying this for a long time. I believe it's Plomp and Levitt showed that, with intervals, if you take just the fundamental, interval dissonance simply decreases with interval size (m2, M2, m3, M3...M7...) but if the overtone of each note are added in, you eventually get the well-established ...

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