Music Theory 171 Questions on Chapters 3A, 3B and 3C 3A
... 2. What does this say about the relationship between the fifth, the fourth and the
3. What is created between the fifth and the fourth, and what is its ratio?
4. The notes of the major, minor, Phrygian and Middle Eastern tetrachords and listed
on this page. Transpose them to the key of D and ...
... Octave interval is simple ratio
Fifth is a simple ratio
Fourth is a simple ratio
Major third is a simple ratio
Minor third is a simple ratio
... Transitional attempt to create a transposable scale based on simple integer
... • equal musical intervals - equal frequency ratio
• 44on a “multiplicative” number line (=log scale) equal ratios are equidistant
• advantage: in graphs below equal intervals have same length
... A major diatonic scale has
(the 8th would be an
The intervals are not all semitones
whole tone is about a factor of (1.06)2 = 1.12
Music 170 Homework problem set 6 (due Nov. 3) 1. Two pipes, both
... successive harmonics (first an octave, then a fifth, and so on.) Which is the first of these
intervals that is less than a tempered whole tone? A tempered semitone?
4. In the just scale (Rossing page 179), C to E is a perfect major third and E to G is a perfect
minor third. What other intervals aris ...
“Tuning and temperament” by Rudolph Rasch Know who and where
... ¶1 Now you can see why Glarean used 24 × 36 for his full string: it makes it easy to find several
Pythagorean (3:2) fifths.
¶2 “Sharps do not have a place . . . .”: In Pythagorean tuning, enharmonic spelling makes a big
difference. Find the number corresponding to B on Glarean's chart. Use some math ...
On Ben Johnston`s Notation and the Performance
... and thirds. In his book he uses the conventional note-names to represent a
series of perfect fifths. So, for example, the common open strings are written
conventionally as C - G - D - A - E. To make a simple consonant interval with C
and G (thereby completing a triad tuned in the proportion 4:5:6) E ...
... a. Label the lines on the scale generation template attached with fractions
representing the frequency ratios in just tuning.
b. Which interval is worst approximated (in cents) by an equally tempered interval?
Other than the octave, which is best approximated?
c. How many pure fifths are there in th ...
The Pythagorean Comma The Spiral of Fifths and Equal Temperament
... Counting up by seven octaves (ratios of 2/1) from C 32.7 Hz winds up
at C 4185.6 Hz but counting up by twelve fifths (ratios of 3/2) yields C
4242.7 Hz. This discrepancy is known as the Pythagorean Comma and has
been a powerful challenge for instrument makers and tuners. Fixed note
instruments like ...
Lecture 14a: Additional Remarks on Tuning Systems In previous
... Similarly, one can base a 31-note scale on approximating the
meantone fifth 5^(1/4).
2. Expanding Just Intonation Another route that leads to an increased
number of notes in the octave is to allow rational ratios involving
prime factors greater than 5. (Recall that just intonation involves
Chapter 15 - SFA Physics and Astronomy
... tones (even in dead rooms) so long as the
tones are sounded close in time.
Setting intervals for pure sinusoids (no
partials) is difficult if the loudness is small
enough to avoid exciting room modes.
At high loudness levels there are enough
harmonics generated in the room and ear
to permit good ...
... the distance of an interval is one part of its
name, but there’s more: every interval has another
quality to it, which we’ll call inflection.
inflection is a bit harder to understand, partly because
some theorists use
it depends on the type of interval. so let’s start by
the term quality for
Musical Interval and Ratio
... ‘The distance between two notes, measured as the ratio of their pitches, is called an
interval. If the interval between two notes is a ratio of small integers (such as 2/1,3/2, or 4/3),
they sound good together - they are consonant rather than dissonant.
The pure intervals smaller than or equal to a ...
... Construct as a geometric series - successive multiplication by 1.5
How many intervals to create – e.g., how to divide up the octave?
Answer = 12 and still holds true today (for western music anyway)
Interesting that we don’t use his system anymore but standardized on 12
Modern Western Tuning System - Digital Commons @ Kent State
... perfect fifth, while 2:1 or 1:2 represent an ascending or descending octave.
In order to create a 12-tone chromatic scale Pythagoras had to omit the Gb
(which is supposed to be the same note as F#, however this tuning produces two
different frequency rations for these notes) only using the 12 remain ...
Music 181: Structure of the Major Scale
... Half Step; Half Tone; Semitone: Used generically for any interval that can be represented by two adjacent keys on
Whole Tone; Whole Step: Used generically for any interval made up of two half steps. Whole tones are separated
by one key on piano.
`frequency`. - Programma LLP
... second ‘dissonant’? Notice how in the first graphic there is a repeating pattern: every 3rd
wave of the G matches up with every 2nd wave of the C (and in the second graphic how
there is no pattern). This is the secret for creating pleasing sounding note combinations:
Frequencies that match up at reg ...
intervals and scales
... key and an adjacent black piano key. You’ll also notice that there is no black note between E
and F or between B and C, so the interval between those notes is also a semitone.
A whole tone is two semitones: examples are C to D, D to E, F to G, G to A and A to B (there
is a black note between each of ...
notes and equations
... An interval is a ratio between two frequencies. The interval between two musical tones is the ratio
between their fundamental frequencies.
A perfect interval is the ratio between two small integers (typically below 6). Commonly used
perfect intervals are:
Music 11, 7/10/06 Scales/Intervals We already know half steps and
... We already know half steps and whole steps (semitones and tones).
We call these “seconds.”
Adjacent pitch names are always called seconds, but because the space between adjacent
pitch names can vary, there are different types of second:
Major second (M2) = whole step = whole tone
Minor second (m2) = ...
Quarter-comma meantone, or 1/4-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. This method is a variant of Pythagorean tuning. The difference is that in this system the perfect fifth is flattened by one quarter of a syntonic comma, with respect to its just intonation used in Pythagorean tuning (frequency ratio 3:2). The purpose is to obtain justly intoned major thirds (with a frequency ratio equal to 5:4). It was described by Pietro Aron (also spelled Aaron), in his Toscanello de la Musica of 1523, by saying the major thirds should be tuned to be ""sonorous and just, as united as possible."" Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exactitude.