Does anyone know how to express a chromatic scale in intervals
ie~d to A=a fifth so starting from D how would the chromatic scale go?
RORY
D-E : major tone or major second
D-F : minor third and D-F# : major third
D-G : just fourth
D-A : just fifth
D-B : major sixth
D-C : minor seventh and D-C# : major seventh
D-D : octave
I hope it’s right.
Thanks Phcook thats nearly it, but I,m looking for the notes in between as well
RORY
D-Eb/D# : minor tone or minor second
D-E : major tone or major second
D-F : minor third
D-F#/Gb : major third
D-G : just(perfect) fourth
D-G#/Ab: augmented fourth
D-A : just(perfect) fifth
D-A#/Bb: minor sixth
D-B : major sixth
D-C : minor seventh
D-C# : major seventh
D-D : perfect eighth (octave)
almost phcook
INTERVAL RATIO
D-Eb/D# : minor tone or minor second 16/15
D-E : major tone or major second 9/8
D-F : minor third 6/5
D-F#/Gb : major third 5/4
D-G : just(perfect) fourth 4/3
D-G#/Ab: augmented fourth Squar root of 2 (irrational)
D-A : just(perfect) fifth 3/2
D-A#/Bb: minor sixth 8/5
D-B : major sixth 5/3
D-C : minor seventh 7/4
D-C# : major seventh 15/8
D-D : perfect eighth (octave) 2/1
I would quible with Minor tone which is to my understanding an 8/7 interval.
TTFN
John S
John
the minor tone is smaller than the major tone and is 10/9, so that when you have one major tone followed bay one minor tone, you have
(10/9)*(9/8 ) = 5/4 which should be a just third, not a major third.
A major third consists in 2 major tones, that is 9/8*9/8 = 81/64
If somebody is interested by ratios, we can discuss about it, but be careful: we can’t use a tempered scale and say that, for instance, G# is Ab!
Best wishes
I’m new to the theory side of music so forgive me if I make an obvious error. I am just trying to clear something in my head. In Dave Hegarty’s book on the Natural or just intonation scale C natural is given a value of
-3.89cents . But if you work it out as C natural being a minor third above A with A being +1.955 C natural should have a value of 17.596 using the equation that tuning a pure minor third above any given note that the minor third should be +15.6cents.
Rory
I would assume (not knowing for sure) that it is NOT a minor third above A
(not perfectly anyway) however, I don’t follow your numbers so I may be off the wall
Hi Rory
You’ve discovered the problem with natural scales
The majority of people are familiar with equal tempered instruments such as keyboards, Guitars where the difference between each note is the same - i.e. a semitone has the value of 100 cents and accidentals such as G# and Ab are at the same pitch
With bagpipes there is a problem with this in that several pipes can be sounding at once - chanter plus drone (and regulators in our case). It is the reference note from the drone where the difficulty lies in that the chanter must play a scale that is in tune with both the fundamental note of the drone and its harmonics.
This is the scale given by John and PHCook above and is known as Just Intonation. The only ammendment is that when using this type of intonation Ab and G# or F# and Gb will each have different frequencies because they form parts of different scales and are not the same note.
Natural scales and multi-octave instruments do not mix well. An often quoted example being a piano where if you go round in a circle of fifths using just intonation where the difference is just two cents (i.e. C-G-D-A-E-etc) then by the time you get back to your starting note several octaves higher it is 22 cents too sharp (Known as a ‘comma’)
A basic description is given on my website
http://www.bagpipeworld.co.uk/Tuning.htm
For an in depth approach try Benades “Fundamentals of Musical Accoustics” which should be available via the Library service
Thanks all
I was reading the leaflet that goes with a ca30 tuner and it states(if you want to tune a minor third above A set the note name display to C, and make the meter indicate +15.60)
It also gives the information that if you want to tune a pure major third above or a pure minor third above a certain note make the meter indicate(-13.7) or (+15..6)
This works fine on the just intonation values given in dave hegartys book except for the Cnat and thats where I,m lost
I,m sure there.s a simple answer hopefully I,ll find it soon
RORY
Further reading
Try and get a copy of Howard Goodall’s
“Big Bangs, The story of discoveries that changd musical history”.
ISBN 0-099-28354-9
The chapter ‘Accidentals will happen’ is an easy reading approach to temperaments - better than the technical book by Benade.
The c natural (flat 7th) is an ellusive note on pipes as to make it harmonise and it needs to be flat of its theoretical pitch to blend with the drone.
A minor third consists of one major tone and one diatonic semitone, and the ratio for a minor third is 32/27, for instance between E and F, or B and C.
Don’t forget that the scale in cents is for a tempered scale, which consists in 12 “regular” (logarithmically speaking) semitones.
For Cnat:
take A=440, then you get Cnat = 440*32/27 = 521,48Hz
Take A = 440, you should have B = (9/8 )*440 = 495Hz
If you calculate B with the tempered scale, you’ll have 2 semitones between A and B, so B = A*(1,00057779^200) = 493,88Hz, which is lower.
If you calculate with the tempered scale, you find 3 semitones between A and C, so you should caculate
Cnat = A*(1,00057779^300 ) = 523,25Hz
which is 294,13 cents above A
The difference is 5,87cents
Never refer to the tempered scale for pipes!
All the best
Philippe