why do a capella singers go flat…? the mathematics of tuning systems in music colin graham...
TRANSCRIPT
![Page 1: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/1.jpg)
Why do a capella singers go flat…?The mathematics of tuning systems in musicColin Graham@ColinTGraham
![Page 2: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/2.jpg)
Some points to consider Division of the
octave
![Page 3: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/3.jpg)
Some points to consider Division of the
octave Number of pitches
to be used
![Page 4: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/4.jpg)
Some points to consider Division of the
octave Number of pitches
to be used
Tuning of the pitches
![Page 5: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/5.jpg)
Western tuning systems Equal
temperament Based on dividing
into 12 equal parts
![Page 6: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/6.jpg)
Western tuning systems Equal
temperament Pythagorean
tuning
Based on dividing into 12 equal parts
Based on ‘perfect fourths’ and ‘fifths’
![Page 7: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/7.jpg)
Western tuning systems Equal
temperament Pythagorean
tuning Just intonation
Based on dividing into 12 equal parts
Based on ‘perfect fourths’ and ‘fifths’
Based on whole-number ratios
![Page 8: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/8.jpg)
Fundamentally harmonic…
![Page 9: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/9.jpg)
A matter of ratios… 5/12 = 5/6 = 5/3 = 10/3 = 20/3
![Page 10: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/10.jpg)
A matter of ratios… 5/12 = 5/6 = 5/3 = 10/3 = 20/3
Get used to it, if you want to read about tuning theories!
![Page 11: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/11.jpg)
A matter of ratios… 5/12 = 5/6 = 5/3 = 10/3 = 20/3
Get used to it, if you want to read about tuning theories!
![Page 12: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/12.jpg)
What to choose?
EqualTempered
Justintoned
Pythagorean
tuning
466.2 7/4 = 457.8 16/9 = 465.1
392.0 3/2= 392.4
329.6 5/4 = 327.1 81/64 = 331.1
261.6
Frequencies in Hertz based on A = 440Hz
![Page 13: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/13.jpg)
Now the fun begins!
![Page 14: Why do a capella singers go flat…? The mathematics of tuning systems in music Colin Graham @ColinTGraham](https://reader035.vdocuments.site/reader035/viewer/2022081518/5518a167550346b31f8b48a6/html5/thumbnails/14.jpg)
Now the fun begins!