Tuning Systems & Interval Ratios: Difference between revisions

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== Objectives ==
{{FSM}}
* Students will understand the concept of tuning systems and temperaments.
* Students will understand the basics of twelve-tone tuning systems
* Students will be able to derive harmonic frequencies according to simple arithmetic calculations (using harmonics or interval ratios).


== Resources ==
==Objectives==


*Students will understand the concept of tuning systems and temperaments.
*Student will understand the basis of 12-TET tuning (including definitions of cents and semitones)
*Student will know the general differences between 12-TET and just intonation.
*Students will be able to derive harmonic frequencies according to simple arithmetic calculations (using harmonics or interval ratios).
*Student will have a basic understanding of tuning discrepancies based on harmonics and interval ratios
*Student will understand the concept of beats and how they are used to tune an instrument
*Student will be exposed to tuning variations and fluidity in Indian Raga, Javanese Gamelan, Mariachi, Tuva Throat Singing, and Maqam
*Student will understand the relationship between diatonic intervals and frequency ratios
*Student will be able to derive intervals from frequency calculations


== Class Activities ==
==Resources==
* Demonstration of different tuning systems and temperaments


== Assignments ==
====Readings====


*[https://drive.google.com/file/d/1YX8hD26kSaUAQXP4VbYRuwUqggBNoisd/view?usp=sharing Handout on Simple Intervals and the Harmonic Series]
*[https://www.kylegann.com/microtonality.html Gann, "Information on Alternate Tunings"]
*''Music Crash Courses'': [http://www.musiccrashcourses.com/lessons/tuning_systems.html Tuning Systems]
*Lewis, [http://leware.net/temper/temper.htm "Understanding Temperaments"]
*Tobey, ''A Feeling for Harmony'':
**[http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/FFH1_CH1/1M_RatiosCommas1.html Chapter 1M: Music Math Ratios Part 1]
**[http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/FFH1_CH2/2C_Consonance-Dissonance.html Chapter 2C: Consonance and Dissonance]
**[http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/FFH1_CH2/2E_JustIntonation.html Chapter 2E: Just Intonation]
**[http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/FFH1_CH2/2M_HarmonicSeries.html Chapter 2M: Harmonic Series]
**[http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/FFH1_CH2/2D_Pythagorean-Intonation.html Chapter 2D: Pythagorean Intonation]
**Optional Material on Commas - [http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/FFH1_CH1/1N_Pythagorean_Comma.html Chapter 1N: The Pythagorean Comma], [http://legacy.earlham.edu/~tobeyfo/musictheory/Book1/FFH1_CH2/2F_SyntonicComma.html 3E: The Other Commas]


== Assessments ==
====te'''Instructor References'''====


*Wolfe, ''Physclips'': [https://www.animations.physics.unsw.edu.au/jw/Tartini-tones-temperament.html Tartini Tones, Consonance, Temperament, Harmony, And Scales]
*Forster, Excerpts from ''Musical Mathematics:''
**[https://www.chrysalis-foundation.org/musical-mathematics-pages/just-intonation/ Just Intonation]
**[https://www.chrysalis-foundation.org/musical-mathematics-pages/origins-of-length-ratios/ Origin of Length Ratios]
**[https://www.chrysalis-foundation.org/musical-mathematics-pages/philolaus-and-euclid/ Greek Classification of Ratios, Tetrachords, Scales, and Modes]
*Rubinstein, "[https://www.math.uwaterloo.ca/~mrubinst/tuning/tuning.html Well vs. Equal Temperament"]


== Notes ==
===='''Listening and Videos'''====
 
*Cris Forsters Instruments and Music:
**[https://www.chrysalis-foundation.org/instruments-and-music/chrysalis-i/ Chrysalis (Just Intonation)]
**[https://www.chrysalis-foundation.org/instruments-and-music/just-keys/ Just Keys (Just Intonation Keyboard)]
*The Rasa: [https://www.youtube.com/watch?v=t24geQfXTyA "Microtonal Star Wars Cantina Band"]
*12Tone:
**[https://www.youtube.com/watch?v=bWG6CGKMnNA How Many Notes Are There?]
**[https://www.youtube.com/watch?v=8syA7S_5E3A Can You Tell These Notes Apart? (The Syntonic Comma)]
*MinutePhysics: [https://www.youtube.com/watch?v=1Hqm0dYKUx4 Why It's Impossible to Tune a Piano]
*Huykens-Foker Foundation: [http://www.huygens-fokker.org/microtonality/temperament.html Temperament Examples]
 
====Tools====
 
*[https://offtonic.com/synth/index.html Offtonic: Microtonal Synthesizer]
*Academo: [https://academo.org/demos/19-tet-keyboard/ 19TET Keyboard]
*Sevish: [https://sevish.com/scaleworkshop/ Scale Workshop]
*Apple Logic Pro Manual: [https://support.apple.com/guide/logicpro/tuning-settings-lgcp452f2693/mac Tuning Settings]
*Norris:
**[http://www.michaelnorris.info/theory/harmonicseriescalculator Harmonic Series Calculator]
**[http://www.michaelnorris.info/theory/frequencytonoteconverter Frequency to Note Converter]
*Wolfram: [https://demonstrations.wolfram.com/PythagoreanMeantoneAndEqualTemperamentMusicalScales/ Pythagorean, Meantone, and Equal Temperament Scales]
*Thompson, [http://micro.soonlabel.com/Scott_Thompson/edjiruler.html Just Intonation Interval Calculator]
*[http://www.huygens-fokker.org/scala/ Scala] (software)
 
==Class Activities==
 
*Demonstration of different tuning systems and temperaments
*Demonstration of interval ratios using a monochord.
*Calculation of intervals using just intonation ratios - discussion of tuning discrepancies
*Demonstration of beats
 
==Assignments==
 
 
==Notes==
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[[Category:Theory 1]]
[[Category:Fundamentals of Sound & Music]]
[[Category:Acoustics]]
[[Category:Harmony]]

Latest revision as of 19:04, 21 December 2024

This lesson is part of the Fundamentals of Sound & Music module.

Objectives

  • Students will understand the concept of tuning systems and temperaments.
  • Student will understand the basis of 12-TET tuning (including definitions of cents and semitones)
  • Student will know the general differences between 12-TET and just intonation.
  • Students will be able to derive harmonic frequencies according to simple arithmetic calculations (using harmonics or interval ratios).
  • Student will have a basic understanding of tuning discrepancies based on harmonics and interval ratios
  • Student will understand the concept of beats and how they are used to tune an instrument
  • Student will be exposed to tuning variations and fluidity in Indian Raga, Javanese Gamelan, Mariachi, Tuva Throat Singing, and Maqam
  • Student will understand the relationship between diatonic intervals and frequency ratios
  • Student will be able to derive intervals from frequency calculations

Resources

Readings

teInstructor References

Listening and Videos

Tools

Class Activities

  • Demonstration of different tuning systems and temperaments
  • Demonstration of interval ratios using a monochord.
  • Calculation of intervals using just intonation ratios - discussion of tuning discrepancies
  • Demonstration of beats

Assignments

Notes

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