Tuning Systems & Interval Ratios: Difference between revisions
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*Student will have a basic understanding of tuning discrepancies based on harmonics and 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 understand the concept of beats and how they are used to tune an instrument | ||
*Student will be exposed to tuning variations in Indian Raga, Javanese Gamelan, and Maqam | *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 understand the relationship between diatonic intervals and frequency ratios | ||
*Student will be able to derive intervals from frequency calculations | *Student will be able to derive intervals from frequency calculations | ||
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==Resources== | ==Resources== | ||
==== Readings ==== | ====Readings==== | ||
*[https://drive.google.com/ | *[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"] | *[https://www.kylegann.com/microtonality.html Gann, "Information on Alternate Tunings"] | ||
*''Music Crash Courses'': [http://www.musiccrashcourses.com/lessons/tuning_systems.html Tuning Systems] | *''Music Crash Courses'': [http://www.musiccrashcourses.com/lessons/tuning_systems.html Tuning Systems] | ||
*Lewis, [http://leware.net/temper/temper.htm "Understanding Temperaments"] | *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] | |||
==== '''Instructor References''' ==== | ====te'''Instructor References'''==== | ||
* Wolfe, ''Physclips'': [https://www.animations.physics.unsw.edu.au/jw/Tartini-tones-temperament.html Tartini Tones, Consonance, Temperament, Harmony, And Scales] | *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:'' | *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/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/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] | **[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"] | *Rubinstein, "[https://www.math.uwaterloo.ca/~mrubinst/tuning/tuning.html Well vs. Equal Temperament"] | ||
==== '''Listening and Videos''' ==== | ===='''Listening and Videos'''==== | ||
* Cris Forsters Instruments and Music: | *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/chrysalis-i/ Chrysalis (Just Intonation)] | ||
** [https://www.chrysalis-foundation.org/instruments-and-music/just-keys/ Just Keys (Just Intonation Keyboard)] | **[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"] | *The Rasa: [https://www.youtube.com/watch?v=t24geQfXTyA "Microtonal Star Wars Cantina Band"] | ||
* 12Tone: | *12Tone: | ||
** [https://www.youtube.com/watch?v=bWG6CGKMnNA How Many Notes Are There?] | **[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)] | **[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] | *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] | *Huykens-Foker Foundation: [http://www.huygens-fokker.org/microtonality/temperament.html Temperament Examples] | ||
==== Tools ==== | ====Tools==== | ||
* [https://offtonic.com/synth/index.html Offtonic: Microtonal Synthesizer] | *[https://offtonic.com/synth/index.html Offtonic: Microtonal Synthesizer] | ||
* Academo: [https://academo.org/demos/19-tet-keyboard/ 19TET Keyboard] | *Academo: [https://academo.org/demos/19-tet-keyboard/ 19TET Keyboard] | ||
* Sevish: [https://sevish.com/scaleworkshop/ Scale Workshop] | *Sevish: [https://sevish.com/scaleworkshop/ Scale Workshop] | ||
* Apple Logic Pro Manual: [https://support.apple.com/guide/logicpro/tuning-settings-lgcp452f2693/mac Tuning Settings] | *Apple Logic Pro Manual: [https://support.apple.com/guide/logicpro/tuning-settings-lgcp452f2693/mac Tuning Settings] | ||
* Norris: | *Norris: | ||
** [http://www.michaelnorris.info/theory/harmonicseriescalculator Harmonic Series Calculator] | **[http://www.michaelnorris.info/theory/harmonicseriescalculator Harmonic Series Calculator] | ||
** [http://www.michaelnorris.info/theory/frequencytonoteconverter Frequency to Note Converter] | **[http://www.michaelnorris.info/theory/frequencytonoteconverter Frequency to Note Converter] | ||
* Wolfram: [https://demonstrations.wolfram.com/PythagoreanMeantoneAndEqualTemperamentMusicalScales/ Pythagorean, Meantone, and Equal Temperament Scales] | *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] | *Thompson, [http://micro.soonlabel.com/Scott_Thompson/edjiruler.html Just Intonation Interval Calculator] | ||
* [http://www.huygens-fokker.org/scala/ Scala] (software) | *[http://www.huygens-fokker.org/scala/ Scala] (software) | ||
==Class Activities== | ==Class Activities== | ||
*Demonstration of different tuning systems and temperaments | *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 | *Calculation of intervals using just intonation ratios - discussion of tuning discrepancies | ||
*Demonstration of beats | *Demonstration of beats | ||
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
- Handout on Simple Intervals and the Harmonic Series
- Gann, "Information on Alternate Tunings"
- Music Crash Courses: Tuning Systems
- Lewis, "Understanding Temperaments"
- Tobey, A Feeling for Harmony:
teInstructor References
- Wolfe, Physclips: Tartini Tones, Consonance, Temperament, Harmony, And Scales
- Forster, Excerpts from Musical Mathematics:
- Rubinstein, "Well vs. Equal Temperament"
Listening and Videos
- Cris Forsters Instruments and Music:
- The Rasa: "Microtonal Star Wars Cantina Band"
- 12Tone:
- MinutePhysics: Why It's Impossible to Tune a Piano
- Huykens-Foker Foundation: Temperament Examples
Tools
- Offtonic: Microtonal Synthesizer
- Academo: 19TET Keyboard
- Sevish: Scale Workshop
- Apple Logic Pro Manual: Tuning Settings
- Norris:
- Wolfram: Pythagorean, Meantone, and Equal Temperament Scales
- Thompson, Just Intonation Interval Calculator
- 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