**Title:** Seeing Music

**Description:**
In this Illuminations lesson, students calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Seeing Music

**Description:**In this Illuminations lesson, students calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Seeing Music, Hearing Waves

**Description:**
Using this reproducible activity sheet, from an Illuminations lesson, students calculate the frequencies of two octaves of a chromatic musical scale in standard pitch. They then experiment with different combinations of notes and related sine waves to observe why some combinations of musical notes sound harmonious and others have a dissonance.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Seeing Music, Hearing Waves

**Description:**Using this reproducible activity sheet, from an Illuminations lesson, students calculate the frequencies of two octaves of a chromatic musical scale in standard pitch. They then experiment with different combinations of notes and related sine waves to observe why some combinations of musical notes sound harmonious and others have a dissonance.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Seeing Music, Hearing Waves: Selected Answers and Solutions

**Description:**
This reproducible teacher sheet, from an Illuminations lesson, provides selected solutions to an activity in which students calculate the frequencies of two octaves of a chromatic musical scale in standard pitch. Students then experiment with different combinations of notes and related sine waves to observe why some combinations of musical notes sound harmonious and others have a dissonance.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Seeing Music, Hearing Waves: Selected Answers and Solutions

**Description:**This reproducible teacher sheet, from an Illuminations lesson, provides selected solutions to an activity in which students calculate the frequencies of two octaves of a chromatic musical scale in standard pitch. Students then experiment with different combinations of notes and related sine waves to observe why some combinations of musical notes sound harmonious and others have a dissonance.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** To Fret or Not to Fret

**Description:**
In this unit of two lessons, from Illuminations, students explore geometric sequences and exponential functions by considering the placement of frets on stringed instruments. They study the placement of frets on a fretted instrument then use their discoveries to place frets on a fretless instrument.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**To Fret or Not to Fret

**Description:**In this unit of two lessons, from Illuminations, students explore geometric sequences and exponential functions by considering the placement of frets on stringed instruments. They study the placement of frets on a fretted instrument then use their discoveries to place frets on a fretless instrument.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** To Fret or...

**Description:**
This reproducible activity, from an Illuminations lesson, features questions dealing with measuring distances on fretted stringed instruments.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics

**Title:**To Fret or...

**Description:**This reproducible activity, from an Illuminations lesson, features questions dealing with measuring distances on fretted stringed instruments.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Not to Fret

**Description:**
This reproducible activity sheet, from an Illuminations lesson, presents a line drawing of a guitar's neck showing the location of the nut and the 12th fret. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Not to Fret

**Description:**This reproducible activity sheet, from an Illuminations lesson, presents a line drawing of a guitar's neck showing the location of the nut and the 12th fret. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** To Fret or Not to Fret

**Description:**
This reproducible worksheet, from an Illuminations lesson, presents a series of questions related to fretted instruments and geometric sequences. In the lesson, students compare geometric sequences with exponential functions.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**To Fret or Not to Fret

**Description:**This reproducible worksheet, from an Illuminations lesson, presents a series of questions related to fretted instruments and geometric sequences. In the lesson, students compare geometric sequences with exponential functions.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Exploring Measurement, Sequences, and Curves with Stringed Instruments

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students measure lengths on stringed musical instruments. They discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Exploring Measurement, Sequences, and Curves with Stringed Instruments

**Description:**In this lesson, one of a multi-part unit from Illuminations, students measure lengths on stringed musical instruments. They discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Fretting

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use their discoveries from the first lesson to place frets on a fretless instrument. They then compare geometric sequences with exponential functions.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Arts,Mathematics

**Title:**Fretting

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use their discoveries from the first lesson to place frets on a fretless instrument. They then compare geometric sequences with exponential functions.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12