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Pythagorean tuning

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3; as Novalis put it, "The musical proportions seem to me to be correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2, ≈702 cents wide. The system had been attributed to Pythagoras by modern authors of music theory, while Ptolemy, Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium", "tonus", "tonus" in Latin, to Eratosthenes; the so-called "Pythagorean tuning" was used by musicians up to the beginning of the 16th century. "The Pythagorean system would appear to be ideal because of the purity of the fifths, but some consider other intervals the major third, to be so badly out of tune that major chords a dissonance."The Pythagorean scale is any scale which can be constructed from only pure perfect fifths and octaves.

In Greek music it was used to tune tetrachords and the twelve tone Pythagorean temperament was developed by medieval music theorists using the same method of tuning in perfect fifths, however there is no evidence that Pythagoras himself went beyond the tetrachord. A distinction can be made between a 12-tone Pythagorean temperament. Extended Pythagorean tuning corresponds 1-on-1 with western music notation and there is no limit to the number of fifths. In 12-tone Pythagorean temperament however one is limited by 12-tones per octave and one cannot play most music according to the Pythagorean system corresponding to the enharmonic notation, instead one finds that for instance the diminished sixth becomes a "wolf fifth". 12-tone Pythagorean temperament is based on a stack of intervals called perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1. Starting from D for example, six other notes are produced by moving six times a ratio 3:2 up, the remaining ones by moving the same ratio down: E♭–B♭–F–C–G–D–A–E–B–F♯–C♯–G♯This succession of eleven 3:2 intervals spans across a wide range of frequency.

Since notes differing in frequency by a factor of 2 are given the same name, it is customary to divide or multiply the frequencies of some of these notes by 2 or by a power of 2. The purpose of this adjustment is to move the 12 notes within a smaller range of frequency, namely within the interval between the base note D and the D above it; this interval is called the basic octave. For instance, the A is tuned such that its frequency equals 3:2 times the frequency of D—if D is tuned to a frequency of 288 Hz A is tuned to 432 Hz; the E above A is tuned such that its frequency equals 3:2 times the frequency of A, or 9:4 times the frequency of D—with A at 432 Hz, this puts E at 648 Hz. Since this E is outside the above-mentioned basic octave, it is usual to halve its frequency to move it within the basic octave. Therefore, E is tuned to 324 Hz, a 9:8 above D; the B at 3:2 above that E is tuned to the ratio 27:16 and so on. Starting from the same point working the other way, G is tuned as 3:2 below D, which means that it is assigned a frequency equal to 2:3 times the frequency of D—with D at 288 Hz, this puts G at 192 Hz.

This frequency is doubled to bring it into the basic octave. When extending this tuning however, a problem arises: no stack of 3:2 intervals will fit into any stack of 2:1 intervals. For instance a stack such as this, obtained by adding one more note to the stack shown above A♭–E♭–B♭–F–C–G–D–A–E–B–F♯–C♯–G♯will be similar but not identical in size to a stack of 7 octaves. More it will be about a quarter of a semitone larger, called the Pythagorean comma. Thus, A ♭ and G ♯, when brought into the basic octave, will not coincide; the table below illustrates this, showing for each note in the basic octave the conventional name of the interval from D, the formula to compute its frequency ratio, its size in cents, the difference in cents between its size and the size of the corresponding one in the tempered scale. In the formulas, the ratios 3:2 or 2:3 represent an ascending or descending perfect fifth (i.e. an increase or decrease in frequency by a perfect fifth, while 2:1 or 1:2 represent an rising or lowering octave.

The major scale based on C, obtained from this tuning is: In equal temperament, pairs of enharmonic notes such as A♭ and G♯ are thought of as being the same note—however, as the above table indicates, in Pythagorean tuning they have different ratios with respect to D, which means they are at a different frequency. This discrepancy, of about 23.46 cents, or nearly one quarter of a semitone, is known as a Pythagorean comma. To get around this problem, Pythagorean tuning constructs only twelve notes as above, with eleven fifths between them. For example, one may use only the 12 notes from E♭ to G♯. This, as shown above, implies that only eleven just fifths are used to build the entire chromatic scale; the remaining interval is left badly out-of-tune, meaning that any music which combines those two notes is unplayable in this tuning. A out-of-tune interval such as this one is k

Dhamtari district

Dhamtari is abbreviated from "Dhamma" + "Tarai" district and is situated in the fertile plains of the Chhattisgarh region. This district is situated at 81 ° 33' E longitude. Dhamtari district was formed on 6 July 1998 dividing the Raipur district the capital of Chhattisgarh along with Mahasamund; as a result, the boundaries of the Raipur district is converted into the districts e.g. Raipur and Dhamtari. Dhamtari and Nagari are included in Dhamtari district as tehsils and Dhamtari, Kurud and Magarlod are included as blocks; the total area of the district is 305 meters above mean sea level. The district is surrounded by District Raipur in the north and District Kanker as well as Bastar in the south, part of Orissa state in east and District Durg and Kanker in west. Mahanadi is the principal river of this district and Mahanadi is so far named as Kankannadi, Neelotpala, Jairath, etc, its tributaries being Pairy, Jonk and Shivnath. The fertility of lands of Dhamtari district can be attributed to the presence of these rivers.

The chief crop of this region is paddy. Mahanadi. Dhamtari district falls between two Lok Sabha constituencies and three Assembly constituencies. National Highway No. 30 Raipur – Vizianagaram passes through Dhamtari. Raipur is 78 km from Dhamtari. A unique feature of Dhamtari is the total number of rice mills, more than 136. In the east, Satpura range is located, it is popularly known. Kanker district lies in the west. In North lies Raipur, the heart and capital city of Chhattisgarh. Southwards lies the boundary of Odisha state. Ravishankar Sagar dam that irrigates 57000 Hectare of land and acts as a main supply unit of safe drinking water resource for state capital Raipur as well as supply to Bhilai Steel Plant lies at 11 km from the District capital. Work of 10 MW hydro-electric power plant is progressing and is to be completed soon. Asia's first Siphon dam was built in the year 1914 at Madamsilli. Besides Madamsilli, Sondur dam, Dudhawa dam are the major projects; the present collector of Dhamtari is Shri C. R. Prasanna.

The Mahanadi River is the principal river of this district and till this area it is named as Kankannadi, Neelotpala, Jairath etc. Its tributaries are Seonath, Sondur, Joan and Shivnath; the fertility of lands of Dhamtari district can be attributed to the presence of these rivers. The chief crop of this region is paddy. Mahanadi one of the major river in central India originates in the hills of Sihawa flows in an easterly direction into the Bay of Bengal; the National Highway No. 07 Raipur – Vizianagaram passes through Dhamtari. Raipur is 78 km from Dhamtari. Dhamtari has over 136 rice mills. Ravishankar Sagar dam that irrigates 570 square kilometres of land and acts as a main supply unit of safe drinking water resource for state capital Raipur as well as supply to Bhilai Steel Plant lies 11 km from the district capital. Two hydro-power plants of 10 MW and 1.2 MW are installed there. Asia's first Syphen dam was built in 1914 at Madamsilli. Besides Madamsilli, Sondur dam and Dudhawa dam are the major projects.

52 per cent of the geographic area is covered by forests. The district has a tropical climate. According to the 2011 census Dhamtari district has a population of 799,781 equal to the nation of Comoros or the US state of South Dakota; this gives it a ranking of 485th in India. The district has a population density of 209 inhabitants per square kilometre, its population growth rate over the decade 2001-2011 was 13.11%. Dhamtari has a sex ratio of 1010 females for every 1000 males, a literacy rate of 90.0%. At the time of the 2011 Census of India, 98.12% of the population in the district spoke Chhattisgarhi, 0.57% Marathi and 0.49% Sindhi as their first language. Out of the three assemblies in the district the Sihawa Constituency is inhabited by the majority of tribal all over the district with a significant majority population in the district, with a good population in Dhamtari and Kurud constituencies also; this district is situated at 81 ° 33' longitude. Dhamtari district was formed on 6 July 1998 dividing the Raipur district the capital of Chhattisgarh along with Mahasamund.

Raipur district was broken up into the districts of Raipur and Dhamtari. Dhamtari and Nagari are included in Dhamtari district as tehsils and blocks; the total area of the district is 4084 km², its altitude is 305 m above sea level. The district is surrounded by Raipur District to the north and south, part of Orissa state to the east and west. Dhamtari district falls between two Lok Sabha constituencies and three assembly constituencies: Dhamtari and Sihawa. Official website

Kento Handa

Kento Handa is a Japanese actor, remembered most by fans of his role as Takumi Inui/Kamen Rider Faiz in Kamen Rider 555. He plays many musical instruments including the guitar, bass and the piano, his album "HOMEMADE" was released in 2017, his album Seikatsu was released in 2018. Prayers – Tasuku Kamen Rider 555 – Kamen Rider Faiz / Takumi Inui Hana Yori Dango – Seto Mamoru Engine Sentai Go-onger – Retsutaka Kamen Rider Zi-O – Kamen Rider Faiz / Takumi Inui Kamen Rider 555: Paradise Lost – Inui Takumi / Kamen Rider Faiz / Wolf Orphnoch Drift 3: TAKA – Takao Drift 4: HAYABUSA – Takao Engine Sentai Go-onger: Boom Boom! Bang Bang! GekijōBang!! – Retsutaka Heisei Riders vs. Shōwa Riders: Kamen Rider Taisen feat. Super Sentai – Inui Takumi / Kamen Rider Faiz, Riderman Super Hero Taisen GP: Kamen Rider 3 – Inui Takumi / Kamen Rider Faiz d-Video Special: Kamen Rider 4 - Inui Takumi / Kamen Rider Faiz, Great Leader of SHOCKER Musashi - Nagaoka Okinaga Kento Handa on IMDb

1994–95 Segunda Divisão de Honra

The 1994–95 Segunda Divisão de Honra season was the 5th season of the competition and the 61st season of recognised second-tier football in Portugal. The league was contested by 18 teams with Leça FC winning the championship and gaining promotion to the Primeira Liga along with SC Campomaiorense and FC Felgueiras. At the other end of the table Portimonense SC, Amora FC and SCU Torreense were relegated to the Segunda Divisão. Portugal 1994/95 - RSSSF Portuguese II Liga 1994/1995 - footballzz.co.uk

Batemans Bay (bay)

Batemans Bay is an open oceanic embayment, located in the South Coast region of New South Wales, Australia. The bay forms the mouth of the Clyde River and its primary outflow is to the Tasman Sea of the South Pacific Ocean. Batemans Bay is fed by the Clyde River and its tributaries, drawing its catchment from the eastern slopes of the Budawang Range and the Great Dividing Range from within the Budawang, Clyde River and Monga national parks. Cullendulla Creek flows into Batemans Bay, between the townships of Surfside and Longbeach, west of Square Head; the total catchment area of the bay is 28 square kilometres and the bay holds an estimated 383,484 megalitres of water at an average depth of 11.1 metres. The surface area of the bay comprises 34.5 square kilometres and stretches from the confluence of the Clyde River with the bay east of the town of Batemans Bay, near Snapper Island. The traditional custodians of the land surrounding Batemans Bay are the Indigenous Australian Yuin people of the Walbunja clan.

A number of sites surrounding the bay are considered culturally significant to the Aboriginal peoples. On 22 April 1770, European explorer, Captain James Cook first sighted the bay when navigating his way around Australia on his ship, HMS Endeavour. Cook may have named the bay in honour of Nathaniel Bateman. Alternatively, the name was chosen in honour of John Bateman, 2nd Viscount Bateman, a former Lord Commissioner of the Admiralty in the 1750s. List of lakes of Australia

Rizoupoli

Rizoupoli is a neighborhood of Athens, Greece. It is the northernmost neighborhood of Athens municipality along with the small district Probonas; the district is located between Patissia and Nea Philadelphia and is home to the Georgios Kamaras Stadium. Rizoupoli is named after Ioannis Rizopoulos, a businessman and land developer of the early 20th century. Rizopoulos's historic mansion stood in the area until 2002, when the Greek government agreed for its demolition. After the Asia Minor Catastrophe many refugees from Ionia and other places of Asia Minor settled in Rizoupoli. In 1948, the football stadium of Rizoupoli was built and became the home stadium of Apollon Smyrni, a historic club founded in Smyrni in 1891. A big cave with an area of 2,500 m2 is located in Rizoupoli, it is called Profitis Ilias. In the interior the cave, remains dating from the stone age have been found